id sid tid token lemma pos fumecheng-4967 1 1 facta facta PROPN fumecheng-4967 1 2 universitatis universitatis PROPN fumecheng-4967 1 3 series series NOUN fumecheng-4967 1 4 : : PUNCT fumecheng-4967 1 5 mechanical mechanical ADJ fumecheng-4967 1 6 engineering engineering NOUN fumecheng-4967 1 7 vol vol NOUN fumecheng-4967 1 8 . . PROPN fumecheng-4967 2 1 17 17 NUM fumecheng-4967 2 2 , , PUNCT fumecheng-4967 2 3 no no DET fumecheng-4967 2 4 2 2 NUM fumecheng-4967 2 5 , , PUNCT fumecheng-4967 2 6 2019 2019 NUM fumecheng-4967 2 7 , , PUNCT fumecheng-4967 2 8 pp pp ADJ fumecheng-4967 2 9 . . PUNCT fumecheng-4967 3 1 217 217 NUM fumecheng-4967 3 2 242 242 NUM fumecheng-4967 3 3 https://doi.org/10.22190/fume190227027f https://doi.org/10.22190/fume190227027f NOUN fumecheng-4967 3 4 © © PROPN fumecheng-4967 3 5 2019 2019 NUM fumecheng-4967 3 6 by by ADP fumecheng-4967 3 7 university university PROPN fumecheng-4967 3 8 of of ADP fumecheng-4967 3 9 niš niš PROPN fumecheng-4967 3 10 , , PUNCT fumecheng-4967 3 11 serbia serbia PROPN fumecheng-4967 3 12 | | ADV fumecheng-4967 3 13 creative creative ADJ fumecheng-4967 3 14 commons common NOUN fumecheng-4967 3 15 license license NOUN fumecheng-4967 3 16 : : PUNCT fumecheng-4967 3 17 cc cc VERB fumecheng-4967 3 18 by by ADP fumecheng-4967 3 19 - - PUNCT fumecheng-4967 3 20 nc nc VERB fumecheng-4967 3 21 - - PUNCT fumecheng-4967 3 22 nd nd ADV fumecheng-4967 3 23 original original ADJ fumecheng-4967 3 24 scientific scientific ADJ fumecheng-4967 3 25 paper paper NOUN fumecheng-4967 3 26 * * PUNCT fumecheng-4967 3 27 methods method NOUN fumecheng-4967 3 28 of of ADP fumecheng-4967 3 29 the the DET fumecheng-4967 3 30 pattern pattern NOUN fumecheng-4967 3 31 formation formation NOUN fumecheng-4967 3 32 in in ADP fumecheng-4967 3 33 numerical numerical ADJ fumecheng-4967 3 34 modeling modeling NOUN fumecheng-4967 3 35 of of ADP fumecheng-4967 3 36 biological biological ADJ fumecheng-4967 3 37 problems problem NOUN fumecheng-4967 3 38 alexander alexander PROPN fumecheng-4967 3 39 e. e. PROPN fumecheng-4967 3 40 filippov filippov PROPN fumecheng-4967 3 41 1,2 1,2 NUM fumecheng-4967 3 42 , , PUNCT fumecheng-4967 3 43 stanislav stanislav PROPN fumecheng-4967 3 44 n. n. PROPN fumecheng-4967 3 45 gorb gorb PROPN fumecheng-4967 3 46 1 1 NUM fumecheng-4967 3 47 1 1 NUM fumecheng-4967 3 48 functional functional ADJ fumecheng-4967 3 49 morphology morphology NOUN fumecheng-4967 3 50 and and CCONJ fumecheng-4967 3 51 biomechanics biomechanic NOUN fumecheng-4967 3 52 , , PUNCT fumecheng-4967 3 53 zoological zoological ADJ fumecheng-4967 3 54 institute institute PROPN fumecheng-4967 3 55 , , PUNCT fumecheng-4967 3 56 kiel kiel PROPN fumecheng-4967 3 57 university university PROPN fumecheng-4967 3 58 , , PUNCT fumecheng-4967 3 59 germany germany PROPN fumecheng-4967 3 60 2 2 NUM fumecheng-4967 3 61 donetsk donetsk NOUN fumecheng-4967 3 62 institute institute NOUN fumecheng-4967 3 63 for for ADP fumecheng-4967 3 64 physics physics NOUN fumecheng-4967 3 65 and and CCONJ fumecheng-4967 3 66 engineering engineering PROPN fumecheng-4967 3 67 , , PUNCT fumecheng-4967 3 68 national national PROPN fumecheng-4967 3 69 academy academy PROPN fumecheng-4967 3 70 of of ADP fumecheng-4967 3 71 sciences sciences PROPN fumecheng-4967 3 72 of of ADP fumecheng-4967 3 73 ukraine ukraine PROPN fumecheng-4967 3 74 abstract abstract NOUN fumecheng-4967 3 75 . . PUNCT fumecheng-4967 4 1 evolution evolution NOUN fumecheng-4967 4 2 of of ADP fumecheng-4967 4 3 different different ADJ fumecheng-4967 4 4 systems system NOUN fumecheng-4967 4 5 can can AUX fumecheng-4967 4 6 be be AUX fumecheng-4967 4 7 described describe VERB fumecheng-4967 4 8 in in ADP fumecheng-4967 4 9 terms term NOUN fumecheng-4967 4 10 of of ADP fumecheng-4967 4 11 their their PRON fumecheng-4967 4 12 relaxation relaxation NOUN fumecheng-4967 4 13 to to ADP fumecheng-4967 4 14 the the DET fumecheng-4967 4 15 minimums minimum NOUN fumecheng-4967 4 16 of of ADP fumecheng-4967 4 17 some some DET fumecheng-4967 4 18 effective effective ADJ fumecheng-4967 4 19 potential potential ADJ fumecheng-4967 4 20 relief relief NOUN fumecheng-4967 4 21 . . PUNCT fumecheng-4967 5 1 this this DET fumecheng-4967 5 2 observation observation NOUN fumecheng-4967 5 3 leads lead VERB fumecheng-4967 5 4 us we PRON fumecheng-4967 5 5 to to PART fumecheng-4967 5 6 face face VERB fumecheng-4967 5 7 us we PRON fumecheng-4967 5 8 with with ADP fumecheng-4967 5 9 a a DET fumecheng-4967 5 10 question question NOUN fumecheng-4967 5 11 how how SCONJ fumecheng-4967 5 12 to to PART fumecheng-4967 5 13 generate generate VERB fumecheng-4967 5 14 corresponding corresponding ADJ fumecheng-4967 5 15 potential potential ADJ fumecheng-4967 5 16 patterns pattern NOUN fumecheng-4967 5 17 which which PRON fumecheng-4967 5 18 describe describe VERB fumecheng-4967 5 19 adequately adequately ADV fumecheng-4967 5 20 various various ADJ fumecheng-4967 5 21 physical physical ADJ fumecheng-4967 5 22 and and CCONJ fumecheng-4967 5 23 biological biological ADJ fumecheng-4967 5 24 systems system NOUN fumecheng-4967 5 25 . . PUNCT fumecheng-4967 6 1 in in ADP fumecheng-4967 6 2 this this DET fumecheng-4967 6 3 review review NOUN fumecheng-4967 6 4 , , PUNCT fumecheng-4967 6 5 we we PRON fumecheng-4967 6 6 present present VERB fumecheng-4967 6 7 a a DET fumecheng-4967 6 8 number number NOUN fumecheng-4967 6 9 of of ADP fumecheng-4967 6 10 different different ADJ fumecheng-4967 6 11 ways way NOUN fumecheng-4967 6 12 of of ADP fumecheng-4967 6 13 generating generate VERB fumecheng-4967 6 14 such such ADJ fumecheng-4967 6 15 potentials potential NOUN fumecheng-4967 6 16 demanded demand VERB fumecheng-4967 6 17 by by ADP fumecheng-4967 6 18 the the DET fumecheng-4967 6 19 problems problem NOUN fumecheng-4967 6 20 of of ADP fumecheng-4967 6 21 different different ADJ fumecheng-4967 6 22 kinds kind NOUN fumecheng-4967 6 23 . . PUNCT fumecheng-4967 7 1 for for ADP fumecheng-4967 7 2 example example NOUN fumecheng-4967 7 3 , , PUNCT fumecheng-4967 7 4 we we PRON fumecheng-4967 7 5 reproduce reproduce VERB fumecheng-4967 7 6 such such DET fumecheng-4967 7 7 a a DET fumecheng-4967 7 8 generation generation NOUN fumecheng-4967 7 9 in in ADP fumecheng-4967 7 10 the the DET fumecheng-4967 7 11 framework framework NOUN fumecheng-4967 7 12 of of ADP fumecheng-4967 7 13 a a DET fumecheng-4967 7 14 simple simple ADJ fumecheng-4967 7 15 theory theory NOUN fumecheng-4967 7 16 of of ADP fumecheng-4967 7 17 phase phase NOUN fumecheng-4967 7 18 transitions transition NOUN fumecheng-4967 7 19 , , PUNCT fumecheng-4967 7 20 automatic automatic ADJ fumecheng-4967 7 21 blocking blocking NOUN fumecheng-4967 7 22 of of ADP fumecheng-4967 7 23 the the DET fumecheng-4967 7 24 growing grow VERB fumecheng-4967 7 25 phase phase NOUN fumecheng-4967 7 26 nucleation nucleation NOUN fumecheng-4967 7 27 and and CCONJ fumecheng-4967 7 28 universal universal ADJ fumecheng-4967 7 29 large large ADJ fumecheng-4967 7 30 scale scale NOUN fumecheng-4967 7 31 structure structure NOUN fumecheng-4967 7 32 . . PUNCT fumecheng-4967 8 1 being be AUX fumecheng-4967 8 2 frozen freeze VERB fumecheng-4967 8 3 at at ADP fumecheng-4967 8 4 late late ADJ fumecheng-4967 8 5 stages stage NOUN fumecheng-4967 8 6 of of ADP fumecheng-4967 8 7 their their PRON fumecheng-4967 8 8 evolution evolution NOUN fumecheng-4967 8 9 they they PRON fumecheng-4967 8 10 form form VERB fumecheng-4967 8 11 majority majority NOUN fumecheng-4967 8 12 of of ADP fumecheng-4967 8 13 meta meta ADJ fumecheng-4967 8 14 - - PUNCT fumecheng-4967 8 15 stable stable ADJ fumecheng-4967 8 16 structures structure NOUN fumecheng-4967 8 17 which which PRON fumecheng-4967 8 18 we we PRON fumecheng-4967 8 19 observe observe VERB fumecheng-4967 8 20 in in ADP fumecheng-4967 8 21 real real ADJ fumecheng-4967 8 22 world world NOUN fumecheng-4967 8 23 . . PUNCT fumecheng-4967 9 1 counting count VERB fumecheng-4967 9 2 on on ADP fumecheng-4967 9 3 above above ADV fumecheng-4967 9 4 - - PUNCT fumecheng-4967 9 5 mentioned mention VERB fumecheng-4967 9 6 universality universality NOUN fumecheng-4967 9 7 of of ADP fumecheng-4967 9 8 naturally naturally ADV fumecheng-4967 9 9 - - PUNCT fumecheng-4967 9 10 generated generate VERB fumecheng-4967 9 11 fractal fractal ADJ fumecheng-4967 9 12 structures structure NOUN fumecheng-4967 9 13 and and CCONJ fumecheng-4967 9 14 their their PRON fumecheng-4967 9 15 further further ADJ fumecheng-4967 9 16 utilization utilization NOUN fumecheng-4967 9 17 in in ADP fumecheng-4967 9 18 numerical numerical ADJ fumecheng-4967 9 19 simulations simulation NOUN fumecheng-4967 9 20 of of ADP fumecheng-4967 9 21 biological biological ADJ fumecheng-4967 9 22 problems problem NOUN fumecheng-4967 9 23 , , PUNCT fumecheng-4967 9 24 we we PRON fumecheng-4967 9 25 reproduce reproduce VERB fumecheng-4967 9 26 also also ADV fumecheng-4967 9 27 formal formal ADJ fumecheng-4967 9 28 algorithms algorithm NOUN fumecheng-4967 9 29 of of ADP fumecheng-4967 9 30 generation generation NOUN fumecheng-4967 9 31 of of ADP fumecheng-4967 9 32 such such ADJ fumecheng-4967 9 33 structures structure NOUN fumecheng-4967 9 34 based base VERB fumecheng-4967 9 35 on on ADP fumecheng-4967 9 36 random random ADJ fumecheng-4967 9 37 deposition deposition NOUN fumecheng-4967 9 38 technique technique NOUN fumecheng-4967 9 39 and and CCONJ fumecheng-4967 9 40 fourier fourier NOUN fumecheng-4967 9 41 - - PUNCT fumecheng-4967 9 42 transform transform NOUN fumecheng-4967 9 43 approaches approach NOUN fumecheng-4967 9 44 . . PUNCT fumecheng-4967 10 1 key key ADJ fumecheng-4967 10 2 words word NOUN fumecheng-4967 10 3 : : PUNCT fumecheng-4967 10 4 pattern pattern NOUN fumecheng-4967 10 5 formation formation NOUN fumecheng-4967 10 6 , , PUNCT fumecheng-4967 10 7 phase phase NOUN fumecheng-4967 10 8 transitions transition NOUN fumecheng-4967 10 9 , , PUNCT fumecheng-4967 10 10 large large ADJ fumecheng-4967 10 11 river river NOUN fumecheng-4967 10 12 effect effect NOUN fumecheng-4967 10 13 , , PUNCT fumecheng-4967 10 14 nucleation nucleation NOUN fumecheng-4967 10 15 , , PUNCT fumecheng-4967 10 16 biological biological ADJ fumecheng-4967 10 17 applications application NOUN fumecheng-4967 10 18 , , PUNCT fumecheng-4967 10 19 frozen frozen ADJ fumecheng-4967 10 20 kinetics kinetic NOUN fumecheng-4967 10 21 1 1 NUM fumecheng-4967 10 22 . . X fumecheng-4967 10 23 introduction introduction NOUN fumecheng-4967 10 24 a a DET fumecheng-4967 10 25 large large ADJ fumecheng-4967 10 26 problem problem NOUN fumecheng-4967 10 27 of of ADP fumecheng-4967 10 28 experimental experimental ADJ fumecheng-4967 10 29 biology biology NOUN fumecheng-4967 10 30 is be AUX fumecheng-4967 10 31 that that SCONJ fumecheng-4967 10 32 we we PRON fumecheng-4967 10 33 are be AUX fumecheng-4967 10 34 dealing deal VERB fumecheng-4967 10 35 with with ADP fumecheng-4967 10 36 systems system NOUN fumecheng-4967 10 37 which which PRON fumecheng-4967 10 38 are be AUX fumecheng-4967 10 39 very very ADV fumecheng-4967 10 40 fragile fragile ADJ fumecheng-4967 10 41 and and CCONJ fumecheng-4967 10 42 sensitive sensitive ADJ fumecheng-4967 10 43 and and CCONJ fumecheng-4967 10 44 behave behave VERB fumecheng-4967 10 45 statistically statistically ADV fumecheng-4967 10 46 , , PUNCT fumecheng-4967 10 47 which which PRON fumecheng-4967 10 48 means mean VERB fumecheng-4967 10 49 that that SCONJ fumecheng-4967 10 50 often often ADV fumecheng-4967 10 51 no no DET fumecheng-4967 10 52 kind kind NOUN fumecheng-4967 10 53 of of ADP fumecheng-4967 10 54 experiment experiment NOUN fumecheng-4967 10 55 is be AUX fumecheng-4967 10 56 possible possible ADJ fumecheng-4967 10 57 , , PUNCT fumecheng-4967 10 58 and and CCONJ fumecheng-4967 10 59 if if SCONJ fumecheng-4967 10 60 so so ADV fumecheng-4967 10 61 , , PUNCT fumecheng-4967 10 62 only only ADV fumecheng-4967 10 63 at at ADP fumecheng-4967 10 64 extremely extremely ADV fumecheng-4967 10 65 high high ADJ fumecheng-4967 10 66 costs cost NOUN fumecheng-4967 10 67 and and CCONJ fumecheng-4967 10 68 usually usually ADV fumecheng-4967 10 69 without without ADP fumecheng-4967 10 70 proper proper ADJ fumecheng-4967 10 71 control control NOUN fumecheng-4967 10 72 samples sample NOUN fumecheng-4967 10 73 / / SYM fumecheng-4967 10 74 experiments experiment NOUN fumecheng-4967 10 75 . . PUNCT fumecheng-4967 11 1 this this PRON fumecheng-4967 11 2 is be AUX fumecheng-4967 11 3 one one NUM fumecheng-4967 11 4 of of ADP fumecheng-4967 11 5 the the DET fumecheng-4967 11 6 most most ADV fumecheng-4967 11 7 important important ADJ fumecheng-4967 11 8 fundamental fundamental ADJ fumecheng-4967 11 9 differences difference NOUN fumecheng-4967 11 10 between between ADP fumecheng-4967 11 11 experimental experimental ADJ fumecheng-4967 11 12 biology biology NOUN fumecheng-4967 11 13 and and CCONJ fumecheng-4967 11 14 other other ADJ fumecheng-4967 11 15 experimental experimental ADJ fumecheng-4967 11 16 disciplines discipline NOUN fumecheng-4967 11 17 dealing deal VERB fumecheng-4967 11 18 with with ADP fumecheng-4967 11 19 nonbiological nonbiological ADJ fumecheng-4967 11 20 matter matter NOUN fumecheng-4967 11 21 . . PUNCT fumecheng-4967 12 1 again again ADV fumecheng-4967 12 2 , , PUNCT fumecheng-4967 12 3 the the DET fumecheng-4967 12 4 most most ADV fumecheng-4967 12 5 helpful helpful ADJ fumecheng-4967 12 6 approach approach NOUN fumecheng-4967 12 7 in in ADP fumecheng-4967 12 8 this this DET fumecheng-4967 12 9 context context NOUN fumecheng-4967 12 10 would would AUX fumecheng-4967 12 11 be be AUX fumecheng-4967 12 12 modeling modeling NOUN fumecheng-4967 12 13 , , PUNCT fumecheng-4967 12 14 which which PRON fumecheng-4967 12 15 can can AUX fumecheng-4967 12 16 then then ADV fumecheng-4967 12 17 be be AUX fumecheng-4967 12 18 used use VERB fumecheng-4967 12 19 as as ADP fumecheng-4967 12 20 an an DET fumecheng-4967 12 21 experimental experimental ADJ fumecheng-4967 12 22 platform platform NOUN fumecheng-4967 12 23 “ " PUNCT fumecheng-4967 12 24 in in ADP fumecheng-4967 12 25 silico silico NOUN fumecheng-4967 12 26 ” " PUNCT fumecheng-4967 12 27 in in ADP fumecheng-4967 12 28 order order NOUN fumecheng-4967 12 29 to to PART fumecheng-4967 12 30 predict predict VERB fumecheng-4967 12 31 received receive VERB fumecheng-4967 12 32 february february PROPN fumecheng-4967 12 33 27 27 NUM fumecheng-4967 12 34 , , PUNCT fumecheng-4967 12 35 2019 2019 NUM fumecheng-4967 12 36 / / SYM fumecheng-4967 12 37 accepted accept VERB fumecheng-4967 12 38 may may PROPN fumecheng-4967 12 39 18 18 NUM fumecheng-4967 12 40 , , PUNCT fumecheng-4967 12 41 2019 2019 NUM fumecheng-4967 12 42 corresponding correspond VERB fumecheng-4967 12 43 author author NOUN fumecheng-4967 12 44 : : PUNCT fumecheng-4967 12 45 alexander alexander PROPN fumecheng-4967 12 46 e. e. PROPN fumecheng-4967 12 47 filippov filippov PROPN fumecheng-4967 12 48 donetsk donetsk PROPN fumecheng-4967 12 49 institute institute PROPN fumecheng-4967 12 50 for for ADP fumecheng-4967 12 51 physics physics NOUN fumecheng-4967 12 52 and and CCONJ fumecheng-4967 12 53 engineering engineering PROPN fumecheng-4967 12 54 , , PUNCT fumecheng-4967 12 55 national national PROPN fumecheng-4967 12 56 academy academy PROPN fumecheng-4967 12 57 of of ADP fumecheng-4967 12 58 sciences sciences PROPN fumecheng-4967 12 59 of of ADP fumecheng-4967 12 60 ukraine ukraine NOUN fumecheng-4967 12 61 , , PUNCT fumecheng-4967 12 62 donetsk donetsk PROPN fumecheng-4967 12 63 , , PUNCT fumecheng-4967 12 64 ukraine ukraine NOUN fumecheng-4967 12 65 e e NOUN fumecheng-4967 12 66 - - NOUN fumecheng-4967 12 67 mail mail NOUN fumecheng-4967 12 68 : : PUNCT fumecheng-4967 12 69 filippov_ae@yahoo.com filippov_ae@yahoo.com X fumecheng-4967 13 1 218 218 NUM fumecheng-4967 13 2 a.e a.e PROPN fumecheng-4967 13 3 . . PROPN fumecheng-4967 13 4 filippov filippov PROPN fumecheng-4967 13 5 , , PUNCT fumecheng-4967 13 6 s.n s.n PROPN fumecheng-4967 13 7 . . PROPN fumecheng-4967 13 8 gorb gorb PROPN fumecheng-4967 13 9 outcomes outcome NOUN fumecheng-4967 13 10 in in ADP fumecheng-4967 13 11 real real ADJ fumecheng-4967 13 12 biological biological ADJ fumecheng-4967 13 13 experiments experiment NOUN fumecheng-4967 13 14 . . PUNCT fumecheng-4967 14 1 in in ADP fumecheng-4967 14 2 some some DET fumecheng-4967 14 3 cases case NOUN fumecheng-4967 14 4 , , PUNCT fumecheng-4967 14 5 a a DET fumecheng-4967 14 6 „ „ PUNCT fumecheng-4967 14 7 virtual‟ virtual‟ PROPN fumecheng-4967 14 8 experiment experiment NOUN fumecheng-4967 14 9 may may AUX fumecheng-4967 14 10 even even ADV fumecheng-4967 14 11 be be AUX fumecheng-4967 14 12 the the DET fumecheng-4967 14 13 only only ADJ fumecheng-4967 14 14 viable viable ADJ fumecheng-4967 14 15 possibility possibility NOUN fumecheng-4967 14 16 . . PUNCT fumecheng-4967 15 1 these these DET fumecheng-4967 15 2 considerations consideration NOUN fumecheng-4967 15 3 lead lead VERB fumecheng-4967 15 4 to to ADP fumecheng-4967 15 5 the the DET fumecheng-4967 15 6 insight insight NOUN fumecheng-4967 15 7 that that SCONJ fumecheng-4967 15 8 in in ADP fumecheng-4967 15 9 many many ADJ fumecheng-4967 15 10 instances instance NOUN fumecheng-4967 15 11 experimental experimental ADJ fumecheng-4967 15 12 biology biology NOUN fumecheng-4967 15 13 can can AUX fumecheng-4967 15 14 profit profit VERB fumecheng-4967 15 15 from from ADP fumecheng-4967 15 16 new new ADJ fumecheng-4967 15 17 methods method NOUN fumecheng-4967 15 18 made make VERB fumecheng-4967 15 19 possible possible ADJ fumecheng-4967 15 20 by by ADP fumecheng-4967 15 21 novel novel NOUN fumecheng-4967 15 22 modeling modeling NOUN fumecheng-4967 15 23 techniques technique NOUN fumecheng-4967 15 24 that that PRON fumecheng-4967 15 25 take take VERB fumecheng-4967 15 26 advantage advantage NOUN fumecheng-4967 15 27 of of ADP fumecheng-4967 15 28 the the DET fumecheng-4967 15 29 recent recent ADJ fumecheng-4967 15 30 developments development NOUN fumecheng-4967 15 31 in in ADP fumecheng-4967 15 32 modeling modeling NOUN fumecheng-4967 15 33 and and CCONJ fumecheng-4967 15 34 visualization visualization NOUN fumecheng-4967 15 35 . . PUNCT fumecheng-4967 16 1 in in ADP fumecheng-4967 16 2 many many ADJ fumecheng-4967 16 3 concrete concrete ADJ fumecheng-4967 16 4 examples example NOUN fumecheng-4967 16 5 we we PRON fumecheng-4967 16 6 will will AUX fumecheng-4967 16 7 need need VERB fumecheng-4967 16 8 numerical numerical ADJ fumecheng-4967 16 9 generation generation NOUN fumecheng-4967 16 10 of of ADP fumecheng-4967 16 11 the the DET fumecheng-4967 16 12 effective effective ADJ fumecheng-4967 16 13 potential potential NOUN fumecheng-4967 16 14 . . PUNCT fumecheng-4967 17 1 if if SCONJ fumecheng-4967 17 2 effective effective ADJ fumecheng-4967 17 3 potential potential NOUN fumecheng-4967 17 4 is be AUX fumecheng-4967 17 5 known know VERB fumecheng-4967 17 6 and and CCONJ fumecheng-4967 17 7 dynamic dynamic ADJ fumecheng-4967 17 8 equations equation NOUN fumecheng-4967 17 9 are be AUX fumecheng-4967 17 10 properly properly ADV fumecheng-4967 17 11 written write VERB fumecheng-4967 17 12 , , PUNCT fumecheng-4967 17 13 the the DET fumecheng-4967 17 14 system system NOUN fumecheng-4967 17 15 is be AUX fumecheng-4967 17 16 attracted attract VERB fumecheng-4967 17 17 to to ADP fumecheng-4967 17 18 the the DET fumecheng-4967 17 19 correct correct ADJ fumecheng-4967 17 20 configurations configuration NOUN fumecheng-4967 17 21 by by ADP fumecheng-4967 17 22 itself itself PRON fumecheng-4967 17 23 . . PUNCT fumecheng-4967 18 1 the the DET fumecheng-4967 18 2 potential potential NOUN fumecheng-4967 18 3 can can AUX fumecheng-4967 18 4 appear appear VERB fumecheng-4967 18 5 in in ADP fumecheng-4967 18 6 real real ADJ fumecheng-4967 18 7 space space NOUN fumecheng-4967 18 8 , , PUNCT fumecheng-4967 18 9 or or CCONJ fumecheng-4967 18 10 in in ADP fumecheng-4967 18 11 some some DET fumecheng-4967 18 12 imaginary imaginary ADJ fumecheng-4967 18 13 space space NOUN fumecheng-4967 18 14 of of ADP fumecheng-4967 18 15 parameters parameter NOUN fumecheng-4967 18 16 . . PUNCT fumecheng-4967 19 1 in in ADP fumecheng-4967 19 2 some some DET fumecheng-4967 19 3 sense sense NOUN fumecheng-4967 19 4 , , PUNCT fumecheng-4967 19 5 it it PRON fumecheng-4967 19 6 does do AUX fumecheng-4967 19 7 not not PART fumecheng-4967 19 8 matter matter VERB fumecheng-4967 19 9 . . PUNCT fumecheng-4967 20 1 however however ADV fumecheng-4967 20 2 , , PUNCT fumecheng-4967 20 3 it it PRON fumecheng-4967 20 4 can can AUX fumecheng-4967 20 5 matter matter VERB fumecheng-4967 20 6 and and CCONJ fumecheng-4967 20 7 it it PRON fumecheng-4967 20 8 should should AUX fumecheng-4967 20 9 matter matter VERB fumecheng-4967 20 10 from from ADP fumecheng-4967 20 11 either either CCONJ fumecheng-4967 20 12 physical physical ADJ fumecheng-4967 20 13 or or CCONJ fumecheng-4967 20 14 biological biological ADJ fumecheng-4967 20 15 points point NOUN fumecheng-4967 20 16 of of ADP fumecheng-4967 20 17 view view NOUN fumecheng-4967 20 18 for for ADP fumecheng-4967 20 19 particular particular ADJ fumecheng-4967 20 20 problems problem NOUN fumecheng-4967 20 21 , , PUNCT fumecheng-4967 20 22 where where SCONJ fumecheng-4967 20 23 the the DET fumecheng-4967 20 24 potential potential NOUN fumecheng-4967 20 25 has have VERB fumecheng-4967 20 26 some some DET fumecheng-4967 20 27 specific specific ADJ fumecheng-4967 20 28 meaning meaning NOUN fumecheng-4967 20 29 . . PUNCT fumecheng-4967 21 1 in in ADP fumecheng-4967 21 2 this this DET fumecheng-4967 21 3 review review NOUN fumecheng-4967 21 4 , , PUNCT fumecheng-4967 21 5 we we PRON fumecheng-4967 21 6 will will AUX fumecheng-4967 21 7 present present VERB fumecheng-4967 21 8 some some DET fumecheng-4967 21 9 practically practically ADV fumecheng-4967 21 10 useful useful ADJ fumecheng-4967 21 11 and and CCONJ fumecheng-4967 21 12 technically technically ADV fumecheng-4967 21 13 convenient convenient ADJ fumecheng-4967 21 14 examples example NOUN fumecheng-4967 21 15 of of ADP fumecheng-4967 21 16 effective effective ADJ fumecheng-4967 21 17 potentials potential NOUN fumecheng-4967 21 18 ( ( PUNCT fumecheng-4967 21 19 or or CCONJ fumecheng-4967 21 20 patterns pattern NOUN fumecheng-4967 21 21 , , PUNCT fumecheng-4967 21 22 if if SCONJ fumecheng-4967 21 23 we we PRON fumecheng-4967 21 24 are be AUX fumecheng-4967 21 25 talking talk VERB fumecheng-4967 21 26 more more ADV fumecheng-4967 21 27 definitely definitely ADV fumecheng-4967 21 28 about about ADP fumecheng-4967 21 29 their their PRON fumecheng-4967 21 30 formation formation NOUN fumecheng-4967 21 31 in in ADP fumecheng-4967 21 32 2d 2d NUM fumecheng-4967 21 33 or or CCONJ fumecheng-4967 21 34 3d 3d NUM fumecheng-4967 21 35 spaces space NOUN fumecheng-4967 21 36 ) ) PUNCT fumecheng-4967 21 37 . . PUNCT fumecheng-4967 22 1 from from ADP fumecheng-4967 22 2 the the DET fumecheng-4967 22 3 very very ADJ fumecheng-4967 22 4 beginning beginning NOUN fumecheng-4967 22 5 , , PUNCT fumecheng-4967 22 6 one one PRON fumecheng-4967 22 7 can can AUX fumecheng-4967 22 8 divide divide VERB fumecheng-4967 22 9 them they PRON fumecheng-4967 22 10 into into ADP fumecheng-4967 22 11 two two NUM fumecheng-4967 22 12 large large ADJ fumecheng-4967 22 13 classes class NOUN fumecheng-4967 22 14 . . PUNCT fumecheng-4967 23 1 2 2 X fumecheng-4967 23 2 . . X fumecheng-4967 23 3 simple simple ADJ fumecheng-4967 23 4 theory theory NOUN fumecheng-4967 23 5 of of ADP fumecheng-4967 23 6 phase phase NOUN fumecheng-4967 23 7 transitions transition NOUN fumecheng-4967 23 8 and and CCONJ fumecheng-4967 23 9 pattern pattern NOUN fumecheng-4967 23 10 formation formation NOUN fumecheng-4967 23 11 one one NUM fumecheng-4967 23 12 kind kind NOUN fumecheng-4967 23 13 the the DET fumecheng-4967 23 14 potentials potential NOUN fumecheng-4967 23 15 are be AUX fumecheng-4967 23 16 abstract abstract ADJ fumecheng-4967 23 17 numerically numerically ADV fumecheng-4967 23 18 generated generate VERB fumecheng-4967 23 19 formations formation NOUN fumecheng-4967 23 20 which which PRON fumecheng-4967 23 21 are be AUX fumecheng-4967 23 22 simple simple ADJ fumecheng-4967 23 23 enough enough ADV fumecheng-4967 23 24 and and CCONJ fumecheng-4967 23 25 convenient convenient ADJ fumecheng-4967 23 26 for for ADP fumecheng-4967 23 27 the the DET fumecheng-4967 23 28 theoretical theoretical ADJ fumecheng-4967 23 29 numerical numerical ADJ fumecheng-4967 23 30 simulations simulation NOUN fumecheng-4967 23 31 . . PUNCT fumecheng-4967 24 1 the the DET fumecheng-4967 24 2 other other ADJ fumecheng-4967 24 3 ones one NOUN fumecheng-4967 24 4 are be AUX fumecheng-4967 24 5 provoked provoke VERB fumecheng-4967 24 6 by by ADP fumecheng-4967 24 7 the the DET fumecheng-4967 24 8 studies study NOUN fumecheng-4967 24 9 of of ADP fumecheng-4967 24 10 the the DET fumecheng-4967 24 11 specific specific ADJ fumecheng-4967 24 12 , , PUNCT fumecheng-4967 24 13 experimentally experimentally ADV fumecheng-4967 24 14 observed observe VERB fumecheng-4967 24 15 systems system NOUN fumecheng-4967 24 16 . . PUNCT fumecheng-4967 25 1 in in ADP fumecheng-4967 25 2 this this DET fumecheng-4967 25 3 latter latter ADJ fumecheng-4967 25 4 case case NOUN fumecheng-4967 25 5 , , PUNCT fumecheng-4967 25 6 the the DET fumecheng-4967 25 7 degree degree NOUN fumecheng-4967 25 8 of of ADP fumecheng-4967 25 9 simplicity simplicity NOUN fumecheng-4967 25 10 of of ADP fumecheng-4967 25 11 the the DET fumecheng-4967 25 12 potential potential NOUN fumecheng-4967 25 13 or or CCONJ fumecheng-4967 25 14 the the DET fumecheng-4967 25 15 procedure procedure NOUN fumecheng-4967 25 16 of of ADP fumecheng-4967 25 17 its its PRON fumecheng-4967 25 18 generation generation NOUN fumecheng-4967 25 19 is be AUX fumecheng-4967 25 20 not not PART fumecheng-4967 25 21 so so ADV fumecheng-4967 25 22 important important ADJ fumecheng-4967 25 23 because because SCONJ fumecheng-4967 25 24 in in ADP fumecheng-4967 25 25 such such DET fumecheng-4967 25 26 a a DET fumecheng-4967 25 27 case case NOUN fumecheng-4967 25 28 we we PRON fumecheng-4967 25 29 are be AUX fumecheng-4967 25 30 more more ADV fumecheng-4967 25 31 interested interested ADJ fumecheng-4967 25 32 in in ADP fumecheng-4967 25 33 the the DET fumecheng-4967 25 34 potential potential ADJ fumecheng-4967 25 35 ( ( PUNCT fumecheng-4967 25 36 surface surface NOUN fumecheng-4967 25 37 , , PUNCT fumecheng-4967 25 38 pattern pattern NOUN fumecheng-4967 25 39 , , PUNCT fumecheng-4967 25 40 density density NOUN fumecheng-4967 25 41 distribution distribution NOUN fumecheng-4967 25 42 , , PUNCT fumecheng-4967 25 43 etc etc X fumecheng-4967 25 44 . . X fumecheng-4967 25 45 ) ) PUNCT fumecheng-4967 25 46 by by ADP fumecheng-4967 25 47 itself itself PRON fumecheng-4967 25 48 at at ADP fumecheng-4967 25 49 the the DET fumecheng-4967 25 50 final final ADJ fumecheng-4967 25 51 stage stage NOUN fumecheng-4967 25 52 of of ADP fumecheng-4967 25 53 the the DET fumecheng-4967 25 54 study study NOUN fumecheng-4967 25 55 , , PUNCT fumecheng-4967 25 56 or or CCONJ fumecheng-4967 25 57 maybe maybe ADV fumecheng-4967 25 58 even even ADV fumecheng-4967 25 59 as as ADP fumecheng-4967 25 60 a a DET fumecheng-4967 25 61 goal goal NOUN fumecheng-4967 25 62 of of ADP fumecheng-4967 25 63 the the DET fumecheng-4967 25 64 particular particular ADJ fumecheng-4967 25 65 research research NOUN fumecheng-4967 25 66 . . PUNCT fumecheng-4967 26 1 for for ADP fumecheng-4967 26 2 example example NOUN fumecheng-4967 26 3 , , PUNCT fumecheng-4967 26 4 if if SCONJ fumecheng-4967 26 5 we we PRON fumecheng-4967 26 6 would would AUX fumecheng-4967 26 7 like like VERB fumecheng-4967 26 8 to to PART fumecheng-4967 26 9 know know VERB fumecheng-4967 26 10 how how SCONJ fumecheng-4967 26 11 this this DET fumecheng-4967 26 12 particular particular ADJ fumecheng-4967 26 13 picture picture NOUN fumecheng-4967 26 14 could could AUX fumecheng-4967 26 15 appear appear VERB fumecheng-4967 26 16 self self NOUN fumecheng-4967 26 17 - - PUNCT fumecheng-4967 26 18 consistently consistently ADV fumecheng-4967 26 19 . . PUNCT fumecheng-4967 27 1 keeping keep VERB fumecheng-4967 27 2 this this PRON fumecheng-4967 27 3 in in ADP fumecheng-4967 27 4 mind mind NOUN fumecheng-4967 27 5 , , PUNCT fumecheng-4967 27 6 we we PRON fumecheng-4967 27 7 will will AUX fumecheng-4967 27 8 continuously continuously ADV fumecheng-4967 27 9 jump jump VERB fumecheng-4967 27 10 between between ADP fumecheng-4967 27 11 these these DET fumecheng-4967 27 12 two two NUM fumecheng-4967 27 13 opposite opposite ADJ fumecheng-4967 27 14 limits limit NOUN fumecheng-4967 27 15 . . PUNCT fumecheng-4967 28 1 sometimes sometimes ADV fumecheng-4967 28 2 , , PUNCT fumecheng-4967 28 3 using use VERB fumecheng-4967 28 4 very very ADV fumecheng-4967 28 5 abstract abstract ADJ fumecheng-4967 28 6 models model NOUN fumecheng-4967 28 7 to to PART fumecheng-4967 28 8 illustrate illustrate VERB fumecheng-4967 28 9 general general ADJ fumecheng-4967 28 10 ideas idea NOUN fumecheng-4967 28 11 , , PUNCT fumecheng-4967 28 12 or or CCONJ fumecheng-4967 28 13 simply simply ADV fumecheng-4967 28 14 to to PART fumecheng-4967 28 15 generate generate VERB fumecheng-4967 28 16 the the DET fumecheng-4967 28 17 equations equation NOUN fumecheng-4967 28 18 , , PUNCT fumecheng-4967 28 19 reproducing reproduce VERB fumecheng-4967 28 20 what what PRON fumecheng-4967 28 21 we we PRON fumecheng-4967 28 22 have have AUX fumecheng-4967 28 23 observed observe VERB fumecheng-4967 28 24 , , PUNCT fumecheng-4967 28 25 even even ADV fumecheng-4967 28 26 without without ADP fumecheng-4967 28 27 complete complete ADJ fumecheng-4967 28 28 motivation motivation NOUN fumecheng-4967 28 29 . . PUNCT fumecheng-4967 29 1 but but CCONJ fumecheng-4967 29 2 , , PUNCT fumecheng-4967 29 3 sometimes sometimes ADV fumecheng-4967 29 4 , , PUNCT fumecheng-4967 29 5 we we PRON fumecheng-4967 29 6 will will AUX fumecheng-4967 29 7 devote devote VERB fumecheng-4967 29 8 almost almost ADV fumecheng-4967 29 9 the the DET fumecheng-4967 29 10 whole whole ADJ fumecheng-4967 29 11 study study NOUN fumecheng-4967 29 12 to to ADP fumecheng-4967 29 13 an an DET fumecheng-4967 29 14 extraction extraction NOUN fumecheng-4967 29 15 of of ADP fumecheng-4967 29 16 the the DET fumecheng-4967 29 17 equations equation NOUN fumecheng-4967 29 18 or or CCONJ fumecheng-4967 29 19 procedures procedure NOUN fumecheng-4967 29 20 from from ADP fumecheng-4967 29 21 particular particular ADJ fumecheng-4967 29 22 nature nature NOUN fumecheng-4967 29 23 of of ADP fumecheng-4967 29 24 the the DET fumecheng-4967 29 25 problem problem NOUN fumecheng-4967 29 26 under under ADP fumecheng-4967 29 27 consideration consideration NOUN fumecheng-4967 29 28 . . PUNCT fumecheng-4967 30 1 the the DET fumecheng-4967 30 2 same same ADJ fumecheng-4967 30 3 note note NOUN fumecheng-4967 30 4 can can AUX fumecheng-4967 30 5 be be AUX fumecheng-4967 30 6 done do VERB fumecheng-4967 30 7 about about ADP fumecheng-4967 30 8 dimensionality dimensionality NOUN fumecheng-4967 30 9 of of ADP fumecheng-4967 30 10 the the DET fumecheng-4967 30 11 surface surface NOUN fumecheng-4967 30 12 ( ( PUNCT fumecheng-4967 30 13 potential potential ADJ fumecheng-4967 30 14 , , PUNCT fumecheng-4967 30 15 line line NOUN fumecheng-4967 30 16 , , PUNCT fumecheng-4967 30 17 etc etc X fumecheng-4967 30 18 . . X fumecheng-4967 30 19 ) ) PUNCT fumecheng-4967 31 1 generated generate VERB fumecheng-4967 31 2 by by ADP fumecheng-4967 31 3 a a DET fumecheng-4967 31 4 procedure procedure NOUN fumecheng-4967 31 5 . . PUNCT fumecheng-4967 32 1 in in ADP fumecheng-4967 32 2 some some DET fumecheng-4967 32 3 cases case NOUN fumecheng-4967 32 4 it it PRON fumecheng-4967 32 5 is be AUX fumecheng-4967 32 6 enough enough ADJ fumecheng-4967 32 7 to to PART fumecheng-4967 32 8 create create VERB fumecheng-4967 32 9 1d 1d NUM fumecheng-4967 32 10 line line NOUN fumecheng-4967 32 11 with with ADP fumecheng-4967 32 12 specific specific ADJ fumecheng-4967 32 13 properties property NOUN fumecheng-4967 32 14 . . PUNCT fumecheng-4967 33 1 it it PRON fumecheng-4967 33 2 is be AUX fumecheng-4967 33 3 important important ADJ fumecheng-4967 33 4 to to PART fumecheng-4967 33 5 note note VERB fumecheng-4967 33 6 that that SCONJ fumecheng-4967 33 7 even even ADV fumecheng-4967 33 8 for for ADP fumecheng-4967 33 9 such such ADJ fumecheng-4967 33 10 “ " PUNCT fumecheng-4967 33 11 trivial trivial ADJ fumecheng-4967 33 12 ” " PUNCT fumecheng-4967 33 13 case case NOUN fumecheng-4967 33 14 our our PRON fumecheng-4967 33 15 motivation motivation NOUN fumecheng-4967 33 16 can can AUX fumecheng-4967 33 17 be be AUX fumecheng-4967 33 18 different different ADJ fumecheng-4967 33 19 . . PUNCT fumecheng-4967 34 1 for for ADP fumecheng-4967 34 2 example example NOUN fumecheng-4967 34 3 , , PUNCT fumecheng-4967 34 4 it it PRON fumecheng-4967 34 5 can can AUX fumecheng-4967 34 6 be be AUX fumecheng-4967 34 7 made make VERB fumecheng-4967 34 8 just just ADV fumecheng-4967 34 9 for for ADP fumecheng-4967 34 10 simplicity simplicity NOUN fumecheng-4967 34 11 of of ADP fumecheng-4967 34 12 further further ADJ fumecheng-4967 34 13 application application NOUN fumecheng-4967 34 14 of of ADP fumecheng-4967 34 15 the the DET fumecheng-4967 34 16 generated generate VERB fumecheng-4967 34 17 object object NOUN fumecheng-4967 34 18 . . PUNCT fumecheng-4967 35 1 however however ADV fumecheng-4967 35 2 , , PUNCT fumecheng-4967 35 3 in in ADP fumecheng-4967 35 4 many many ADJ fumecheng-4967 35 5 cases case NOUN fumecheng-4967 35 6 , , PUNCT fumecheng-4967 35 7 it it PRON fumecheng-4967 35 8 can can AUX fumecheng-4967 35 9 be be AUX fumecheng-4967 35 10 even even ADV fumecheng-4967 35 11 more more ADV fumecheng-4967 35 12 correct correct ADJ fumecheng-4967 35 13 than than SCONJ fumecheng-4967 35 14 to to PART fumecheng-4967 35 15 generate generate VERB fumecheng-4967 35 16 and and CCONJ fumecheng-4967 35 17 apply apply VERB fumecheng-4967 35 18 2d 2d NUM fumecheng-4967 35 19 pattern pattern NOUN fumecheng-4967 35 20 and and CCONJ fumecheng-4967 35 21 use use VERB fumecheng-4967 35 22 it it PRON fumecheng-4967 35 23 . . PUNCT fumecheng-4967 36 1 it it PRON fumecheng-4967 36 2 can can AUX fumecheng-4967 36 3 be be AUX fumecheng-4967 36 4 proven prove VERB fumecheng-4967 36 5 that that SCONJ fumecheng-4967 36 6 for for ADP fumecheng-4967 36 7 many many ADJ fumecheng-4967 36 8 problems problem NOUN fumecheng-4967 36 9 of of ADP fumecheng-4967 36 10 contact contact NOUN fumecheng-4967 36 11 mechanics mechanic NOUN fumecheng-4967 36 12 , , PUNCT fumecheng-4967 36 13 real real ADJ fumecheng-4967 36 14 3d 3d NUM fumecheng-4967 36 15 problem problem NOUN fumecheng-4967 36 16 can can AUX fumecheng-4967 36 17 be be AUX fumecheng-4967 36 18 exactly exactly ADV fumecheng-4967 36 19 transformed transform VERB fumecheng-4967 36 20 to to ADP fumecheng-4967 36 21 the the DET fumecheng-4967 36 22 1d 1d NUM fumecheng-4967 36 23 model model NOUN fumecheng-4967 36 24 ! ! PUNCT fumecheng-4967 37 1 it it PRON fumecheng-4967 37 2 is be AUX fumecheng-4967 37 3 so so ADV fumecheng-4967 37 4 - - PUNCT fumecheng-4967 37 5 called call VERB fumecheng-4967 37 6 method method NOUN fumecheng-4967 37 7 of of ADP fumecheng-4967 37 8 dimensionality dimensionality NOUN fumecheng-4967 37 9 reduction reduction NOUN fumecheng-4967 37 10 ( ( PUNCT fumecheng-4967 37 11 mdr mdr NOUN fumecheng-4967 37 12 ) ) PUNCT fumecheng-4967 37 13 invented invent VERB fumecheng-4967 37 14 and and CCONJ fumecheng-4967 37 15 actively actively ADV fumecheng-4967 37 16 developed develop VERB fumecheng-4967 37 17 last last ADV fumecheng-4967 37 18 during during ADP fumecheng-4967 37 19 decades decade NOUN fumecheng-4967 37 20 by by ADP fumecheng-4967 37 21 valentin valentin NOUN fumecheng-4967 37 22 popov popov PROPN fumecheng-4967 37 23 and and CCONJ fumecheng-4967 37 24 coworkers coworker NOUN fumecheng-4967 37 25 [ [ X fumecheng-4967 37 26 1 1 NUM fumecheng-4967 37 27 ] ] PUNCT fumecheng-4967 37 28 . . PUNCT fumecheng-4967 38 1 the the DET fumecheng-4967 38 2 cases case NOUN fumecheng-4967 38 3 of of ADP fumecheng-4967 38 4 the the DET fumecheng-4967 38 5 mdr mdr PROPN fumecheng-4967 38 6 application application NOUN fumecheng-4967 38 7 we we PRON fumecheng-4967 38 8 will will AUX fumecheng-4967 38 9 mention mention VERB fumecheng-4967 38 10 in in ADP fumecheng-4967 38 11 this this DET fumecheng-4967 38 12 paper paper NOUN fumecheng-4967 38 13 and and CCONJ fumecheng-4967 38 14 specially specially ADV fumecheng-4967 38 15 discuss discuss VERB fumecheng-4967 38 16 them they PRON fumecheng-4967 38 17 in in ADP fumecheng-4967 38 18 corresponding corresponding ADJ fumecheng-4967 38 19 sections section NOUN fumecheng-4967 38 20 . . PUNCT fumecheng-4967 39 1 it it PRON fumecheng-4967 39 2 should should AUX fumecheng-4967 39 3 be be AUX fumecheng-4967 39 4 additionally additionally ADV fumecheng-4967 39 5 mentioned mention VERB fumecheng-4967 39 6 that that SCONJ fumecheng-4967 39 7 the the DET fumecheng-4967 39 8 absolute absolute ADJ fumecheng-4967 39 9 majority majority NOUN fumecheng-4967 39 10 of of ADP fumecheng-4967 39 11 patterns pattern NOUN fumecheng-4967 39 12 , , PUNCT fumecheng-4967 39 13 we we PRON fumecheng-4967 39 14 have have AUX fumecheng-4967 39 15 used use VERB fumecheng-4967 39 16 in in ADP fumecheng-4967 39 17 studies study NOUN fumecheng-4967 39 18 of of ADP fumecheng-4967 39 19 biological biological ADJ fumecheng-4967 39 20 problems problem NOUN fumecheng-4967 39 21 under under ADP fumecheng-4967 39 22 consideration consideration NOUN fumecheng-4967 39 23 , , PUNCT fumecheng-4967 39 24 were be AUX fumecheng-4967 39 25 generated generate VERB fumecheng-4967 39 26 by by ADP fumecheng-4967 39 27 simulations simulation NOUN fumecheng-4967 39 28 of of ADP fumecheng-4967 39 29 physical physical ADJ fumecheng-4967 39 30 or or CCONJ fumecheng-4967 39 31 chemical chemical NOUN fumecheng-4967 39 32 kinetic kinetic NOUN fumecheng-4967 39 33 processes process NOUN fumecheng-4967 39 34 . . PUNCT fumecheng-4967 40 1 below below ADV fumecheng-4967 40 2 , , PUNCT fumecheng-4967 40 3 we we PRON fumecheng-4967 40 4 basically basically ADV fumecheng-4967 40 5 report report VERB fumecheng-4967 40 6 on on ADP fumecheng-4967 40 7 the the DET fumecheng-4967 40 8 methods method NOUN fumecheng-4967 40 9 of of ADP fumecheng-4967 40 10 physical physical ADJ fumecheng-4967 40 11 kinetics kinetic NOUN fumecheng-4967 40 12 . . PUNCT fumecheng-4967 41 1 for for ADP fumecheng-4967 41 2 example example NOUN fumecheng-4967 41 3 , , PUNCT fumecheng-4967 41 4 the the DET fumecheng-4967 41 5 ideas idea NOUN fumecheng-4967 41 6 from from ADP fumecheng-4967 41 7 fluctuation fluctuation NOUN fumecheng-4967 41 8 theory theory NOUN fumecheng-4967 41 9 , , PUNCT fumecheng-4967 41 10 phase phase NOUN fumecheng-4967 41 11 separation separation NOUN fumecheng-4967 41 12 , , PUNCT fumecheng-4967 41 13 and and CCONJ fumecheng-4967 41 14 phase phase NOUN fumecheng-4967 41 15 transitions transition NOUN fumecheng-4967 41 16 can can AUX fumecheng-4967 41 17 be be AUX fumecheng-4967 41 18 applied apply VERB fumecheng-4967 41 19 for for ADP fumecheng-4967 41 20 pattern pattern NOUN fumecheng-4967 41 21 generation generation NOUN fumecheng-4967 41 22 . . PUNCT fumecheng-4967 42 1 of of ADP fumecheng-4967 42 2 course course NOUN fumecheng-4967 42 3 , , PUNCT fumecheng-4967 42 4 it it PRON fumecheng-4967 42 5 is be AUX fumecheng-4967 42 6 practically practically ADV fumecheng-4967 42 7 impossible impossible ADJ fumecheng-4967 42 8 methods method NOUN fumecheng-4967 42 9 of of ADP fumecheng-4967 42 10 the the DET fumecheng-4967 42 11 pattern pattern NOUN fumecheng-4967 42 12 formation formation NOUN fumecheng-4967 42 13 in in ADP fumecheng-4967 42 14 numerical numerical ADJ fumecheng-4967 42 15 modeling modeling NOUN fumecheng-4967 42 16 of of ADP fumecheng-4967 42 17 biological biological ADJ fumecheng-4967 42 18 problems problem NOUN fumecheng-4967 42 19 219 219 NUM fumecheng-4967 42 20 to to PART fumecheng-4967 42 21 reproduce reproduce VERB fumecheng-4967 42 22 all all DET fumecheng-4967 42 23 the the DET fumecheng-4967 42 24 mathematical mathematical ADJ fumecheng-4967 42 25 foundations foundation NOUN fumecheng-4967 42 26 of of ADP fumecheng-4967 42 27 this this DET fumecheng-4967 42 28 branch branch NOUN fumecheng-4967 42 29 of of ADP fumecheng-4967 42 30 science science NOUN fumecheng-4967 42 31 , , PUNCT fumecheng-4967 42 32 which which PRON fumecheng-4967 42 33 are be AUX fumecheng-4967 42 34 published publish VERB fumecheng-4967 42 35 in in ADP fumecheng-4967 42 36 hundreds hundred NOUN fumecheng-4967 42 37 of of ADP fumecheng-4967 42 38 the the DET fumecheng-4967 42 39 handbooks handbook NOUN fumecheng-4967 42 40 starting start VERB fumecheng-4967 42 41 from from ADP fumecheng-4967 42 42 the the DET fumecheng-4967 42 43 19 19 NUM fumecheng-4967 42 44 th th NUM fumecheng-4967 42 45 century century NOUN fumecheng-4967 42 46 . . PUNCT fumecheng-4967 43 1 thus thus ADV fumecheng-4967 43 2 , , PUNCT fumecheng-4967 43 3 in in ADP fumecheng-4967 43 4 many many ADJ fumecheng-4967 43 5 cases case NOUN fumecheng-4967 43 6 , , PUNCT fumecheng-4967 43 7 we we PRON fumecheng-4967 43 8 will will AUX fumecheng-4967 43 9 simply simply ADV fumecheng-4967 43 10 suppose suppose VERB fumecheng-4967 43 11 that that SCONJ fumecheng-4967 43 12 it it PRON fumecheng-4967 43 13 is be AUX fumecheng-4967 43 14 either either CCONJ fumecheng-4967 43 15 known know VERB fumecheng-4967 43 16 or or CCONJ fumecheng-4967 43 17 can can AUX fumecheng-4967 43 18 be be AUX fumecheng-4967 43 19 proven prove VERB fumecheng-4967 43 20 . . PUNCT fumecheng-4967 44 1 independently independently ADV fumecheng-4967 44 2 of of ADP fumecheng-4967 44 3 the the DET fumecheng-4967 44 4 accuracy accuracy NOUN fumecheng-4967 44 5 and and CCONJ fumecheng-4967 44 6 correctness correctness NOUN fumecheng-4967 44 7 of of ADP fumecheng-4967 44 8 the the DET fumecheng-4967 44 9 terminology terminology NOUN fumecheng-4967 44 10 , , PUNCT fumecheng-4967 44 11 one one PRON fumecheng-4967 44 12 can can AUX fumecheng-4967 44 13 start start VERB fumecheng-4967 44 14 from from ADP fumecheng-4967 44 15 a a DET fumecheng-4967 44 16 very very ADV fumecheng-4967 44 17 formal formal ADJ fumecheng-4967 44 18 and and CCONJ fumecheng-4967 44 19 methodically methodically ADV fumecheng-4967 44 20 transparent transparent ADJ fumecheng-4967 44 21 approach approach NOUN fumecheng-4967 44 22 . . PUNCT fumecheng-4967 45 1 let let VERB fumecheng-4967 45 2 us we PRON fumecheng-4967 45 3 suppose suppose VERB fumecheng-4967 45 4 that that SCONJ fumecheng-4967 45 5 there there PRON fumecheng-4967 45 6 is be VERB fumecheng-4967 45 7 fluctuating fluctuate VERB fumecheng-4967 45 8 density density NOUN fumecheng-4967 45 9 ρ(x ρ(x NOUN fumecheng-4967 45 10 ) ) PUNCT fumecheng-4967 45 11 randomly randomly ADV fumecheng-4967 45 12 distributed distribute VERB fumecheng-4967 45 13 originally originally ADV fumecheng-4967 45 14 at at ADP fumecheng-4967 45 15 t=0 t=0 PROPN fumecheng-4967 45 16 in in ADP fumecheng-4967 45 17 one one NUM fumecheng-4967 45 18 - - PUNCT fumecheng-4967 45 19 dimensional dimensional ADJ fumecheng-4967 45 20 space space NOUN fumecheng-4967 45 21 { { PUNCT fumecheng-4967 45 22 x x NOUN fumecheng-4967 45 23 } } PUNCT fumecheng-4967 45 24 . . PUNCT fumecheng-4967 46 1 random random ADJ fumecheng-4967 46 2 initial initial ADJ fumecheng-4967 46 3 distribution distribution NOUN fumecheng-4967 46 4 means mean VERB fumecheng-4967 46 5 that that SCONJ fumecheng-4967 46 6 fluctuations fluctuation NOUN fumecheng-4967 46 7 δρ(x δρ(x PROPN fumecheng-4967 46 8 , , PUNCT fumecheng-4967 46 9 t t PROPN fumecheng-4967 46 10 ) ) PUNCT fumecheng-4967 46 11 on on ADP fumecheng-4967 46 12 average average ADJ fumecheng-4967 46 13 are be AUX fumecheng-4967 46 14 equal equal ADJ fumecheng-4967 46 15 to to ADP fumecheng-4967 46 16 zero zero NUM fumecheng-4967 46 17 < < X fumecheng-4967 46 18 δρ(x δρ(x X fumecheng-4967 46 19 , , PUNCT fumecheng-4967 46 20 t)>=0 t)>=0 NOUN fumecheng-4967 46 21 and and CCONJ fumecheng-4967 46 22 originally originally ADV fumecheng-4967 46 23 independent independent ADJ fumecheng-4967 46 24 at at ADP fumecheng-4967 46 25 every every DET fumecheng-4967 46 26 point point NOUN fumecheng-4967 46 27 and and CCONJ fumecheng-4967 46 28 time time NOUN fumecheng-4967 46 29 of of ADP fumecheng-4967 46 30 the the DET fumecheng-4967 46 31 system system NOUN fumecheng-4967 46 32 < < X fumecheng-4967 46 33 δρ(x δρ(x X fumecheng-4967 46 34 , , PUNCT fumecheng-4967 46 35 t)δρ(x´,t´)>=dδ(x t)δρ(x´,t´)>=dδ(x NOUN fumecheng-4967 46 36 - - SYM fumecheng-4967 46 37 x´)ρ(tt x´)ρ(tt NUM fumecheng-4967 46 38 ´ ´ NOUN fumecheng-4967 46 39 ) ) PUNCT fumecheng-4967 46 40 . . PUNCT fumecheng-4967 47 1 it it PRON fumecheng-4967 47 2 is be AUX fumecheng-4967 47 3 so so ADV fumecheng-4967 47 4 - - PUNCT fumecheng-4967 47 5 called call VERB fumecheng-4967 47 6 δ δ NOUN fumecheng-4967 47 7 - - PUNCT fumecheng-4967 47 8 correlated correlate VERB fumecheng-4967 47 9 noise noise NOUN fumecheng-4967 47 10 . . PUNCT fumecheng-4967 48 1 in in ADP fumecheng-4967 48 2 the the DET fumecheng-4967 48 3 majority majority NOUN fumecheng-4967 48 4 of of ADP fumecheng-4967 48 5 real real ADJ fumecheng-4967 48 6 systems system NOUN fumecheng-4967 48 7 the the DET fumecheng-4967 48 8 densities density NOUN fumecheng-4967 48 9 of of ADP fumecheng-4967 48 10 fluctuations fluctuation NOUN fumecheng-4967 48 11 interact interact VERB fumecheng-4967 48 12 . . PUNCT fumecheng-4967 49 1 these these DET fumecheng-4967 49 2 interactions interaction NOUN fumecheng-4967 49 3 can can AUX fumecheng-4967 49 4 cause cause VERB fumecheng-4967 49 5 mutual mutual ADJ fumecheng-4967 49 6 attraction attraction NOUN fumecheng-4967 49 7 and and CCONJ fumecheng-4967 49 8 enforcement enforcement NOUN fumecheng-4967 49 9 of of ADP fumecheng-4967 49 10 the the DET fumecheng-4967 49 11 fluctuations fluctuation NOUN fumecheng-4967 49 12 leading lead VERB fumecheng-4967 49 13 to to ADP fumecheng-4967 49 14 the the DET fumecheng-4967 49 15 nucleation nucleation NOUN fumecheng-4967 49 16 of of ADP fumecheng-4967 49 17 the the DET fumecheng-4967 49 18 regions region NOUN fumecheng-4967 49 19 with with ADP fumecheng-4967 49 20 nonzero nonzero PROPN fumecheng-4967 49 21 density density PROPN fumecheng-4967 49 22 ρ(x ρ(x PROPN fumecheng-4967 49 23 ) ) PUNCT fumecheng-4967 49 24 and and CCONJ fumecheng-4967 49 25 their their PRON fumecheng-4967 49 26 expansion expansion NOUN fumecheng-4967 49 27 in in ADP fumecheng-4967 49 28 space space NOUN fumecheng-4967 49 29 . . PUNCT fumecheng-4967 50 1 one one NUM fumecheng-4967 50 2 of of ADP fumecheng-4967 50 3 the the DET fumecheng-4967 50 4 most most ADV fumecheng-4967 50 5 accepted accepted ADJ fumecheng-4967 50 6 theories theory NOUN fumecheng-4967 50 7 of of ADP fumecheng-4967 50 8 this this DET fumecheng-4967 50 9 process process NOUN fumecheng-4967 50 10 is be AUX fumecheng-4967 50 11 landau landau NOUN fumecheng-4967 50 12 theory theory NOUN fumecheng-4967 50 13 [ [ X fumecheng-4967 50 14 2 2 NUM fumecheng-4967 50 15 ] ] PUNCT fumecheng-4967 50 16 of of ADP fumecheng-4967 50 17 phase phase NOUN fumecheng-4967 50 18 transitions transition NOUN fumecheng-4967 50 19 ( ( PUNCT fumecheng-4967 50 20 which which PRON fumecheng-4967 50 21 can can AUX fumecheng-4967 50 22 be be AUX fumecheng-4967 50 23 treated treat VERB fumecheng-4967 50 24 as as ADP fumecheng-4967 50 25 a a DET fumecheng-4967 50 26 combination combination NOUN fumecheng-4967 50 27 of of ADP fumecheng-4967 50 28 main main ADJ fumecheng-4967 50 29 interactions interaction NOUN fumecheng-4967 50 30 within within ADP fumecheng-4967 50 31 the the DET fumecheng-4967 50 32 system system NOUN fumecheng-4967 50 33 in in ADP fumecheng-4967 50 34 the the DET fumecheng-4967 50 35 framework framework NOUN fumecheng-4967 50 36 of of ADP fumecheng-4967 50 37 the the DET fumecheng-4967 50 38 simplified simplified ADJ fumecheng-4967 50 39 “ " PUNCT fumecheng-4967 50 40 mean mean ADJ fumecheng-4967 50 41 field field NOUN fumecheng-4967 50 42 ” " PUNCT fumecheng-4967 50 43 theory theory NOUN fumecheng-4967 50 44 ) ) PUNCT fumecheng-4967 50 45 . . PUNCT fumecheng-4967 51 1 main main ADJ fumecheng-4967 51 2 idea idea NOUN fumecheng-4967 51 3 of of ADP fumecheng-4967 51 4 landau landau NOUN fumecheng-4967 51 5 theory theory NOUN fumecheng-4967 51 6 is be AUX fumecheng-4967 51 7 that that SCONJ fumecheng-4967 51 8 energy energy NOUN fumecheng-4967 51 9 of of ADP fumecheng-4967 51 10 the the DET fumecheng-4967 51 11 system system NOUN fumecheng-4967 51 12 can can AUX fumecheng-4967 51 13 be be AUX fumecheng-4967 51 14 expressed express VERB fumecheng-4967 51 15 as as ADP fumecheng-4967 51 16 a a DET fumecheng-4967 51 17 function function NOUN fumecheng-4967 51 18 of of ADP fumecheng-4967 51 19 the the DET fumecheng-4967 51 20 so so ADV fumecheng-4967 51 21 - - PUNCT fumecheng-4967 51 22 called call VERB fumecheng-4967 51 23 “ " PUNCT fumecheng-4967 51 24 order order NOUN fumecheng-4967 51 25 parameter parameter NOUN fumecheng-4967 51 26 ” " PUNCT fumecheng-4967 51 27 density density NOUN fumecheng-4967 51 28 . . PUNCT fumecheng-4967 52 1 in in ADP fumecheng-4967 52 2 particular particular ADJ fumecheng-4967 52 3 , , PUNCT fumecheng-4967 52 4 it it PRON fumecheng-4967 52 5 can can AUX fumecheng-4967 52 6 be be AUX fumecheng-4967 52 7 a a DET fumecheng-4967 52 8 functional functional ADJ fumecheng-4967 52 9 u(ρ(x u(ρ(x NOUN fumecheng-4967 52 10 ) ) PUNCT fumecheng-4967 52 11 ) ) PUNCT fumecheng-4967 52 12 of of ADP fumecheng-4967 52 13 spatially spatially ADV fumecheng-4967 52 14 distributed distribute VERB fumecheng-4967 52 15 real real ADJ fumecheng-4967 52 16 density density NOUN fumecheng-4967 52 17 ρ(x ρ(x PROPN fumecheng-4967 52 18 ) ) PUNCT fumecheng-4967 52 19 . . PUNCT fumecheng-4967 53 1 the the DET fumecheng-4967 53 2 simplest simple ADJ fumecheng-4967 53 3 variant variant NOUN fumecheng-4967 53 4 of of ADP fumecheng-4967 53 5 the the DET fumecheng-4967 53 6 theory theory NOUN fumecheng-4967 53 7 corresponds correspond VERB fumecheng-4967 53 8 to to ADP fumecheng-4967 53 9 the the DET fumecheng-4967 53 10 case case NOUN fumecheng-4967 53 11 , , PUNCT fumecheng-4967 53 12 when when SCONJ fumecheng-4967 53 13 local local ADJ fumecheng-4967 53 14 form form NOUN fumecheng-4967 53 15 u(ρ(x))→u(ρ u(ρ(x))→u(ρ PROPN fumecheng-4967 53 16 ) ) PUNCT fumecheng-4967 53 17 of of ADP fumecheng-4967 53 18 the the DET fumecheng-4967 53 19 energy energy NOUN fumecheng-4967 53 20 ( ( PUNCT fumecheng-4967 53 21 depending depend VERB fumecheng-4967 53 22 on on ADP fumecheng-4967 53 23 uniform uniform ADJ fumecheng-4967 53 24 variable variable ADJ fumecheng-4967 53 25 ρ ρ PROPN fumecheng-4967 53 26 ) ) PUNCT fumecheng-4967 53 27 has have VERB fumecheng-4967 53 28 two two NUM fumecheng-4967 53 29 minimums minimum NOUN fumecheng-4967 53 30 corresponding correspond VERB fumecheng-4967 53 31 to to AUX fumecheng-4967 53 32 “ " PUNCT fumecheng-4967 53 33 ordered order VERB fumecheng-4967 53 34 ” " PUNCT fumecheng-4967 53 35 ρ ρ PROPN fumecheng-4967 53 36 = = PROPN fumecheng-4967 53 37 ρ0≠0 ρ0≠0 NUM fumecheng-4967 53 38 and and CCONJ fumecheng-4967 53 39 “ " PUNCT fumecheng-4967 53 40 disordered disordered ADJ fumecheng-4967 53 41 ” " PUNCT fumecheng-4967 53 42 ρ=0 ρ=0 NOUN fumecheng-4967 53 43 states state NOUN fumecheng-4967 53 44 . . PUNCT fumecheng-4967 54 1 depending depend VERB fumecheng-4967 54 2 of of ADP fumecheng-4967 54 3 the the DET fumecheng-4967 54 4 relationship relationship NOUN fumecheng-4967 54 5 between between ADP fumecheng-4967 54 6 the the DET fumecheng-4967 54 7 energy energy NOUN fumecheng-4967 54 8 minimums minimum NOUN fumecheng-4967 54 9 u(ρ0 u(ρ0 NOUN fumecheng-4967 54 10 ) ) PUNCT fumecheng-4967 54 11 and and CCONJ fumecheng-4967 54 12 u(ρ=0 u(ρ=0 PROPN fumecheng-4967 54 13 ) ) PUNCT fumecheng-4967 54 14 one one NUM fumecheng-4967 54 15 or or CCONJ fumecheng-4967 54 16 another another DET fumecheng-4967 54 17 state state NOUN fumecheng-4967 54 18 is be AUX fumecheng-4967 54 19 energetically energetically ADV fumecheng-4967 54 20 preferable preferable ADJ fumecheng-4967 54 21 . . PUNCT fumecheng-4967 55 1 for for ADP fumecheng-4967 55 2 example example NOUN fumecheng-4967 55 3 , , PUNCT fumecheng-4967 55 4 if if SCONJ fumecheng-4967 55 5 u(ρ0)=dδ(xx´)ρ(tt t)δρ(x´,t´)>=dδ(xx´)ρ(tt NOUN fumecheng-4967 76 16 ´ ´ NOUN fumecheng-4967 76 17 ) ) PUNCT fumecheng-4967 76 18 tend tend VERB fumecheng-4967 76 19 to to ADP fumecheng-4967 76 20 the the DET fumecheng-4967 76 21 ordered order VERB fumecheng-4967 76 22 state state NOUN fumecheng-4967 76 23 with with ADP fumecheng-4967 76 24 < < X fumecheng-4967 76 25 δρ(x δρ(x X fumecheng-4967 76 26 , , PUNCT fumecheng-4967 76 27 t)>=0 t)>=0 NOUN fumecheng-4967 76 28 and and CCONJ fumecheng-4967 76 29 < < X fumecheng-4967 76 30 ρ(x ρ(x NOUN fumecheng-4967 76 31 , , PUNCT fumecheng-4967 76 32 t→∞)>=ρ0 t→∞)>=ρ0 X fumecheng-4967 76 33 = = NOUN fumecheng-4967 76 34 const const ADJ fumecheng-4967 76 35 . . PUNCT fumecheng-4967 77 1 in in ADP fumecheng-4967 77 2 this this DET fumecheng-4967 77 3 place place NOUN fumecheng-4967 77 4 , , PUNCT fumecheng-4967 77 5 the the DET fumecheng-4967 77 6 reader reader NOUN fumecheng-4967 77 7 can can AUX fumecheng-4967 77 8 ask ask VERB fumecheng-4967 77 9 us we PRON fumecheng-4967 77 10 : : PUNCT fumecheng-4967 77 11 why why SCONJ fumecheng-4967 77 12 do do AUX fumecheng-4967 77 13 we we PRON fumecheng-4967 77 14 need need VERB fumecheng-4967 77 15 so so ADV fumecheng-4967 77 16 complex complex ADJ fumecheng-4967 77 17 description description NOUN fumecheng-4967 77 18 , , PUNCT fumecheng-4967 77 19 if if SCONJ fumecheng-4967 77 20 after after SCONJ fumecheng-4967 77 21 all all DET fumecheng-4967 77 22 everything everything PRON fumecheng-4967 77 23 tends tend VERB fumecheng-4967 77 24 to to ADP fumecheng-4967 77 25 the the DET fumecheng-4967 77 26 simple simple ADJ fumecheng-4967 77 27 constant constant ADJ fumecheng-4967 77 28 ρ0 ρ0 PROPN fumecheng-4967 77 29 = = NOUN fumecheng-4967 77 30 const const NOUN fumecheng-4967 77 31 ? ? PUNCT fumecheng-4967 78 1 the the DET fumecheng-4967 78 2 main main ADJ fumecheng-4967 78 3 problem problem NOUN fumecheng-4967 78 4 here here ADV fumecheng-4967 78 5 lies lie VERB fumecheng-4967 78 6 in in ADP fumecheng-4967 78 7 the the DET fumecheng-4967 78 8 words word NOUN fumecheng-4967 78 9 “ " PUNCT fumecheng-4967 78 10 after after ADV fumecheng-4967 78 11 all all ADV fumecheng-4967 78 12 ” " PUNCT fumecheng-4967 78 13 . . PUNCT fumecheng-4967 79 1 we we PRON fumecheng-4967 79 2 are be AUX fumecheng-4967 79 3 not not PART fumecheng-4967 79 4 interested interested ADJ fumecheng-4967 79 5 in in ADP fumecheng-4967 79 6 trivial trivial ADJ fumecheng-4967 79 7 final final NOUN fumecheng-4967 79 8 of of ADP fumecheng-4967 79 9 the the DET fumecheng-4967 79 10 kinetic kinetic ADJ fumecheng-4967 79 11 process process NOUN fumecheng-4967 79 12 , , PUNCT fumecheng-4967 79 13 but but CCONJ fumecheng-4967 79 14 in in ADP fumecheng-4967 79 15 its its PRON fumecheng-4967 79 16 intermediate intermediate ADJ fumecheng-4967 79 17 state state NOUN fumecheng-4967 79 18 . . PUNCT fumecheng-4967 80 1 absolute absolute ADJ fumecheng-4967 80 2 majority majority NOUN fumecheng-4967 80 3 of of ADP fumecheng-4967 80 4 real real ADJ fumecheng-4967 80 5 surfaces surface NOUN fumecheng-4967 80 6 and and CCONJ fumecheng-4967 80 7 substances substance NOUN fumecheng-4967 80 8 are be AUX fumecheng-4967 80 9 “ " PUNCT fumecheng-4967 80 10 frozen frozen ADJ fumecheng-4967 80 11 ” " PUNCT fumecheng-4967 80 12 in in ADP fumecheng-4967 80 13 an an DET fumecheng-4967 80 14 intermediate intermediate ADJ fumecheng-4967 80 15 states state NOUN fumecheng-4967 80 16 of of ADP fumecheng-4967 80 17 the the DET fumecheng-4967 80 18 kinetic kinetic ADJ fumecheng-4967 80 19 process process NOUN fumecheng-4967 80 20 and and CCONJ fumecheng-4967 80 21 namely namely ADV fumecheng-4967 80 22 at at ADP fumecheng-4967 80 23 these these DET fumecheng-4967 80 24 stages stage NOUN fumecheng-4967 80 25 they they PRON fumecheng-4967 80 26 produce produce VERB fumecheng-4967 80 27 methods method NOUN fumecheng-4967 80 28 of of ADP fumecheng-4967 80 29 the the DET fumecheng-4967 80 30 pattern pattern NOUN fumecheng-4967 80 31 formation formation NOUN fumecheng-4967 80 32 in in ADP fumecheng-4967 80 33 numerical numerical ADJ fumecheng-4967 80 34 modeling modeling NOUN fumecheng-4967 80 35 of of ADP fumecheng-4967 80 36 biological biological ADJ fumecheng-4967 80 37 problems problem NOUN fumecheng-4967 80 38 221 221 NUM fumecheng-4967 80 39 practically practically ADV fumecheng-4967 80 40 important important ADJ fumecheng-4967 80 41 patterns pattern NOUN fumecheng-4967 80 42 with with ADP fumecheng-4967 80 43 non non ADJ fumecheng-4967 80 44 - - ADJ fumecheng-4967 80 45 uniform uniform ADJ fumecheng-4967 80 46 ρ(x ρ(x NOUN fumecheng-4967 80 47 ) ) PUNCT fumecheng-4967 80 48 with with ADP fumecheng-4967 80 49 nonzero nonzero PROPN fumecheng-4967 80 50 gradients gradient NOUN fumecheng-4967 80 51 ∇ρ ∇ρ PROPN fumecheng-4967 80 52 . . PUNCT fumecheng-4967 81 1 moreover moreover ADV fumecheng-4967 81 2 , , PUNCT fumecheng-4967 81 3 in in ADP fumecheng-4967 81 4 many many ADJ fumecheng-4967 81 5 cases case NOUN fumecheng-4967 81 6 ( ( PUNCT fumecheng-4967 81 7 for for ADP fumecheng-4967 81 8 more more ADJ fumecheng-4967 81 9 complex complex ADJ fumecheng-4967 81 10 systems system NOUN fumecheng-4967 81 11 than than SCONJ fumecheng-4967 81 12 we we PRON fumecheng-4967 81 13 study study VERB fumecheng-4967 81 14 right right ADV fumecheng-4967 81 15 now now ADV fumecheng-4967 81 16 ) ) PUNCT fumecheng-4967 81 17 even even ADV fumecheng-4967 81 18 final final ADJ fumecheng-4967 81 19 stage stage NOUN fumecheng-4967 81 20 of of ADP fumecheng-4967 81 21 the the DET fumecheng-4967 81 22 kinetic kinetic ADJ fumecheng-4967 81 23 process process NOUN fumecheng-4967 81 24 are be AUX fumecheng-4967 81 25 domains domain NOUN fumecheng-4967 81 26 and and CCONJ fumecheng-4967 81 27 other other ADJ fumecheng-4967 81 28 structures structure NOUN fumecheng-4967 81 29 with with ADP fumecheng-4967 81 30 non non ADJ fumecheng-4967 81 31 - - ADJ fumecheng-4967 81 32 uniform uniform ADJ fumecheng-4967 81 33 distributions distribution NOUN fumecheng-4967 81 34 ρ(x ρ(x PROPN fumecheng-4967 81 35 ) ) PUNCT fumecheng-4967 81 36 . . PUNCT fumecheng-4967 82 1 below below ADP fumecheng-4967 82 2 we we PRON fumecheng-4967 82 3 will will AUX fumecheng-4967 82 4 study study VERB fumecheng-4967 82 5 some some PRON fumecheng-4967 82 6 of of ADP fumecheng-4967 82 7 them they PRON fumecheng-4967 82 8 , , PUNCT fumecheng-4967 82 9 but but CCONJ fumecheng-4967 82 10 now now ADV fumecheng-4967 82 11 let let VERB fumecheng-4967 82 12 us we PRON fumecheng-4967 82 13 return return VERB fumecheng-4967 82 14 to to ADP fumecheng-4967 82 15 the the DET fumecheng-4967 82 16 simplest simple ADJ fumecheng-4967 82 17 ( ( PUNCT fumecheng-4967 82 18 ! ! PUNCT fumecheng-4967 82 19 ) ) PUNCT fumecheng-4967 82 20 case case NOUN fumecheng-4967 82 21 . . PUNCT fumecheng-4967 83 1 combining combine VERB fumecheng-4967 83 2 eqs eqs PROPN fumecheng-4967 83 3 . . PUNCT fumecheng-4967 84 1 ( ( PUNCT fumecheng-4967 84 2 1 1 X fumecheng-4967 84 3 ) ) PUNCT fumecheng-4967 84 4 and and CCONJ fumecheng-4967 84 5 ( ( PUNCT fumecheng-4967 84 6 3 3 X fumecheng-4967 84 7 ) ) PUNCT fumecheng-4967 84 8 one one NOUN fumecheng-4967 84 9 can can AUX fumecheng-4967 84 10 write write VERB fumecheng-4967 84 11 energy energy NOUN fumecheng-4967 84 12 functional functional ADJ fumecheng-4967 84 13 in in ADP fumecheng-4967 84 14 the the DET fumecheng-4967 84 15 following follow VERB fumecheng-4967 84 16 form form NOUN fumecheng-4967 84 17 [ [ X fumecheng-4967 84 18 3 3 NUM fumecheng-4967 84 19 ] ] SYM fumecheng-4967 84 20 : : PUNCT fumecheng-4967 84 21 2 2 NUM fumecheng-4967 84 22 2 2 NUM fumecheng-4967 84 23 3 3 NUM fumecheng-4967 84 24 4 4 NUM fumecheng-4967 84 25 2 2 NUM fumecheng-4967 84 26 [ [ PUNCT fumecheng-4967 84 27 ( ( PUNCT fumecheng-4967 84 28 ) ) PUNCT fumecheng-4967 84 29 ] ] PUNCT fumecheng-4967 85 1 [ [ PUNCT fumecheng-4967 85 2 ( ( PUNCT fumecheng-4967 85 3 ( ( PUNCT fumecheng-4967 85 4 ) ) PUNCT fumecheng-4967 85 5 ) ) PUNCT fumecheng-4967 85 6 ( ( PUNCT fumecheng-4967 85 7 ) ) PUNCT fumecheng-4967 85 8 ( ( PUNCT fumecheng-4967 85 9 ) ) PUNCT fumecheng-4967 85 10 ( ( PUNCT fumecheng-4967 85 11 ) ) PUNCT fumecheng-4967 85 12 ... ... PUNCT fumecheng-4967 85 13 ] ] PUNCT fumecheng-4967 85 14 2 2 NUM fumecheng-4967 85 15 2 2 NUM fumecheng-4967 85 16 3 3 NUM fumecheng-4967 85 17 4 4 NUM fumecheng-4967 85 18 [ [ PUNCT fumecheng-4967 85 19 ( ( PUNCT fumecheng-4967 85 20 ( ( PUNCT fumecheng-4967 85 21 ) ) PUNCT fumecheng-4967 85 22 ) ) PUNCT fumecheng-4967 85 23 ( ( PUNCT fumecheng-4967 85 24 ( ( PUNCT fumecheng-4967 85 25 ) ) PUNCT fumecheng-4967 85 26 ) ) PUNCT fumecheng-4967 85 27 ] ] PUNCT fumecheng-4967 86 1 2 2 NUM fumecheng-4967 86 2 c c NOUN fumecheng-4967 86 3 b b NOUN fumecheng-4967 86 4 g g NOUN fumecheng-4967 86 5 x x X fumecheng-4967 86 6 dx dx PROPN fumecheng-4967 86 7 x x PUNCT fumecheng-4967 86 8 x x PUNCT fumecheng-4967 86 9 x x PUNCT fumecheng-4967 86 10 x x PUNCT fumecheng-4967 86 11 c c NOUN fumecheng-4967 86 12 dx dx PROPN fumecheng-4967 86 13 x x X fumecheng-4967 87 1 f f NOUN fumecheng-4967 87 2 x x SYM fumecheng-4967 87 3   PROPN fumecheng-4967 87 4   PUNCT fumecheng-4967 87 5   NOUN fumecheng-4967 87 6   PUNCT fumecheng-4967 87 7   PRON fumecheng-4967 87 8   PUNCT fumecheng-4967 87 9   PUNCT fumecheng-4967 87 10   PROPN fumecheng-4967 87 11   PROPN fumecheng-4967 87 12   NOUN fumecheng-4967 87 13   VERB fumecheng-4967 87 14   PUNCT fumecheng-4967 87 15   PUNCT fumecheng-4967 87 16   PROPN fumecheng-4967 87 17   ADV fumecheng-4967 87 18   ADP fumecheng-4967 87 19   X fumecheng-4967 87 20   X fumecheng-4967 87 21   X fumecheng-4967 87 22   X fumecheng-4967 87 23   X fumecheng-4967 87 24 ( ( PUNCT fumecheng-4967 87 25 4 4 NUM fumecheng-4967 87 26 ) ) PUNCT fumecheng-4967 87 27 however however ADV fumecheng-4967 87 28 , , PUNCT fumecheng-4967 87 29 if if SCONJ fumecheng-4967 87 30 it it PRON fumecheng-4967 87 31 is be AUX fumecheng-4967 87 32 still still ADV fumecheng-4967 87 33 not not PART fumecheng-4967 87 34 enough enough ADJ fumecheng-4967 87 35 to to PART fumecheng-4967 87 36 write write VERB fumecheng-4967 87 37 down down ADP fumecheng-4967 87 38 complete complete ADJ fumecheng-4967 87 39 equation equation NOUN fumecheng-4967 87 40 for for ADP fumecheng-4967 87 41 the the DET fumecheng-4967 87 42 fluctuating fluctuate VERB fumecheng-4967 87 43 density density NOUN fumecheng-4967 88 1 [ [ X fumecheng-4967 88 2 4 4 NUM fumecheng-4967 88 3 ] ] NUM fumecheng-4967 88 4 : : PUNCT fumecheng-4967 88 5 ( ( PUNCT fumecheng-4967 88 6 , , PUNCT fumecheng-4967 88 7 ) ) PUNCT fumecheng-4967 88 8 / / PUNCT fumecheng-4967 88 9 [ [ PUNCT fumecheng-4967 88 10 ( ( PUNCT fumecheng-4967 88 11 , , PUNCT fumecheng-4967 88 12 ) ) PUNCT fumecheng-4967 88 13 ] ] PUNCT fumecheng-4967 88 14 / / PUNCT fumecheng-4967 88 15 ( ( PUNCT fumecheng-4967 88 16 , , PUNCT fumecheng-4967 88 17 ) ) PUNCT fumecheng-4967 88 18 x x SYM fumecheng-4967 88 19 t t NOUN fumecheng-4967 88 20 t t X fumecheng-4967 88 21 x x SYM fumecheng-4967 88 22 t t PROPN fumecheng-4967 88 23 x x SYM fumecheng-4967 88 24 t t PROPN fumecheng-4967 88 25   ADJ fumecheng-4967 88 26   PROPN fumecheng-4967 88 27   PROPN fumecheng-4967 88 28   NOUN fumecheng-4967 88 29   PUNCT fumecheng-4967 88 30   ADP fumecheng-4967 88 31   NUM fumecheng-4967 88 32 ( ( PUNCT fumecheng-4967 88 33 5 5 NUM fumecheng-4967 88 34 ) ) PUNCT fumecheng-4967 88 35 if if SCONJ fumecheng-4967 88 36 ρ(x ρ(x PROPN fumecheng-4967 88 37 , , PUNCT fumecheng-4967 88 38 t t PROPN fumecheng-4967 88 39 ) ) PUNCT fumecheng-4967 88 40 really really ADV fumecheng-4967 88 41 fluctuates fluctuate VERB fumecheng-4967 88 42 , , PUNCT fumecheng-4967 88 43 it it PRON fumecheng-4967 88 44 is be AUX fumecheng-4967 88 45 not not PART fumecheng-4967 88 46 only only ADV fumecheng-4967 88 47 random random ADJ fumecheng-4967 88 48 value value NOUN fumecheng-4967 88 49 < < X fumecheng-4967 88 50 δρ(x δρ(x X fumecheng-4967 88 51 , , PUNCT fumecheng-4967 88 52 t)δρ(x´,t´)>=dδ(x t)δρ(x´,t´)>=dδ(x NOUN fumecheng-4967 88 53 - - PUNCT fumecheng-4967 88 54 x´)ρ(tt x´)ρ(tt NOUN fumecheng-4967 88 55 ´ ´ NOUN fumecheng-4967 88 56 ) ) PUNCT fumecheng-4967 88 57 with with ADP fumecheng-4967 88 58 intensity intensity NOUN fumecheng-4967 88 59 of of ADP fumecheng-4967 88 60 d d PROPN fumecheng-4967 88 61 at at ADP fumecheng-4967 88 62 the the DET fumecheng-4967 88 63 beginning beginning NOUN fumecheng-4967 88 64 of of ADP fumecheng-4967 88 65 the the DET fumecheng-4967 88 66 process process NOUN fumecheng-4967 88 67 , , PUNCT fumecheng-4967 88 68 but but CCONJ fumecheng-4967 88 69 it it PRON fumecheng-4967 88 70 continues continue VERB fumecheng-4967 88 71 to to PART fumecheng-4967 88 72 fluctuate fluctuate VERB fumecheng-4967 88 73 further far ADV fumecheng-4967 88 74 . . PUNCT fumecheng-4967 89 1 it it PRON fumecheng-4967 89 2 means mean VERB fumecheng-4967 89 3 that that SCONJ fumecheng-4967 89 4 eq eq ADP fumecheng-4967 89 5 . . PUNCT fumecheng-4967 90 1 ( ( PUNCT fumecheng-4967 90 2 5 5 X fumecheng-4967 90 3 ) ) PUNCT fumecheng-4967 90 4 should should AUX fumecheng-4967 90 5 include include VERB fumecheng-4967 90 6 also also ADV fumecheng-4967 90 7 a a DET fumecheng-4967 90 8 source source NOUN fumecheng-4967 90 9 of of ADP fumecheng-4967 90 10 random random ADJ fumecheng-4967 90 11 fluctuations fluctuation NOUN fumecheng-4967 90 12 δ(x δ(x PROPN fumecheng-4967 90 13 , , PUNCT fumecheng-4967 90 14 t t PROPN fumecheng-4967 90 15 ) ) PUNCT fumecheng-4967 90 16 . . PUNCT fumecheng-4967 91 1 mathematically mathematically ADV fumecheng-4967 91 2 , , PUNCT fumecheng-4967 91 3 it it PRON fumecheng-4967 91 4 has have VERB fumecheng-4967 91 5 the the DET fumecheng-4967 91 6 same same ADJ fumecheng-4967 91 7 properties property NOUN fumecheng-4967 91 8 as as ADP fumecheng-4967 91 9 the the DET fumecheng-4967 91 10 initial initial ADJ fumecheng-4967 91 11 condition condition NOUN fumecheng-4967 91 12 for for ADP fumecheng-4967 91 13 the the DET fumecheng-4967 91 14 fluctuations fluctuation NOUN fumecheng-4967 91 15 of of ADP fumecheng-4967 91 16 density density NOUN fumecheng-4967 91 17 : : PUNCT fumecheng-4967 91 18 ( ( PUNCT fumecheng-4967 91 19 , , PUNCT fumecheng-4967 91 20 ) ) PUNCT fumecheng-4967 91 21 0x 0x NOUN fumecheng-4967 91 22 t t NOUN fumecheng-4967 91 23   NOUN fumecheng-4967 91 24 , , PUNCT fumecheng-4967 91 25 ( ( PUNCT fumecheng-4967 91 26 , , PUNCT fumecheng-4967 91 27 ) ) PUNCT fumecheng-4967 91 28 ( ( PUNCT fumecheng-4967 91 29 ' ' PUNCT fumecheng-4967 91 30 , , PUNCT fumecheng-4967 91 31 ' ' PUNCT fumecheng-4967 91 32 ) ) PUNCT fumecheng-4967 91 33 ( ( PUNCT fumecheng-4967 91 34 ' ' PUNCT fumecheng-4967 91 35 ) ) PUNCT fumecheng-4967 91 36 ( ( PUNCT fumecheng-4967 91 37 ' ' NUM fumecheng-4967 91 38 ) ) PUNCT fumecheng-4967 91 39 x x SYM fumecheng-4967 92 1 t t NOUN fumecheng-4967 92 2 x x X fumecheng-4967 92 3 t t PROPN fumecheng-4967 93 1 d d X fumecheng-4967 93 2 x x X fumecheng-4967 93 3 x x SYM fumecheng-4967 93 4 t t PROPN fumecheng-4967 93 5 t t X fumecheng-4967 93 6   PROPN fumecheng-4967 93 7   PROPN fumecheng-4967 93 8   NOUN fumecheng-4967 93 9   NOUN fumecheng-4967 94 1   NUM fumecheng-4967 94 2   NUM fumecheng-4967 94 3 . . PUNCT fumecheng-4967 95 1 ( ( PUNCT fumecheng-4967 95 2 6 6 NUM fumecheng-4967 95 3 ) ) PUNCT fumecheng-4967 95 4 this this DET fumecheng-4967 95 5 random random ADJ fumecheng-4967 95 6 source source NOUN fumecheng-4967 95 7 stays stay VERB fumecheng-4967 95 8 in in ADP fumecheng-4967 95 9 the the DET fumecheng-4967 95 10 right right ADJ fumecheng-4967 95 11 hand hand NOUN fumecheng-4967 95 12 side side NOUN fumecheng-4967 95 13 of of ADP fumecheng-4967 95 14 the the DET fumecheng-4967 95 15 equation equation NOUN fumecheng-4967 95 16 of of ADP fumecheng-4967 95 17 motion motion NOUN fumecheng-4967 95 18 ( ( PUNCT fumecheng-4967 95 19 , , PUNCT fumecheng-4967 95 20 ) ) PUNCT fumecheng-4967 95 21 / / PUNCT fumecheng-4967 96 1 [ [ PUNCT fumecheng-4967 96 2 ( ( PUNCT fumecheng-4967 96 3 , , PUNCT fumecheng-4967 96 4 ) ) PUNCT fumecheng-4967 96 5 ] ] PUNCT fumecheng-4967 96 6 / / PUNCT fumecheng-4967 96 7 ( ( PUNCT fumecheng-4967 96 8 , , PUNCT fumecheng-4967 96 9 ) ) PUNCT fumecheng-4967 96 10 ( ( PUNCT fumecheng-4967 96 11 , , PUNCT fumecheng-4967 96 12 ) ) PUNCT fumecheng-4967 96 13 x x SYM fumecheng-4967 97 1 t t NOUN fumecheng-4967 97 2 t t PROPN fumecheng-4967 97 3 x x SYM fumecheng-4967 97 4 t t X fumecheng-4967 97 5 x x SYM fumecheng-4967 97 6 t t NOUN fumecheng-4967 97 7 x x SYM fumecheng-4967 97 8 t t PROPN fumecheng-4967 97 9   ADJ fumecheng-4967 98 1   PROPN fumecheng-4967 98 2   NOUN fumecheng-4967 98 3   PROPN fumecheng-4967 98 4   NOUN fumecheng-4967 98 5   PROPN fumecheng-4967 98 6   ADP fumecheng-4967 98 7   VERB fumecheng-4967 98 8   NOUN fumecheng-4967 98 9 ( ( PUNCT fumecheng-4967 98 10 7 7 NUM fumecheng-4967 98 11 ) ) PUNCT fumecheng-4967 98 12 and and CCONJ fumecheng-4967 98 13 cause cause VERB fumecheng-4967 98 14 generation generation NOUN fumecheng-4967 98 15 of of ADP fumecheng-4967 98 16 new new ADJ fumecheng-4967 98 17 fluctuations fluctuation NOUN fumecheng-4967 98 18 during during ADP fumecheng-4967 98 19 the the DET fumecheng-4967 98 20 whole whole ADJ fumecheng-4967 98 21 process process NOUN fumecheng-4967 98 22 of of ADP fumecheng-4967 98 23 the the DET fumecheng-4967 98 24 density density NOUN fumecheng-4967 98 25 nucleation nucleation NOUN fumecheng-4967 98 26 . . PUNCT fumecheng-4967 99 1 eq eq X fumecheng-4967 99 2 . . PUNCT fumecheng-4967 100 1 ( ( PUNCT fumecheng-4967 100 2 7 7 X fumecheng-4967 100 3 ) ) PUNCT fumecheng-4967 100 4 is be AUX fumecheng-4967 100 5 already already ADV fumecheng-4967 100 6 equation equation NOUN fumecheng-4967 100 7 of of ADP fumecheng-4967 100 8 motion motion NOUN fumecheng-4967 100 9 for for ADP fumecheng-4967 100 10 this this DET fumecheng-4967 100 11 simplest simple ADJ fumecheng-4967 100 12 ( ( PUNCT fumecheng-4967 100 13 ! ! PUNCT fumecheng-4967 100 14 ) ) PUNCT fumecheng-4967 100 15 model model NOUN fumecheng-4967 100 16 . . PUNCT fumecheng-4967 101 1 taking take VERB fumecheng-4967 101 2 into into ADP fumecheng-4967 101 3 account account NOUN fumecheng-4967 101 4 explicit explicit ADJ fumecheng-4967 101 5 form form NOUN fumecheng-4967 101 6 eq eq ADJ fumecheng-4967 101 7 . . PUNCT fumecheng-4967 102 1 ( ( PUNCT fumecheng-4967 102 2 4 4 NUM fumecheng-4967 102 3 ) ) PUNCT fumecheng-4967 102 4 of of ADP fumecheng-4967 102 5 the the DET fumecheng-4967 102 6 functional functional ADJ fumecheng-4967 102 7 φ[ρ(x φ[ρ(x NUM fumecheng-4967 102 8 ) ) PUNCT fumecheng-4967 102 9 ] ] PUNCT fumecheng-4967 102 10 and and CCONJ fumecheng-4967 102 11 performing perform VERB fumecheng-4967 102 12 the the DET fumecheng-4967 102 13 variation variation NOUN fumecheng-4967 102 14 δφ[ρ(x δφ[ρ(x PROPN fumecheng-4967 102 15 , , PUNCT fumecheng-4967 102 16 t)]/δρ(x t)]/δρ(x NOUN fumecheng-4967 102 17 , , PUNCT fumecheng-4967 102 18 t t PROPN fumecheng-4967 102 19 ) ) PUNCT fumecheng-4967 102 20 one one NOUN fumecheng-4967 102 21 can can AUX fumecheng-4967 102 22 write write VERB fumecheng-4967 102 23 the the DET fumecheng-4967 102 24 form form NOUN fumecheng-4967 102 25 of of ADP fumecheng-4967 102 26 the the DET fumecheng-4967 102 27 kinetic kinetic ADJ fumecheng-4967 102 28 equation equation NOUN fumecheng-4967 102 29 that that PRON fumecheng-4967 102 30 is be AUX fumecheng-4967 102 31 more more ADV fumecheng-4967 102 32 convenient convenient ADJ fumecheng-4967 102 33 for for ADP fumecheng-4967 102 34 the the DET fumecheng-4967 102 35 solution solution NOUN fumecheng-4967 102 36 : : PUNCT fumecheng-4967 102 37 2 2 NUM fumecheng-4967 102 38 3 3 NUM fumecheng-4967 102 39 4 4 NUM fumecheng-4967 102 40 ( ( PUNCT fumecheng-4967 102 41 , , PUNCT fumecheng-4967 102 42 ) ) PUNCT fumecheng-4967 102 43 / / PUNCT fumecheng-4967 103 1 [ [ PUNCT fumecheng-4967 103 2 ( ( PUNCT fumecheng-4967 103 3 , , PUNCT fumecheng-4967 103 4 ) ) PUNCT fumecheng-4967 103 5 ( ( PUNCT fumecheng-4967 103 6 , , PUNCT fumecheng-4967 103 7 ) ) PUNCT fumecheng-4967 103 8 ( ( PUNCT fumecheng-4967 103 9 , , PUNCT fumecheng-4967 103 10 ) ) PUNCT fumecheng-4967 103 11 ( ( PUNCT fumecheng-4967 103 12 , , PUNCT fumecheng-4967 103 13 ) ) PUNCT fumecheng-4967 103 14 ] ] PUNCT fumecheng-4967 103 15 ( ( PUNCT fumecheng-4967 103 16 , , PUNCT fumecheng-4967 103 17 ) ) PUNCT fumecheng-4967 103 18 x x SYM fumecheng-4967 104 1 t t NOUN fumecheng-4967 104 2 t t NOUN fumecheng-4967 104 3 c c NOUN fumecheng-4967 104 4 x x SYM fumecheng-4967 104 5 t t NOUN fumecheng-4967 104 6 x x X fumecheng-4967 104 7 t t PROPN fumecheng-4967 104 8 b b PROPN fumecheng-4967 104 9 x x SYM fumecheng-4967 104 10 t t PROPN fumecheng-4967 104 11 g g PROPN fumecheng-4967 104 12 x x SYM fumecheng-4967 104 13 t t PROPN fumecheng-4967 104 14 x x SYM fumecheng-4967 104 15 t t PROPN fumecheng-4967 104 16   ADJ fumecheng-4967 104 17   PROPN fumecheng-4967 104 18   PROPN fumecheng-4967 104 19   NOUN fumecheng-4967 104 20   PROPN fumecheng-4967 104 21   PUNCT fumecheng-4967 104 22   PUNCT fumecheng-4967 104 23   PRON fumecheng-4967 104 24   NUM fumecheng-4967 104 25   ADP fumecheng-4967 104 26   NOUN fumecheng-4967 104 27   ADP fumecheng-4967 104 28   ADP fumecheng-4967 104 29   X fumecheng-4967 104 30 ( ( PUNCT fumecheng-4967 104 31 8) 8) NUM fumecheng-4967 104 32 where where SCONJ fumecheng-4967 104 33 δρ(x δρ(x VERB fumecheng-4967 104 34 ) ) PUNCT fumecheng-4967 104 35 is be AUX fumecheng-4967 104 36 laplasian laplasian ADJ fumecheng-4967 104 37 operator operator NOUN fumecheng-4967 104 38 which which PRON fumecheng-4967 104 39 in in ADP fumecheng-4967 104 40 1d 1d NUM fumecheng-4967 104 41 case case NOUN fumecheng-4967 104 42 is be AUX fumecheng-4967 104 43 equal equal ADJ fumecheng-4967 104 44 simply simply ADV fumecheng-4967 104 45 to to PART fumecheng-4967 104 46 second second ADJ fumecheng-4967 105 1 derivative derivative ADJ fumecheng-4967 105 2 δρ(x)=∂ δρ(x)=∂ PROPN fumecheng-4967 105 3 2 2 NUM fumecheng-4967 105 4 ρ(x)/∂x ρ(x)/∂x PROPN fumecheng-4967 105 5 2 2 NUM fumecheng-4967 105 6 . . PUNCT fumecheng-4967 106 1 starting start VERB fumecheng-4967 106 2 from from ADP fumecheng-4967 106 3 the the DET fumecheng-4967 106 4 random random ADJ fumecheng-4967 106 5 distribution distribution NOUN fumecheng-4967 106 6 , , PUNCT fumecheng-4967 106 7 the the DET fumecheng-4967 106 8 density density NOUN fumecheng-4967 106 9 evolves evolve VERB fumecheng-4967 106 10 with with ADP fumecheng-4967 106 11 time time NOUN fumecheng-4967 106 12 according accord VERB fumecheng-4967 106 13 to to ADP fumecheng-4967 106 14 the the DET fumecheng-4967 106 15 eq eq NOUN fumecheng-4967 106 16 . . PUNCT fumecheng-4967 107 1 ( ( PUNCT fumecheng-4967 107 2 8) 8) NUM fumecheng-4967 107 3 . . PUNCT fumecheng-4967 108 1 the the DET fumecheng-4967 108 2 barrier barrier NOUN fumecheng-4967 108 3 in in ADP fumecheng-4967 108 4 the the DET fumecheng-4967 108 5 local local ADJ fumecheng-4967 108 6 part part NOUN fumecheng-4967 108 7 of of ADP fumecheng-4967 108 8 energy energy NOUN fumecheng-4967 108 9 f(ρ(x f(ρ(x NOUN fumecheng-4967 108 10 ) ) PUNCT fumecheng-4967 108 11 ) ) PUNCT fumecheng-4967 108 12 does do AUX fumecheng-4967 108 13 not not PART fumecheng-4967 108 14 allow allow VERB fumecheng-4967 108 15 majority majority NOUN fumecheng-4967 108 16 of of ADP fumecheng-4967 108 17 the the DET fumecheng-4967 108 18 density density NOUN fumecheng-4967 108 19 fluctuations fluctuation NOUN fumecheng-4967 108 20 to to PART fumecheng-4967 108 21 grow grow VERB fumecheng-4967 108 22 immediately immediately ADV fumecheng-4967 108 23 to to ADP fumecheng-4967 108 24 the the DET fumecheng-4967 108 25 minimum minimum NOUN fumecheng-4967 108 26 corresponding corresponding NOUN fumecheng-4967 108 27 to to ADP fumecheng-4967 108 28 the the DET fumecheng-4967 108 29 nonzero nonzero PROPN fumecheng-4967 108 30 equilibrium equilibrium NOUN fumecheng-4967 108 31 density density NOUN fumecheng-4967 108 32 ρ0 ρ0 PROPN fumecheng-4967 108 33 = = SYM fumecheng-4967 108 34 const const NOUN fumecheng-4967 108 35 . . PUNCT fumecheng-4967 109 1 the the DET fumecheng-4967 109 2 only only ADJ fumecheng-4967 109 3 relatively relatively ADV fumecheng-4967 109 4 large large ADJ fumecheng-4967 109 5 fluctuations fluctuation NOUN fumecheng-4967 109 6 can can AUX fumecheng-4967 109 7 pass pass VERB fumecheng-4967 109 8 the the DET fumecheng-4967 109 9 barrier barrier NOUN fumecheng-4967 109 10 and and CCONJ fumecheng-4967 109 11 grow grow VERB fumecheng-4967 109 12 . . PUNCT fumecheng-4967 110 1 they they PRON fumecheng-4967 110 2 grow grow VERB fumecheng-4967 110 3 in in ADP fumecheng-4967 110 4 both both DET fumecheng-4967 110 5 senses sense NOUN fumecheng-4967 110 6 : : PUNCT fumecheng-4967 110 7 their their PRON fumecheng-4967 110 8 amplitude amplitude NOUN fumecheng-4967 110 9 at at ADP fumecheng-4967 110 10 maximum maximum ADJ fumecheng-4967 110 11 tends tend NOUN fumecheng-4967 110 12 to to ADP fumecheng-4967 110 13 ρ0 ρ0 PROPN fumecheng-4967 110 14 and and CCONJ fumecheng-4967 110 15 they they PRON fumecheng-4967 110 16 expand expand VERB fumecheng-4967 110 17 in in ADP fumecheng-4967 110 18 space space NOUN fumecheng-4967 110 19 [ [ X fumecheng-4967 110 20 5 5 NUM fumecheng-4967 110 21 , , PUNCT fumecheng-4967 110 22 6 6 NUM fumecheng-4967 110 23 ] ] PUNCT fumecheng-4967 110 24 . . PUNCT fumecheng-4967 111 1 the the DET fumecheng-4967 111 2 same same ADJ fumecheng-4967 111 3 logics logic NOUN fumecheng-4967 111 4 can can AUX fumecheng-4967 111 5 be be AUX fumecheng-4967 111 6 easily easily ADV fumecheng-4967 111 7 expanded expand VERB fumecheng-4967 111 8 into into ADP fumecheng-4967 111 9 2d 2d NUM fumecheng-4967 111 10 space space NOUN fumecheng-4967 111 11 where where SCONJ fumecheng-4967 111 12 corresponding corresponding ADJ fumecheng-4967 111 13 pattern pattern NOUN fumecheng-4967 111 14 of of ADP fumecheng-4967 111 15 the the DET fumecheng-4967 111 16 density density NOUN fumecheng-4967 111 17 will will AUX fumecheng-4967 111 18 appear appear VERB fumecheng-4967 111 19 . . PUNCT fumecheng-4967 112 1 typical typical ADJ fumecheng-4967 112 2 intermediate intermediate ADJ fumecheng-4967 112 3 configuration configuration NOUN fumecheng-4967 112 4 with with ADP fumecheng-4967 112 5 different different ADJ fumecheng-4967 112 6 nuclei nucleus NOUN fumecheng-4967 112 7 of of ADP fumecheng-4967 112 8 nonzero nonzero PROPN fumecheng-4967 112 9 density density NOUN fumecheng-4967 112 10 is be AUX fumecheng-4967 112 11 shown show VERB fumecheng-4967 112 12 in in ADP fumecheng-4967 112 13 fig.2 fig.2 PROPN fumecheng-4967 112 14 . . PUNCT fumecheng-4967 113 1 if if SCONJ fumecheng-4967 113 2 there there PRON fumecheng-4967 113 3 is be VERB fumecheng-4967 113 4 physical physical ADJ fumecheng-4967 113 5 reason reason NOUN fumecheng-4967 113 6 to to PART fumecheng-4967 113 7 freeze freeze VERB fumecheng-4967 113 8 this this DET fumecheng-4967 113 9 configuration configuration NOUN fumecheng-4967 113 10 , , PUNCT fumecheng-4967 113 11 we we PRON fumecheng-4967 113 12 would would AUX fumecheng-4967 113 13 get get VERB fumecheng-4967 113 14 almost almost ADV fumecheng-4967 113 15 static static ADJ fumecheng-4967 113 16 representation representation NOUN fumecheng-4967 113 17 of of ADP fumecheng-4967 113 18 the the DET fumecheng-4967 113 19 non non ADJ fumecheng-4967 113 20 - - ADJ fumecheng-4967 113 21 uniform uniform ADJ fumecheng-4967 113 22 pattern pattern NOUN fumecheng-4967 113 23 of of ADP fumecheng-4967 113 24 density density NOUN fumecheng-4967 113 25 . . PUNCT fumecheng-4967 114 1 the the DET fumecheng-4967 114 2 simplest simple ADJ fumecheng-4967 114 3 possible possible ADJ fumecheng-4967 114 4 reason reason NOUN fumecheng-4967 114 5 for for ADP fumecheng-4967 114 6 this this PRON fumecheng-4967 114 7 may may AUX fumecheng-4967 114 8 be be AUX fumecheng-4967 114 9 very very ADV fumecheng-4967 114 10 small small ADJ fumecheng-4967 114 11 damping damp VERB fumecheng-4967 114 12 constant constant ADJ fumecheng-4967 114 13   NUM fumecheng-4967 114 14 which which PRON fumecheng-4967 114 15 controls control VERB fumecheng-4967 114 16 222 222 NUM fumecheng-4967 114 17 a.e a.e PROPN fumecheng-4967 114 18 . . PROPN fumecheng-4967 114 19 filippov filippov PROPN fumecheng-4967 114 20 , , PUNCT fumecheng-4967 114 21 s.n s.n PROPN fumecheng-4967 114 22 . . PROPN fumecheng-4967 114 23 gorb gorb PROPN fumecheng-4967 114 24 rate rate NOUN fumecheng-4967 114 25 of of ADP fumecheng-4967 114 26 the the DET fumecheng-4967 114 27 kinetic kinetic ADJ fumecheng-4967 114 28 process process NOUN fumecheng-4967 114 29 in in ADP fumecheng-4967 114 30 eq eq ADP fumecheng-4967 114 31 . . PUNCT fumecheng-4967 115 1 ( ( PUNCT fumecheng-4967 115 2 8) 8) NUM fumecheng-4967 115 3 . . PUNCT fumecheng-4967 116 1 if if SCONJ fumecheng-4967 116 2 the the DET fumecheng-4967 116 3 characteristic characteristic ADJ fumecheng-4967 116 4 time time NOUN fumecheng-4967 116 5 1 1 NUM fumecheng-4967 116 6 / / SYM fumecheng-4967 116 7 γ γ NOUN fumecheng-4967 116 8 of of ADP fumecheng-4967 116 9 evolution evolution NOUN fumecheng-4967 116 10 of of ADP fumecheng-4967 116 11 the the DET fumecheng-4967 116 12 distribution distribution NOUN fumecheng-4967 116 13 ρ(x ρ(x NOUN fumecheng-4967 116 14 , , PUNCT fumecheng-4967 116 15 t t PROPN fumecheng-4967 116 16 ) ) PUNCT fumecheng-4967 116 17 to to ADP fumecheng-4967 116 18 the the DET fumecheng-4967 116 19 equilibrium equilibrium NOUN fumecheng-4967 116 20 ρ0 ρ0 PROPN fumecheng-4967 116 21 is be AUX fumecheng-4967 116 22 extremely extremely ADV fumecheng-4967 116 23 long long ADJ fumecheng-4967 116 24 in in ADP fumecheng-4967 116 25 comparison comparison NOUN fumecheng-4967 116 26 with with ADP fumecheng-4967 116 27 other other ADJ fumecheng-4967 116 28 times time NOUN fumecheng-4967 116 29 of of ADP fumecheng-4967 116 30 a a DET fumecheng-4967 116 31 problem problem NOUN fumecheng-4967 116 32 , , PUNCT fumecheng-4967 116 33 one one PRON fumecheng-4967 116 34 can can AUX fumecheng-4967 116 35 ignore ignore VERB fumecheng-4967 116 36 the the DET fumecheng-4967 116 37 evolution evolution NOUN fumecheng-4967 116 38 of of ADP fumecheng-4967 116 39 the the DET fumecheng-4967 116 40 density density NOUN fumecheng-4967 116 41 at at ADV fumecheng-4967 116 42 all all ADV fumecheng-4967 116 43 and and CCONJ fumecheng-4967 116 44 treat treat VERB fumecheng-4967 116 45 its its PRON fumecheng-4967 116 46 intermediate intermediate ADJ fumecheng-4967 116 47 distribution distribution NOUN fumecheng-4967 116 48 as as ADP fumecheng-4967 116 49 practically practically ADV fumecheng-4967 116 50 static static ADJ fumecheng-4967 116 51 . . PUNCT fumecheng-4967 117 1 it it PRON fumecheng-4967 117 2 has have VERB fumecheng-4967 117 3 some some DET fumecheng-4967 117 4 ideological ideological ADJ fumecheng-4967 117 5 analogy analogy NOUN fumecheng-4967 117 6 with with ADP fumecheng-4967 117 7 the the DET fumecheng-4967 117 8 galaxies galaxy NOUN fumecheng-4967 117 9 developing develop VERB fumecheng-4967 117 10 for for ADP fumecheng-4967 117 11 billions billion NOUN fumecheng-4967 117 12 of of ADP fumecheng-4967 117 13 years year NOUN fumecheng-4967 117 14 . . PUNCT fumecheng-4967 118 1 it it PRON fumecheng-4967 118 2 is be AUX fumecheng-4967 118 3 much much ADV fumecheng-4967 118 4 longer long ADJ fumecheng-4967 118 5 than than ADP fumecheng-4967 118 6 our our PRON fumecheng-4967 118 7 life life NOUN fumecheng-4967 118 8 and and CCONJ fumecheng-4967 118 9 majority majority NOUN fumecheng-4967 118 10 of of ADP fumecheng-4967 118 11 the the DET fumecheng-4967 118 12 processes process NOUN fumecheng-4967 118 13 on on ADP fumecheng-4967 118 14 our our PRON fumecheng-4967 118 15 planet planet NOUN fumecheng-4967 118 16 . . PUNCT fumecheng-4967 119 1 so so ADV fumecheng-4967 119 2 , , PUNCT fumecheng-4967 119 3 the the DET fumecheng-4967 119 4 galactic galactic ADJ fumecheng-4967 119 5 patterns pattern NOUN fumecheng-4967 119 6 can can AUX fumecheng-4967 119 7 be be AUX fumecheng-4967 119 8 treated treat VERB fumecheng-4967 119 9 as as ADP fumecheng-4967 119 10 practically practically ADV fumecheng-4967 119 11 static static ADJ fumecheng-4967 119 12 ones one NOUN fumecheng-4967 119 13 . . PUNCT fumecheng-4967 120 1 fig fig NOUN fumecheng-4967 120 2 . . PUNCT fumecheng-4967 121 1 2 2 NUM fumecheng-4967 121 2 typical typical ADJ fumecheng-4967 121 3 intermediate intermediate ADJ fumecheng-4967 121 4 pattern pattern NOUN fumecheng-4967 121 5 appearing appear VERB fumecheng-4967 121 6 as as ADP fumecheng-4967 121 7 a a DET fumecheng-4967 121 8 result result NOUN fumecheng-4967 121 9 of of ADP fumecheng-4967 121 10 solution solution NOUN fumecheng-4967 121 11 of of ADP fumecheng-4967 121 12 eq eq PROPN fumecheng-4967 121 13 . . PUNCT fumecheng-4967 122 1 ( ( PUNCT fumecheng-4967 122 2 8) 8) NUM fumecheng-4967 122 3 however however ADV fumecheng-4967 122 4 , , PUNCT fumecheng-4967 122 5 in in ADP fumecheng-4967 122 6 many many ADJ fumecheng-4967 122 7 cases case NOUN fumecheng-4967 122 8 the the DET fumecheng-4967 122 9 kinetic kinetic ADJ fumecheng-4967 122 10 process process NOUN fumecheng-4967 122 11 may may AUX fumecheng-4967 122 12 be be AUX fumecheng-4967 122 13 really really ADV fumecheng-4967 122 14 stopped stop VERB fumecheng-4967 122 15 by by ADP fumecheng-4967 122 16 some some DET fumecheng-4967 122 17 natural natural ADJ fumecheng-4967 122 18 reasons reason NOUN fumecheng-4967 122 19 at at ADP fumecheng-4967 122 20 an an DET fumecheng-4967 122 21 intermediate intermediate ADJ fumecheng-4967 122 22 stage stage NOUN fumecheng-4967 122 23 . . PUNCT fumecheng-4967 123 1 normally normally ADV fumecheng-4967 123 2 it it PRON fumecheng-4967 123 3 happens happen VERB fumecheng-4967 123 4 when when SCONJ fumecheng-4967 123 5 the the DET fumecheng-4967 123 6 system system NOUN fumecheng-4967 123 7 is be AUX fumecheng-4967 123 8 actually actually ADV fumecheng-4967 123 9 open open ADJ fumecheng-4967 123 10 to to ADP fumecheng-4967 123 11 the the DET fumecheng-4967 123 12 external external ADJ fumecheng-4967 123 13 influences influence NOUN fumecheng-4967 123 14 or or CCONJ fumecheng-4967 123 15 consists consist VERB fumecheng-4967 123 16 of of ADP fumecheng-4967 123 17 a a DET fumecheng-4967 123 18 number number NOUN fumecheng-4967 123 19 of of ADP fumecheng-4967 123 20 interacting interact VERB fumecheng-4967 123 21 subsystems subsystem NOUN fumecheng-4967 123 22 . . PUNCT fumecheng-4967 124 1 in in ADP fumecheng-4967 124 2 the the DET fumecheng-4967 124 3 first first ADJ fumecheng-4967 124 4 case case NOUN fumecheng-4967 124 5 , , PUNCT fumecheng-4967 124 6 external external ADJ fumecheng-4967 124 7 forces force NOUN fumecheng-4967 124 8 can can AUX fumecheng-4967 124 9 cause cause VERB fumecheng-4967 124 10 change change NOUN fumecheng-4967 124 11 of of ADP fumecheng-4967 124 12 the the DET fumecheng-4967 124 13 coefficients coefficient NOUN fumecheng-4967 124 14 of of ADP fumecheng-4967 124 15 energy energy NOUN fumecheng-4967 124 16 expansion expansion NOUN fumecheng-4967 124 17 eq eq ADJ fumecheng-4967 124 18 . . PUNCT fumecheng-4967 125 1 ( ( PUNCT fumecheng-4967 125 2 4 4 X fumecheng-4967 125 3 ) ) PUNCT fumecheng-4967 125 4 already already ADV fumecheng-4967 125 5 in in ADP fumecheng-4967 125 6 the the DET fumecheng-4967 125 7 course course NOUN fumecheng-4967 125 8 of of ADP fumecheng-4967 125 9 the the DET fumecheng-4967 125 10 density density NOUN fumecheng-4967 125 11 evolution evolution NOUN fumecheng-4967 125 12 . . PUNCT fumecheng-4967 126 1 as as ADP fumecheng-4967 126 2 result result NOUN fumecheng-4967 126 3 , , PUNCT fumecheng-4967 126 4 the the DET fumecheng-4967 126 5 system system NOUN fumecheng-4967 126 6 starts start VERB fumecheng-4967 126 7 its its PRON fumecheng-4967 126 8 development development NOUN fumecheng-4967 126 9 to to ADP fumecheng-4967 126 10 some some DET fumecheng-4967 126 11 equilibrium equilibrium NOUN fumecheng-4967 126 12 at at ADP fumecheng-4967 126 13 the the DET fumecheng-4967 126 14 given give VERB fumecheng-4967 126 15 form form NOUN fumecheng-4967 126 16 of of ADP fumecheng-4967 126 17 f(ρ f(ρ NOUN fumecheng-4967 126 18 ) ) PUNCT fumecheng-4967 126 19 and and CCONJ fumecheng-4967 126 20 finishes finish VERB fumecheng-4967 126 21 in in ADP fumecheng-4967 126 22 absolutely absolutely ADV fumecheng-4967 126 23 another another DET fumecheng-4967 126 24 equilibrium equilibrium NOUN fumecheng-4967 126 25 corresponding correspond VERB fumecheng-4967 126 26 to to ADP fumecheng-4967 126 27 modified modify VERB fumecheng-4967 126 28 functional functional ADJ fumecheng-4967 126 29 f(ρ f(ρ NOUN fumecheng-4967 126 30 ) ) PUNCT fumecheng-4967 126 31 . . PUNCT fumecheng-4967 127 1 in in ADP fumecheng-4967 127 2 the the DET fumecheng-4967 127 3 second second ADJ fumecheng-4967 127 4 case case NOUN fumecheng-4967 127 5 , , PUNCT fumecheng-4967 127 6 alternating alternate VERB fumecheng-4967 127 7 interactions interaction NOUN fumecheng-4967 127 8 between between ADP fumecheng-4967 127 9 the the DET fumecheng-4967 127 10 subsystems subsystem NOUN fumecheng-4967 127 11 can can AUX fumecheng-4967 127 12 lead lead VERB fumecheng-4967 127 13 to to ADP fumecheng-4967 127 14 the the DET fumecheng-4967 127 15 growth growth NOUN fumecheng-4967 127 16 of of ADP fumecheng-4967 127 17 different different ADJ fumecheng-4967 127 18 densities density NOUN fumecheng-4967 127 19 in in ADP fumecheng-4967 127 20 different different ADJ fumecheng-4967 127 21 domains domain NOUN fumecheng-4967 127 22 of of ADP fumecheng-4967 127 23 the the DET fumecheng-4967 127 24 space space NOUN fumecheng-4967 127 25 . . PUNCT fumecheng-4967 128 1 when when SCONJ fumecheng-4967 128 2 such such ADJ fumecheng-4967 128 3 growing grow VERB fumecheng-4967 128 4 domains domain NOUN fumecheng-4967 128 5 meet meet VERB fumecheng-4967 128 6 each each DET fumecheng-4967 128 7 other other ADJ fumecheng-4967 128 8 , , PUNCT fumecheng-4967 128 9 they they PRON fumecheng-4967 128 10 mutually mutually ADV fumecheng-4967 128 11 block block VERB fumecheng-4967 128 12 further further ADJ fumecheng-4967 128 13 expansion expansion NOUN fumecheng-4967 128 14 and and CCONJ fumecheng-4967 128 15 build build VERB fumecheng-4967 128 16 a a DET fumecheng-4967 128 17 static static NOUN fumecheng-4967 128 18 ( ( PUNCT fumecheng-4967 128 19 or or CCONJ fumecheng-4967 128 20 maybe maybe ADV fumecheng-4967 128 21 very very ADV fumecheng-4967 128 22 slowly slowly ADV fumecheng-4967 128 23 shifting shift VERB fumecheng-4967 128 24 ) ) PUNCT fumecheng-4967 128 25 domain domain NOUN fumecheng-4967 128 26 wall wall NOUN fumecheng-4967 128 27 between between ADP fumecheng-4967 128 28 them they PRON fumecheng-4967 128 29 . . PUNCT fumecheng-4967 129 1 such such ADJ fumecheng-4967 129 2 blocking blocking NOUN fumecheng-4967 129 3 leads lead VERB fumecheng-4967 129 4 to to ADP fumecheng-4967 129 5 the the DET fumecheng-4967 129 6 fixation fixation NOUN fumecheng-4967 129 7 of of ADP fumecheng-4967 129 8 the the DET fumecheng-4967 129 9 domain domain NOUN fumecheng-4967 129 10 structure structure NOUN fumecheng-4967 129 11 and and CCONJ fumecheng-4967 129 12 on on ADP fumecheng-4967 129 13 large large ADJ fumecheng-4967 129 14 scale scale NOUN fumecheng-4967 129 15 forms form VERB fumecheng-4967 129 16 a a DET fumecheng-4967 129 17 pattern pattern NOUN fumecheng-4967 129 18 including include VERB fumecheng-4967 129 19 many many ADJ fumecheng-4967 129 20 domains domain NOUN fumecheng-4967 129 21 of of ADP fumecheng-4967 129 22 different different ADJ fumecheng-4967 129 23 sizes size NOUN fumecheng-4967 129 24 . . PUNCT fumecheng-4967 130 1 the the DET fumecheng-4967 130 2 simplest simple ADJ fumecheng-4967 130 3 way way NOUN fumecheng-4967 130 4 of of ADP fumecheng-4967 130 5 obtaining obtain VERB fumecheng-4967 130 6 such such ADJ fumecheng-4967 130 7 domain domain NOUN fumecheng-4967 130 8 structure structure NOUN fumecheng-4967 130 9 is be AUX fumecheng-4967 130 10 to to PART fumecheng-4967 130 11 use use VERB fumecheng-4967 130 12 expansion expansion NOUN fumecheng-4967 130 13 f(ρ f(ρ NOUN fumecheng-4967 130 14 ) ) PUNCT fumecheng-4967 130 15 with with ADP fumecheng-4967 130 16 even even ADV fumecheng-4967 130 17 terms term NOUN fumecheng-4967 130 18 only only ADV fumecheng-4967 130 19 : : PUNCT fumecheng-4967 130 20 2 2 NUM fumecheng-4967 130 21 2 2 NUM fumecheng-4967 130 22 4 4 NUM fumecheng-4967 130 23 6 6 NUM fumecheng-4967 130 24 2 2 NUM fumecheng-4967 130 25 [ [ PUNCT fumecheng-4967 130 26 ( ( PUNCT fumecheng-4967 130 27 ) ) PUNCT fumecheng-4967 130 28 ] ] PUNCT fumecheng-4967 131 1 [ [ PUNCT fumecheng-4967 131 2 ( ( PUNCT fumecheng-4967 131 3 ( ( PUNCT fumecheng-4967 131 4 ) ) PUNCT fumecheng-4967 131 5 ) ) PUNCT fumecheng-4967 131 6 ( ( PUNCT fumecheng-4967 131 7 ) ) PUNCT fumecheng-4967 131 8 ( ( PUNCT fumecheng-4967 131 9 ) ) PUNCT fumecheng-4967 131 10 ( ( PUNCT fumecheng-4967 131 11 ) ) PUNCT fumecheng-4967 131 12 ... ... PUNCT fumecheng-4967 131 13 ] ] PUNCT fumecheng-4967 131 14 2 2 NUM fumecheng-4967 131 15 2 2 NUM fumecheng-4967 131 16 4 4 NUM fumecheng-4967 131 17 6 6 NUM fumecheng-4967 131 18 [ [ PUNCT fumecheng-4967 131 19 ( ( PUNCT fumecheng-4967 131 20 ( ( PUNCT fumecheng-4967 131 21 ) ) PUNCT fumecheng-4967 131 22 ) ) PUNCT fumecheng-4967 131 23 ( ( PUNCT fumecheng-4967 131 24 ( ( PUNCT fumecheng-4967 131 25 ) ) PUNCT fumecheng-4967 131 26 ) ) PUNCT fumecheng-4967 131 27 ] ] PUNCT fumecheng-4967 132 1 2 2 NUM fumecheng-4967 132 2 c c NOUN fumecheng-4967 132 3 g g NOUN fumecheng-4967 132 4 u u X fumecheng-4967 132 5 x x X fumecheng-4967 132 6 dx dx PROPN fumecheng-4967 132 7 x x PUNCT fumecheng-4967 132 8 x x PUNCT fumecheng-4967 132 9 x x PUNCT fumecheng-4967 132 10 x x PUNCT fumecheng-4967 132 11 c c NOUN fumecheng-4967 132 12 dx dx PROPN fumecheng-4967 133 1 x x X fumecheng-4967 133 2 f f NOUN fumecheng-4967 133 3 x x SYM fumecheng-4967 133 4   PROPN fumecheng-4967 133 5   PUNCT fumecheng-4967 133 6   NOUN fumecheng-4967 133 7   PUNCT fumecheng-4967 133 8   PRON fumecheng-4967 133 9   PUNCT fumecheng-4967 133 10   PUNCT fumecheng-4967 133 11   PROPN fumecheng-4967 133 12   PROPN fumecheng-4967 133 13   NOUN fumecheng-4967 133 14   VERB fumecheng-4967 133 15   PUNCT fumecheng-4967 133 16   PUNCT fumecheng-4967 133 17   PROPN fumecheng-4967 133 18   ADV fumecheng-4967 133 19   ADP fumecheng-4967 133 20   X fumecheng-4967 133 21   X fumecheng-4967 133 22   X fumecheng-4967 133 23   X fumecheng-4967 133 24   X fumecheng-4967 133 25 ( ( PUNCT fumecheng-4967 133 26 9 9 X fumecheng-4967 133 27 ) ) PUNCT fumecheng-4967 133 28 corresponding correspond VERB fumecheng-4967 133 29 equation equation NOUN fumecheng-4967 133 30 of of ADP fumecheng-4967 133 31 motion motion NOUN fumecheng-4967 133 32 with with ADP fumecheng-4967 133 33 the the DET fumecheng-4967 133 34 functional functional ADJ fumecheng-4967 133 35 eq eq X fumecheng-4967 133 36 . . PUNCT fumecheng-4967 134 1 ( ( PUNCT fumecheng-4967 134 2 9 9 X fumecheng-4967 134 3 ) ) PUNCT fumecheng-4967 134 4 leads lead VERB fumecheng-4967 134 5 to to ADP fumecheng-4967 134 6 the the DET fumecheng-4967 134 7 typical typical ADJ fumecheng-4967 134 8 domain domain NOUN fumecheng-4967 134 9 structure structure NOUN fumecheng-4967 134 10 shown show VERB fumecheng-4967 134 11 in in ADP fumecheng-4967 134 12 fig fig NOUN fumecheng-4967 134 13 . . PUNCT fumecheng-4967 135 1 2 2 X fumecheng-4967 135 2 . . X fumecheng-4967 135 3 methods method NOUN fumecheng-4967 135 4 of of ADP fumecheng-4967 135 5 the the DET fumecheng-4967 135 6 pattern pattern NOUN fumecheng-4967 135 7 formation formation NOUN fumecheng-4967 135 8 in in ADP fumecheng-4967 135 9 numerical numerical ADJ fumecheng-4967 135 10 modeling modeling NOUN fumecheng-4967 135 11 of of ADP fumecheng-4967 135 12 biological biological ADJ fumecheng-4967 135 13 problems problem NOUN fumecheng-4967 135 14 223 223 NUM fumecheng-4967 135 15 fig fig NOUN fumecheng-4967 135 16 . . PUNCT fumecheng-4967 136 1 3 3 NUM fumecheng-4967 136 2 formation formation NOUN fumecheng-4967 136 3 of of ADP fumecheng-4967 136 4 the the DET fumecheng-4967 136 5 domain domain NOUN fumecheng-4967 136 6 structure structure NOUN fumecheng-4967 136 7 in in ADP fumecheng-4967 136 8 the the DET fumecheng-4967 136 9 kinetics kinetic NOUN fumecheng-4967 136 10 . . PUNCT fumecheng-4967 137 1 two two NUM fumecheng-4967 137 2 different different ADJ fumecheng-4967 137 3 kinds kind NOUN fumecheng-4967 137 4 of of ADP fumecheng-4967 137 5 domains domain NOUN fumecheng-4967 137 6 are be AUX fumecheng-4967 137 7 shown show VERB fumecheng-4967 137 8 by by ADP fumecheng-4967 137 9 red red ADJ fumecheng-4967 137 10 and and CCONJ fumecheng-4967 137 11 blue blue ADJ fumecheng-4967 137 12 colors color NOUN fumecheng-4967 137 13 , , PUNCT fumecheng-4967 137 14 respectively respectively ADV fumecheng-4967 137 15 3 3 NUM fumecheng-4967 137 16 . . PUNCT fumecheng-4967 137 17 automatic automatic ADJ fumecheng-4967 137 18 blocking blocking NOUN fumecheng-4967 137 19 of of ADP fumecheng-4967 137 20 the the DET fumecheng-4967 137 21 nucleation nucleation NOUN fumecheng-4967 137 22 and and CCONJ fumecheng-4967 137 23 freezing freezing NOUN fumecheng-4967 137 24 of of ADP fumecheng-4967 137 25 the the DET fumecheng-4967 137 26 process process NOUN fumecheng-4967 137 27 in in ADP fumecheng-4967 137 28 both both DET fumecheng-4967 137 29 previous previous ADJ fumecheng-4967 137 30 cases case NOUN fumecheng-4967 137 31 , , PUNCT fumecheng-4967 137 32 telling tell VERB fumecheng-4967 137 33 about about ADP fumecheng-4967 137 34 almost almost ADV fumecheng-4967 137 35 frozen frozen ADJ fumecheng-4967 137 36 kinetics kinetic NOUN fumecheng-4967 137 37 , , PUNCT fumecheng-4967 137 38 we we PRON fumecheng-4967 137 39 have have AUX fumecheng-4967 137 40 supposed suppose VERB fumecheng-4967 137 41 that that SCONJ fumecheng-4967 137 42 it it PRON fumecheng-4967 137 43 this this DET fumecheng-4967 137 44 process process NOUN fumecheng-4967 137 45 is be AUX fumecheng-4967 137 46 simply simply ADV fumecheng-4967 137 47 much much ADV fumecheng-4967 137 48 slower slow ADJ fumecheng-4967 137 49 than than ADP fumecheng-4967 137 50 other other ADJ fumecheng-4967 137 51 ones one NOUN fumecheng-4967 137 52 in in ADP fumecheng-4967 137 53 a a DET fumecheng-4967 137 54 particular particular ADJ fumecheng-4967 137 55 model model NOUN fumecheng-4967 137 56 . . PUNCT fumecheng-4967 138 1 however however ADV fumecheng-4967 138 2 , , PUNCT fumecheng-4967 138 3 it it PRON fumecheng-4967 138 4 was be AUX fumecheng-4967 138 5 shown show VERB fumecheng-4967 138 6 more more ADJ fumecheng-4967 138 7 than than ADP fumecheng-4967 138 8 20 20 NUM fumecheng-4967 138 9 years year NOUN fumecheng-4967 138 10 ago ago ADV fumecheng-4967 138 11 that that SCONJ fumecheng-4967 138 12 since since SCONJ fumecheng-4967 138 13 the the DET fumecheng-4967 138 14 formation formation NOUN fumecheng-4967 138 15 of of ADP fumecheng-4967 138 16 new new ADJ fumecheng-4967 138 17 phase phase NOUN fumecheng-4967 138 18 nuclei nucleus NOUN fumecheng-4967 138 19 includes include VERB fumecheng-4967 138 20 processes process NOUN fumecheng-4967 138 21 that that PRON fumecheng-4967 138 22 prevent prevent VERB fumecheng-4967 138 23 their their PRON fumecheng-4967 138 24 appearance appearance NOUN fumecheng-4967 138 25 and and CCONJ fumecheng-4967 138 26 growth growth NOUN fumecheng-4967 138 27 in in ADP fumecheng-4967 138 28 other other ADJ fumecheng-4967 138 29 regions region NOUN fumecheng-4967 138 30 in in ADP fumecheng-4967 138 31 space space NOUN fumecheng-4967 138 32 , , PUNCT fumecheng-4967 138 33 it it PRON fumecheng-4967 138 34 should should AUX fumecheng-4967 138 35 result result VERB fumecheng-4967 138 36 in in ADP fumecheng-4967 138 37 autostabilization autostabilization NOUN fumecheng-4967 138 38 of of ADP fumecheng-4967 138 39 an an DET fumecheng-4967 138 40 intermediate intermediate ADJ fumecheng-4967 138 41 mixed mixed ADJ fumecheng-4967 138 42 state state NOUN fumecheng-4967 138 43 . . PUNCT fumecheng-4967 139 1 one one PRON fumecheng-4967 139 2 can can AUX fumecheng-4967 139 3 call call VERB fumecheng-4967 139 4 it it PRON fumecheng-4967 139 5 “ " PUNCT fumecheng-4967 139 6 automatic automatic ADJ fumecheng-4967 139 7 blocking blocking NOUN fumecheng-4967 139 8 of of ADP fumecheng-4967 139 9 the the DET fumecheng-4967 139 10 nucleation nucleation NOUN fumecheng-4967 139 11 ” " PUNCT fumecheng-4967 140 1 [ [ X fumecheng-4967 140 2 7 7 NUM fumecheng-4967 140 3 ] ] PUNCT fumecheng-4967 140 4 . . PUNCT fumecheng-4967 141 1 normally normally ADV fumecheng-4967 141 2 it it PRON fumecheng-4967 141 3 is be AUX fumecheng-4967 141 4 caused cause VERB fumecheng-4967 141 5 by by ADP fumecheng-4967 141 6 the the DET fumecheng-4967 141 7 nonlocal nonlocal ADJ fumecheng-4967 141 8 ( ( PUNCT fumecheng-4967 141 9 long long ADJ fumecheng-4967 141 10 - - PUNCT fumecheng-4967 141 11 range range NOUN fumecheng-4967 141 12 ) ) PUNCT fumecheng-4967 141 13 interactions interaction NOUN fumecheng-4967 141 14 which which PRON fumecheng-4967 141 15 are be AUX fumecheng-4967 141 16 caused cause VERB fumecheng-4967 141 17 in in ADP fumecheng-4967 141 18 an an DET fumecheng-4967 141 19 ordered order VERB fumecheng-4967 141 20 process process NOUN fumecheng-4967 141 21 by by ADP fumecheng-4967 141 22 itself itself PRON fumecheng-4967 141 23 . . PUNCT fumecheng-4967 142 1 from from ADP fumecheng-4967 142 2 the the DET fumecheng-4967 142 3 introduction introduction NOUN fumecheng-4967 142 4 , , PUNCT fumecheng-4967 142 5 we we PRON fumecheng-4967 142 6 remember remember VERB fumecheng-4967 142 7 that that SCONJ fumecheng-4967 142 8 numerical numerical ADJ fumecheng-4967 142 9 modeling modeling NOUN fumecheng-4967 142 10 does do AUX fumecheng-4967 142 11 not not PART fumecheng-4967 142 12 like like VERB fumecheng-4967 142 13 nonlocal nonlocal ADJ fumecheng-4967 142 14 interactions interaction NOUN fumecheng-4967 142 15 because because SCONJ fumecheng-4967 142 16 of of ADP fumecheng-4967 142 17 an an DET fumecheng-4967 142 18 extreme extreme ADJ fumecheng-4967 142 19 time time NOUN fumecheng-4967 142 20 consumption consumption NOUN fumecheng-4967 142 21 required require VERB fumecheng-4967 142 22 for for ADP fumecheng-4967 142 23 these these DET fumecheng-4967 142 24 calculations calculation NOUN fumecheng-4967 142 25 . . PUNCT fumecheng-4967 143 1 however however ADV fumecheng-4967 143 2 , , PUNCT fumecheng-4967 143 3 it it PRON fumecheng-4967 143 4 is be AUX fumecheng-4967 143 5 possible possible ADJ fumecheng-4967 143 6 to to PART fumecheng-4967 143 7 show show VERB fumecheng-4967 143 8 that that SCONJ fumecheng-4967 143 9 the the DET fumecheng-4967 143 10 effect effect NOUN fumecheng-4967 143 11 of of ADP fumecheng-4967 143 12 blocking block VERB fumecheng-4967 143 13 long long ADJ fumecheng-4967 143 14 - - PUNCT fumecheng-4967 143 15 range range NOUN fumecheng-4967 143 16 interaction interaction NOUN fumecheng-4967 143 17 can can AUX fumecheng-4967 143 18 be be AUX fumecheng-4967 143 19 approximately approximately ADV fumecheng-4967 143 20 included include VERB fumecheng-4967 143 21 by by ADP fumecheng-4967 143 22 some some DET fumecheng-4967 143 23 local local ADJ fumecheng-4967 143 24 additions addition NOUN fumecheng-4967 143 25 to to ADP fumecheng-4967 143 26 the the DET fumecheng-4967 143 27 above above ADJ fumecheng-4967 143 28 models model NOUN fumecheng-4967 143 29 . . PUNCT fumecheng-4967 144 1 various various ADJ fumecheng-4967 144 2 mechanisms mechanism NOUN fumecheng-4967 144 3 for for ADP fumecheng-4967 144 4 the the DET fumecheng-4967 144 5 formation formation NOUN fumecheng-4967 144 6 of of ADP fumecheng-4967 144 7 an an DET fumecheng-4967 144 8 effective effective ADJ fumecheng-4967 144 9 long long ADJ fumecheng-4967 144 10 - - PUNCT fumecheng-4967 144 11 range range NOUN fumecheng-4967 144 12 interaction interaction NOUN fumecheng-4967 144 13 in in ADP fumecheng-4967 144 14 such such ADJ fumecheng-4967 144 15 systems system NOUN fumecheng-4967 144 16 can can AUX fumecheng-4967 144 17 be be AUX fumecheng-4967 144 18 analyzed analyze VERB fumecheng-4967 144 19 . . PUNCT fumecheng-4967 145 1 here here ADV fumecheng-4967 145 2 we we PRON fumecheng-4967 145 3 will will AUX fumecheng-4967 145 4 mention mention VERB fumecheng-4967 145 5 only only ADV fumecheng-4967 145 6 a a DET fumecheng-4967 145 7 couple couple NOUN fumecheng-4967 145 8 of of ADP fumecheng-4967 145 9 them they PRON fumecheng-4967 145 10 . . PUNCT fumecheng-4967 146 1 normally normally ADV fumecheng-4967 146 2 , , PUNCT fumecheng-4967 146 3 formation formation NOUN fumecheng-4967 146 4 of of ADP fumecheng-4967 146 5 the the DET fumecheng-4967 146 6 substance substance NOUN fumecheng-4967 146 7 ( ( PUNCT fumecheng-4967 146 8 and and CCONJ fumecheng-4967 146 9 the the DET fumecheng-4967 146 10 surface surface NOUN fumecheng-4967 146 11 , , PUNCT fumecheng-4967 146 12 which which PRON fumecheng-4967 146 13 is be AUX fumecheng-4967 146 14 needed need VERB fumecheng-4967 146 15 here here ADV fumecheng-4967 146 16 ) ) PUNCT fumecheng-4967 146 17 includes include VERB fumecheng-4967 146 18 the the DET fumecheng-4967 146 19 reaction reaction NOUN fumecheng-4967 146 20 of of ADP fumecheng-4967 146 21 a a DET fumecheng-4967 146 22 crystal crystal NOUN fumecheng-4967 146 23 lattice lattice NOUN fumecheng-4967 146 24 ( ( PUNCT fumecheng-4967 146 25 striction striction NOUN fumecheng-4967 146 26 ) ) PUNCT fumecheng-4967 146 27 to to ADP fumecheng-4967 146 28 a a DET fumecheng-4967 146 29 change change NOUN fumecheng-4967 146 30 in in ADP fumecheng-4967 146 31 magnitude magnitude NOUN fumecheng-4967 146 32 of of ADP fumecheng-4967 146 33 order order NOUN fumecheng-4967 146 34 parameter parameter ADP fumecheng-4967 146 35 ρ(x ρ(x PROPN fumecheng-4967 146 36 , , PUNCT fumecheng-4967 146 37 t t PROPN fumecheng-4967 146 38 ) ) PUNCT fumecheng-4967 146 39 during during ADP fumecheng-4967 146 40 a a DET fumecheng-4967 146 41 phase phase NOUN fumecheng-4967 146 42 transition transition NOUN fumecheng-4967 146 43 . . PUNCT fumecheng-4967 147 1 one one PRON fumecheng-4967 147 2 can can AUX fumecheng-4967 147 3 show show VERB fumecheng-4967 147 4 that that SCONJ fumecheng-4967 147 5 in in ADP fumecheng-4967 147 6 a a DET fumecheng-4967 147 7 relatively relatively ADV fumecheng-4967 147 8 simple simple ADJ fumecheng-4967 147 9 case case NOUN fumecheng-4967 147 10 of of ADP fumecheng-4967 147 11 an an DET fumecheng-4967 147 12 isotropic isotropic ADJ fumecheng-4967 147 13 medium medium ADJ fumecheng-4967 147 14 and and CCONJ fumecheng-4967 147 15 quadratic quadratic ADJ fumecheng-4967 147 16 striction striction NOUN fumecheng-4967 147 17 , , PUNCT fumecheng-4967 147 18 the the DET fumecheng-4967 147 19 local local ADJ fumecheng-4967 147 20 energy energy NOUN fumecheng-4967 147 21 functional functional NOUN fumecheng-4967 147 22 of of ADP fumecheng-4967 147 23 the the DET fumecheng-4967 147 24 free free ADJ fumecheng-4967 147 25 energy energy NOUN fumecheng-4967 147 26 is be AUX fumecheng-4967 147 27 modified modify VERB fumecheng-4967 147 28 in in ADP fumecheng-4967 147 29 the the DET fumecheng-4967 147 30 following follow VERB fumecheng-4967 147 31 manner manner NOUN fumecheng-4967 147 32 [ [ X fumecheng-4967 147 33 3 3 NUM fumecheng-4967 147 34 ] ] SYM fumecheng-4967 147 35 : : PUNCT fumecheng-4967 147 36 2 2 NUM fumecheng-4967 147 37 2 2 NUM fumecheng-4967 147 38 2 2 NUM fumecheng-4967 147 39 2 2 NUM fumecheng-4967 147 40 2 2 NUM fumecheng-4967 147 41 1 1 NUM fumecheng-4967 147 42 1 1 NUM fumecheng-4967 147 43 , , PUNCT fumecheng-4967 147 44 [ [ PUNCT fumecheng-4967 147 45 ( ( PUNCT fumecheng-4967 147 46 ) ) PUNCT fumecheng-4967 147 47 ] ] PUNCT fumecheng-4967 148 1 [ [ PUNCT fumecheng-4967 148 2 ( ( PUNCT fumecheng-4967 148 3 ( ( PUNCT fumecheng-4967 148 4 ) ) PUNCT fumecheng-4967 148 5 ) ) PUNCT fumecheng-4967 148 6 ( ( PUNCT fumecheng-4967 148 7 ( ( PUNCT fumecheng-4967 148 8 ) ) PUNCT fumecheng-4967 148 9 ) ) PUNCT fumecheng-4967 148 10 2 2 NUM fumecheng-4967 148 11 1 1 NUM fumecheng-4967 148 12 ( ( PUNCT fumecheng-4967 148 13 ( ( PUNCT fumecheng-4967 148 14 ) ) PUNCT fumecheng-4967 148 15 ( ( PUNCT fumecheng-4967 148 16 ) ) PUNCT fumecheng-4967 148 17 ) ) PUNCT fumecheng-4967 148 18 ] ] PUNCT fumecheng-4967 148 19 2 2 NUM fumecheng-4967 148 20 3 3 NUM fumecheng-4967 148 21 u u PROPN fumecheng-4967 148 22 ii ii PROPN fumecheng-4967 148 23 ii ii PROPN fumecheng-4967 148 24 k k PROPN fumecheng-4967 148 25 k k X fumecheng-4967 148 26 ll ll PROPN fumecheng-4967 148 27 l l PROPN fumecheng-4967 148 28 k k NOUN fumecheng-4967 148 29 c c NOUN fumecheng-4967 148 30 x x X fumecheng-4967 148 31 dx dx PROPN fumecheng-4967 148 32 x x X fumecheng-4967 148 33 f f PROPN fumecheng-4967 148 34 x x X fumecheng-4967 149 1 k k NOUN fumecheng-4967 149 2 g g PROPN fumecheng-4967 149 3 x x SYM fumecheng-4967 149 4 u u VERB fumecheng-4967 149 5 u u X fumecheng-4967 149 6 u u NOUN fumecheng-4967 149 7 u u NOUN fumecheng-4967 149 8   PROPN fumecheng-4967 149 9   PROPN fumecheng-4967 149 10   PROPN fumecheng-4967 149 11   ADV fumecheng-4967 149 12   VERB fumecheng-4967 149 13   PUNCT fumecheng-4967 149 14   PUNCT fumecheng-4967 149 15   X fumecheng-4967 149 16   PUNCT fumecheng-4967 149 17   X fumecheng-4967 149 18   ADP fumecheng-4967 149 19   ADP fumecheng-4967 149 20   X fumecheng-4967 149 21   ADP fumecheng-4967 149 22   NOUN fumecheng-4967 149 23   NUM fumecheng-4967 149 24 ( ( PUNCT fumecheng-4967 149 25 10 10 NUM fumecheng-4967 149 26 ) ) PUNCT fumecheng-4967 149 27 if if SCONJ fumecheng-4967 149 28 the the DET fumecheng-4967 149 29 lattice lattice NOUN fumecheng-4967 149 30 vibrations vibration NOUN fumecheng-4967 149 31 manage manage VERB fumecheng-4967 149 32 to to PART fumecheng-4967 149 33 follow follow VERB fumecheng-4967 149 34 the the DET fumecheng-4967 149 35 variations variation NOUN fumecheng-4967 149 36 of of ADP fumecheng-4967 149 37 ρ(x ρ(x PROPN fumecheng-4967 149 38 , , PUNCT fumecheng-4967 149 39 t t PROPN fumecheng-4967 149 40 ) ) PUNCT fumecheng-4967 149 41 , , PUNCT fumecheng-4967 149 42 we we PRON fumecheng-4967 149 43 can can AUX fumecheng-4967 149 44 utilize utilize VERB fumecheng-4967 149 45 condition condition NOUN fumecheng-4967 149 46 δφ[ρ δφ[ρ NOUN fumecheng-4967 149 47 , , PUNCT fumecheng-4967 149 48 u]/δuik=0 u]/δuik=0 NOUN fumecheng-4967 149 49 to to PART fumecheng-4967 149 50 eliminate eliminate VERB fumecheng-4967 149 51 variables variable NOUN fumecheng-4967 149 52 uik uik NOUN fumecheng-4967 149 53 and and CCONJ fumecheng-4967 149 54 get get VERB fumecheng-4967 149 55 , , PUNCT fumecheng-4967 149 56 after after ADP fumecheng-4967 149 57 some some DET fumecheng-4967 149 58 standard standard ADJ fumecheng-4967 149 59 mathematical mathematical ADJ fumecheng-4967 149 60 transformations transformation NOUN fumecheng-4967 149 61 , , PUNCT fumecheng-4967 149 62 an an DET fumecheng-4967 149 63 effective effective ADJ fumecheng-4967 149 64 functional functional NOUN fumecheng-4967 149 65 solely solely ADV fumecheng-4967 149 66 in in ADP fumecheng-4967 149 67 terms term NOUN fumecheng-4967 149 68 of of ADP fumecheng-4967 149 69 field field NOUN fumecheng-4967 149 70 ρ(x ρ(x PROPN fumecheng-4967 149 71 , , PUNCT fumecheng-4967 149 72 t t PROPN fumecheng-4967 149 73 ): ): PUNCT fumecheng-4967 149 74 2 2 NUM fumecheng-4967 149 75 2 2 NUM fumecheng-4967 149 76 2 2 NUM fumecheng-4967 149 77 [ [ PUNCT fumecheng-4967 149 78 ( ( PUNCT fumecheng-4967 149 79 ) ) PUNCT fumecheng-4967 149 80 ] ] PUNCT fumecheng-4967 150 1 [ [ PUNCT fumecheng-4967 150 2 ( ( PUNCT fumecheng-4967 150 3 ( ( PUNCT fumecheng-4967 150 4 ) ) PUNCT fumecheng-4967 150 5 ) ) PUNCT fumecheng-4967 150 6 ( ( PUNCT fumecheng-4967 150 7 ( ( PUNCT fumecheng-4967 150 8 ) ) PUNCT fumecheng-4967 150 9 ) ) PUNCT fumecheng-4967 150 10 ( ( PUNCT fumecheng-4967 150 11 ) ) PUNCT fumecheng-4967 150 12 ' ' PUNCT fumecheng-4967 150 13 ( ( PUNCT fumecheng-4967 150 14 ' ' NUM fumecheng-4967 150 15 ) ) PUNCT fumecheng-4967 150 16 ] ] PUNCT fumecheng-4967 150 17 2 2 NUM fumecheng-4967 150 18 2 2 NUM fumecheng-4967 150 19 c c NOUN fumecheng-4967 150 20 x x X fumecheng-4967 150 21 dx dx PROPN fumecheng-4967 150 22 c c NOUN fumecheng-4967 150 23 x x X fumecheng-4967 150 24 f f NOUN fumecheng-4967 150 25 x x X fumecheng-4967 150 26 x x X fumecheng-4967 150 27 dx dx PROPN fumecheng-4967 150 28 x x PROPN fumecheng-4967 150 29 v v PROPN fumecheng-4967 150 30   VERB fumecheng-4967 150 31   ADV fumecheng-4967 150 32   X fumecheng-4967 150 33   NOUN fumecheng-4967 150 34   ADP fumecheng-4967 150 35   ADP fumecheng-4967 150 36   PROPN fumecheng-4967 150 37   NOUN fumecheng-4967 150 38   X fumecheng-4967 150 39   NUM fumecheng-4967 150 40   PUNCT fumecheng-4967 150 41 ( ( PUNCT fumecheng-4967 150 42 11 11 NUM fumecheng-4967 150 43 ) ) PUNCT fumecheng-4967 150 44 here here ADV fumecheng-4967 150 45 ( ( PUNCT fumecheng-4967 150 46 ( ( PUNCT fumecheng-4967 150 47 ) ) PUNCT fumecheng-4967 150 48 ) ) PUNCT fumecheng-4967 151 1 f f PROPN fumecheng-4967 151 2 x x PROPN fumecheng-4967 151 3 is be AUX fumecheng-4967 151 4 the the DET fumecheng-4967 151 5 renormalized renormalized ADJ fumecheng-4967 151 6 local local ADJ fumecheng-4967 151 7 form form NOUN fumecheng-4967 151 8 of of ADP fumecheng-4967 151 9 f(ρ(x f(ρ(x NOUN fumecheng-4967 151 10 ) ) PUNCT fumecheng-4967 151 11 ) ) PUNCT fumecheng-4967 151 12 with with ADP fumecheng-4967 151 13 the the DET fumecheng-4967 151 14 same same ADJ fumecheng-4967 151 15 structure structure NOUN fumecheng-4967 151 16 as as ADP fumecheng-4967 151 17 the the DET fumecheng-4967 151 18 original original ADJ fumecheng-4967 151 19 function function NOUN fumecheng-4967 151 20 f(p f(p PROPN fumecheng-4967 151 21 ) ) PUNCT fumecheng-4967 151 22 ( ( PUNCT fumecheng-4967 151 23 we we PRON fumecheng-4967 151 24 shall shall AUX fumecheng-4967 151 25 henceforth henceforth ADV fumecheng-4967 151 26 omit omit VERB fumecheng-4967 151 27 the the DET fumecheng-4967 151 28 tilde tilde NOUN fumecheng-4967 151 29 ) ) PUNCT fumecheng-4967 151 30 , , PUNCT fumecheng-4967 151 31 and and CCONJ fumecheng-4967 151 32 constant constant ADJ fumecheng-4967 151 33 κ κ NOUN fumecheng-4967 151 34 is be AUX fumecheng-4967 151 35 defined define VERB fumecheng-4967 151 36 by by ADP fumecheng-4967 151 37 224 224 NUM fumecheng-4967 151 38 a.e a.e PROPN fumecheng-4967 151 39 . . PROPN fumecheng-4967 151 40 filippov filippov PROPN fumecheng-4967 151 41 , , PUNCT fumecheng-4967 151 42 s.n s.n PROPN fumecheng-4967 151 43 . . PROPN fumecheng-4967 151 44 gorb gorb PROPN fumecheng-4967 151 45 expression expression NOUN fumecheng-4967 151 46 2 2 NUM fumecheng-4967 151 47 1 1 NUM fumecheng-4967 151 48 1 1 NUM fumecheng-4967 151 49 ( ( PUNCT fumecheng-4967 151 50 / / SYM fumecheng-4967 151 51 2 2 NUM fumecheng-4967 151 52 ) ) PUNCT fumecheng-4967 152 1 [ [ X fumecheng-4967 152 2 ( ( PUNCT fumecheng-4967 152 3 / / SYM fumecheng-4967 152 4 2 2 NUM fumecheng-4967 152 5 2 2 NUM fumecheng-4967 152 6 /3 /3 NUM fumecheng-4967 152 7 ) ) PUNCT fumecheng-4967 153 1 ( ( PUNCT fumecheng-4967 153 2 / / SYM fumecheng-4967 153 3 2 2 NUM fumecheng-4967 153 4 2 2 NUM fumecheng-4967 153 5 /3 /3 NOUN fumecheng-4967 153 6 ) ) PUNCT fumecheng-4967 154 1 ] ] X fumecheng-4967 154 2 q q X fumecheng-4967 154 3 v v X fumecheng-4967 154 4 k k X fumecheng-4967 154 5 k k PROPN fumecheng-4967 154 6 p p PROPN fumecheng-4967 154 7   PROPN fumecheng-4967 154 8   PUNCT fumecheng-4967 154 9   PROPN fumecheng-4967 154 10   VERB fumecheng-4967 154 11   NOUN fumecheng-4967 154 12 . . PUNCT fumecheng-4967 155 1 constant constant ADJ fumecheng-4967 155 2 p p NOUN fumecheng-4967 155 3 is be AUX fumecheng-4967 155 4 determined determine VERB fumecheng-4967 155 5 by by ADP fumecheng-4967 155 6 the the DET fumecheng-4967 155 7 external external ADJ fumecheng-4967 155 8 pressure pressure NOUN fumecheng-4967 155 9 or or CCONJ fumecheng-4967 155 10 other other ADJ fumecheng-4967 155 11 constraints constraint NOUN fumecheng-4967 155 12 which which PRON fumecheng-4967 155 13 prevent prevent VERB fumecheng-4967 155 14 free free ADJ fumecheng-4967 155 15 expansion expansion NOUN fumecheng-4967 155 16 of of ADP fumecheng-4967 155 17 the the DET fumecheng-4967 155 18 crystal crystal NOUN fumecheng-4967 155 19 ( ( PUNCT fumecheng-4967 155 20 twins twin NOUN fumecheng-4967 155 21 , , PUNCT fumecheng-4967 155 22 defects defect NOUN fumecheng-4967 155 23 , , PUNCT fumecheng-4967 155 24 etc etc X fumecheng-4967 155 25 . . X fumecheng-4967 155 26 ) ) PUNCT fumecheng-4967 156 1 and and CCONJ fumecheng-4967 156 2 , , PUNCT fumecheng-4967 156 3 in in ADP fumecheng-4967 156 4 turn turn NOUN fumecheng-4967 156 5 , , PUNCT fumecheng-4967 156 6 fix fix VERB fumecheng-4967 156 7 the the DET fumecheng-4967 156 8 sign sign NOUN fumecheng-4967 156 9 of of ADP fumecheng-4967 156 10 κ κ NOUN fumecheng-4967 156 11 . . PUNCT fumecheng-4967 157 1 when when SCONJ fumecheng-4967 157 2 p p PROPN fumecheng-4967 157 3 > > X fumecheng-4967 157 4 μ μ PROPN fumecheng-4967 157 5 , , PUNCT fumecheng-4967 157 6 κ>0 κ>0 PROPN fumecheng-4967 157 7 ; ; PUNCT fumecheng-4967 157 8 otherwise otherwise ADV fumecheng-4967 157 9 κ<0 κ<0 NOUN fumecheng-4967 157 10 . . PUNCT fumecheng-4967 157 11 nonlocal nonlocal ADJ fumecheng-4967 157 12 construction construction NOUN fumecheng-4967 157 13 ∫dx[ρ(x ∫dx[ρ(x PROPN fumecheng-4967 157 14 ) ) PUNCT fumecheng-4967 157 15 2∫dx´[ρ(x 2∫dx´[ρ(x NUM fumecheng-4967 157 16 ´ ´ NOUN fumecheng-4967 157 17 ) ) PUNCT fumecheng-4967 157 18 2 2 NUM fumecheng-4967 157 19 ] ] PUNCT fumecheng-4967 157 20 in in ADP fumecheng-4967 157 21 functional functional ADJ fumecheng-4967 157 22 φ[ρ(x φ[ρ(x NUM fumecheng-4967 157 23 ) ) PUNCT fumecheng-4967 157 24 ] ] PUNCT fumecheng-4967 157 25 generates generate VERB fumecheng-4967 157 26 a a DET fumecheng-4967 157 27 term term NOUN fumecheng-4967 157 28 with with ADP fumecheng-4967 157 29 a a DET fumecheng-4967 157 30 long long ADJ fumecheng-4967 157 31 - - PUNCT fumecheng-4967 157 32 range range NOUN fumecheng-4967 157 33 effect effect NOUN fumecheng-4967 157 34 in in ADP fumecheng-4967 157 35 the the DET fumecheng-4967 157 36 equation equation NOUN fumecheng-4967 157 37 of of ADP fumecheng-4967 157 38 motion motion NOUN fumecheng-4967 157 39 for for ADP fumecheng-4967 157 40 the the DET fumecheng-4967 157 41 field field NOUN fumecheng-4967 157 42 variable variable NOUN fumecheng-4967 157 43 2 2 NUM fumecheng-4967 157 44 ( ( PUNCT fumecheng-4967 157 45 , , PUNCT fumecheng-4967 157 46 ) ) PUNCT fumecheng-4967 157 47 / / SYM fumecheng-4967 158 1 [ [ PUNCT fumecheng-4967 158 2 / / SYM fumecheng-4967 158 3 ( ( PUNCT fumecheng-4967 158 4 , , PUNCT fumecheng-4967 158 5 ) ) PUNCT fumecheng-4967 158 6 ' ' PUNCT fumecheng-4967 158 7 ( ( PUNCT fumecheng-4967 158 8 ' ' PUNCT fumecheng-4967 158 9 , , PUNCT fumecheng-4967 158 10 ) ) PUNCT fumecheng-4967 158 11 ] ] PUNCT fumecheng-4967 158 12 ( ( PUNCT fumecheng-4967 158 13 , , PUNCT fumecheng-4967 158 14 ) ) PUNCT fumecheng-4967 158 15 2 2 NUM fumecheng-4967 158 16 x x SYM fumecheng-4967 158 17 t t NOUN fumecheng-4967 158 18 t t NOUN fumecheng-4967 158 19 c c NOUN fumecheng-4967 159 1 f f PROPN fumecheng-4967 159 2 x x SYM fumecheng-4967 159 3 t t NOUN fumecheng-4967 159 4 dx dx PROPN fumecheng-4967 159 5 x x PROPN fumecheng-4967 159 6 t t PROPN fumecheng-4967 159 7 x x PROPN fumecheng-4967 159 8 t t PROPN fumecheng-4967 159 9 v v NUM fumecheng-4967 159 10   ADJ fumecheng-4967 159 11   ADJ fumecheng-4967 159 12   PROPN fumecheng-4967 159 13   PROPN fumecheng-4967 159 14   NOUN fumecheng-4967 159 15   VERB fumecheng-4967 159 16   PROPN fumecheng-4967 159 17   ADJ fumecheng-4967 159 18   PROPN fumecheng-4967 159 19   NUM fumecheng-4967 159 20   VERB fumecheng-4967 159 21   ADP fumecheng-4967 159 22   NUM fumecheng-4967 159 23   ADP fumecheng-4967 159 24   ADP fumecheng-4967 159 25   X fumecheng-4967 159 26   ADP fumecheng-4967 159 27   X fumecheng-4967 159 28 ( ( PUNCT fumecheng-4967 159 29 12 12 NUM fumecheng-4967 159 30 ) ) PUNCT fumecheng-4967 159 31 whose whose DET fumecheng-4967 159 32 presence presence NOUN fumecheng-4967 159 33 significantly significantly ADV fumecheng-4967 159 34 accelerates accelerate VERB fumecheng-4967 159 35 or or CCONJ fumecheng-4967 159 36 slows slow VERB fumecheng-4967 159 37 down down ADP fumecheng-4967 159 38 ( ( PUNCT fumecheng-4967 159 39 or or CCONJ fumecheng-4967 159 40 even even ADV fumecheng-4967 159 41 totally totally ADV fumecheng-4967 159 42 stops stop VERB fumecheng-4967 159 43 ) ) PUNCT fumecheng-4967 159 44 the the DET fumecheng-4967 159 45 ordering ordering NOUN fumecheng-4967 159 46 process process NOUN fumecheng-4967 159 47 , , PUNCT fumecheng-4967 159 48 depending depend VERB fumecheng-4967 159 49 on on ADP fumecheng-4967 159 50 both both CCONJ fumecheng-4967 159 51 the the DET fumecheng-4967 159 52 magnitude magnitude NOUN fumecheng-4967 159 53 and and CCONJ fumecheng-4967 159 54 sign sign NOUN fumecheng-4967 159 55 of of ADP fumecheng-4967 159 56 κ κ NOUN fumecheng-4967 159 57 . . PUNCT fumecheng-4967 159 58 typical typical ADJ fumecheng-4967 159 59 picture picture NOUN fumecheng-4967 159 60 of of ADP fumecheng-4967 159 61 blocked block VERB fumecheng-4967 159 62 almost almost ADV fumecheng-4967 159 63 static static ADJ fumecheng-4967 159 64 domains domain NOUN fumecheng-4967 159 65 is be AUX fumecheng-4967 159 66 shown show VERB fumecheng-4967 159 67 in in ADP fumecheng-4967 159 68 fig fig NOUN fumecheng-4967 159 69 . . PUNCT fumecheng-4967 160 1 4 4 X fumecheng-4967 160 2 . . X fumecheng-4967 160 3 fig fig NOUN fumecheng-4967 160 4 . . PUNCT fumecheng-4967 161 1 4 4 NUM fumecheng-4967 161 2 formation formation NOUN fumecheng-4967 161 3 of of ADP fumecheng-4967 161 4 the the DET fumecheng-4967 161 5 domain domain NOUN fumecheng-4967 161 6 structure structure NOUN fumecheng-4967 161 7 in in ADP fumecheng-4967 161 8 the the DET fumecheng-4967 161 9 kinetics kinetic NOUN fumecheng-4967 161 10 at at ADP fumecheng-4967 161 11 the the DET fumecheng-4967 161 12 presence presence NOUN fumecheng-4967 161 13 of of ADP fumecheng-4967 161 14 self self NOUN fumecheng-4967 161 15 - - PUNCT fumecheng-4967 161 16 blocking blocking NOUN fumecheng-4967 161 17 . . PUNCT fumecheng-4967 162 1 two two NUM fumecheng-4967 162 2 different different ADJ fumecheng-4967 162 3 kinds kind NOUN fumecheng-4967 162 4 of of ADP fumecheng-4967 162 5 domains domain NOUN fumecheng-4967 162 6 are be AUX fumecheng-4967 162 7 shown show VERB fumecheng-4967 162 8 by by ADP fumecheng-4967 162 9 red red ADJ fumecheng-4967 162 10 and and CCONJ fumecheng-4967 162 11 blue blue ADJ fumecheng-4967 162 12 colors color NOUN fumecheng-4967 162 13 , , PUNCT fumecheng-4967 162 14 respectively respectively ADV fumecheng-4967 162 15 . . PUNCT fumecheng-4967 163 1 it it PRON fumecheng-4967 163 2 is be AUX fumecheng-4967 163 3 important important ADJ fumecheng-4967 163 4 to to PART fumecheng-4967 163 5 note note VERB fumecheng-4967 163 6 that that SCONJ fumecheng-4967 163 7 the the DET fumecheng-4967 163 8 last last ADJ fumecheng-4967 163 9 stage stage NOUN fumecheng-4967 163 10 here here ADV fumecheng-4967 163 11 is be AUX fumecheng-4967 163 12 the the DET fumecheng-4967 163 13 practically practically ADV fumecheng-4967 163 14 final final ADJ fumecheng-4967 163 15 one one NUM fumecheng-4967 163 16 and and CCONJ fumecheng-4967 163 17 does do AUX fumecheng-4967 163 18 not not PART fumecheng-4967 163 19 develop develop VERB fumecheng-4967 163 20 further far ADV fumecheng-4967 163 21 with with ADP fumecheng-4967 163 22 time time NOUN fumecheng-4967 163 23 . . PUNCT fumecheng-4967 164 1 let let VERB fumecheng-4967 164 2 us we PRON fumecheng-4967 164 3 discuss discuss VERB fumecheng-4967 164 4 on on ADP fumecheng-4967 164 5 one one NUM fumecheng-4967 164 6 more more ADJ fumecheng-4967 164 7 example example NOUN fumecheng-4967 164 8 of of ADP fumecheng-4967 164 9 an an DET fumecheng-4967 164 10 interaction interaction NOUN fumecheng-4967 164 11 , , PUNCT fumecheng-4967 164 12 which which PRON fumecheng-4967 164 13 leads lead VERB fumecheng-4967 164 14 to to ADP fumecheng-4967 164 15 a a DET fumecheng-4967 164 16 similar similar ADJ fumecheng-4967 164 17 model model NOUN fumecheng-4967 164 18 . . PUNCT fumecheng-4967 165 1 the the DET fumecheng-4967 165 2 local local ADJ fumecheng-4967 165 3 variation variation NOUN fumecheng-4967 165 4 of of ADP fumecheng-4967 165 5 the the DET fumecheng-4967 165 6 order order NOUN fumecheng-4967 165 7 parameter parameter NOUN fumecheng-4967 165 8 is be AUX fumecheng-4967 165 9 accompanied accompany VERB fumecheng-4967 165 10 by by ADP fumecheng-4967 165 11 the the DET fumecheng-4967 165 12 evolution evolution NOUN fumecheng-4967 165 13 or or CCONJ fumecheng-4967 165 14 absorption absorption NOUN fumecheng-4967 165 15 of of ADP fumecheng-4967 165 16 heat heat NOUN fumecheng-4967 165 17 ( ( PUNCT fumecheng-4967 165 18 depending depend VERB fumecheng-4967 165 19 on on ADP fumecheng-4967 165 20 whether whether SCONJ fumecheng-4967 165 21 the the DET fumecheng-4967 165 22 transition transition NOUN fumecheng-4967 165 23 is be AUX fumecheng-4967 165 24 to to ADP fumecheng-4967 165 25 the the DET fumecheng-4967 165 26 lowor lowor ADJ fumecheng-4967 165 27 high high ADJ fumecheng-4967 165 28 - - PUNCT fumecheng-4967 165 29 temperature temperature NOUN fumecheng-4967 165 30 phase phase NOUN fumecheng-4967 165 31 ) ) PUNCT fumecheng-4967 165 32 . . PUNCT fumecheng-4967 166 1 this this PRON fumecheng-4967 166 2 results result VERB fumecheng-4967 166 3 from from ADP fumecheng-4967 166 4 heat heat NOUN fumecheng-4967 166 5 conduction conduction NOUN fumecheng-4967 166 6 in in ADP fumecheng-4967 166 7 heating heating NOUN fumecheng-4967 166 8 ( ( PUNCT fumecheng-4967 166 9 cooling cooling NOUN fumecheng-4967 166 10 ) ) PUNCT fumecheng-4967 166 11 of of ADP fumecheng-4967 166 12 the the DET fumecheng-4967 166 13 surrounding surround VERB fumecheng-4967 166 14 regions region NOUN fumecheng-4967 166 15 of of ADP fumecheng-4967 166 16 space space NOUN fumecheng-4967 166 17 , , PUNCT fumecheng-4967 166 18 which which PRON fumecheng-4967 166 19 , , PUNCT fumecheng-4967 166 20 of of ADP fumecheng-4967 166 21 course course NOUN fumecheng-4967 166 22 , , PUNCT fumecheng-4967 166 23 slows slow VERB fumecheng-4967 166 24 down down ADP fumecheng-4967 166 25 the the DET fumecheng-4967 166 26 transition transition NOUN fumecheng-4967 166 27 process process NOUN fumecheng-4967 166 28 in in ADP fumecheng-4967 166 29 all all DET fumecheng-4967 166 30 cases case NOUN fumecheng-4967 166 31 . . PUNCT fumecheng-4967 167 1 this this DET fumecheng-4967 167 2 mechanism mechanism NOUN fumecheng-4967 167 3 seems seem VERB fumecheng-4967 167 4 to to PART fumecheng-4967 167 5 be be AUX fumecheng-4967 167 6 universal universal ADJ fumecheng-4967 167 7 , , PUNCT fumecheng-4967 167 8 and and CCONJ fumecheng-4967 167 9 its its PRON fumecheng-4967 167 10 effectiveness effectiveness NOUN fumecheng-4967 167 11 is be AUX fumecheng-4967 167 12 determined determine VERB fumecheng-4967 167 13 only only ADV fumecheng-4967 167 14 by by ADP fumecheng-4967 167 15 the the DET fumecheng-4967 167 16 relationship relationship NOUN fumecheng-4967 167 17 between between ADP fumecheng-4967 167 18 the the DET fumecheng-4967 167 19 rates rate NOUN fumecheng-4967 167 20 of of ADP fumecheng-4967 167 21 the the DET fumecheng-4967 167 22 nucleation nucleation NOUN fumecheng-4967 167 23 and and CCONJ fumecheng-4967 167 24 heat heat NOUN fumecheng-4967 167 25 - - PUNCT fumecheng-4967 167 26 conduction conduction NOUN fumecheng-4967 167 27 processes process NOUN fumecheng-4967 167 28 . . PUNCT fumecheng-4967 168 1 the the DET fumecheng-4967 168 2 local local ADJ fumecheng-4967 168 3 heating heating NOUN fumecheng-4967 168 4 ( ( PUNCT fumecheng-4967 168 5 cooling cooling NOUN fumecheng-4967 168 6 ) ) PUNCT fumecheng-4967 168 7 of of ADP fumecheng-4967 168 8 a a DET fumecheng-4967 168 9 system system NOUN fumecheng-4967 168 10 in in ADP fumecheng-4967 168 11 a a DET fumecheng-4967 168 12 region region NOUN fumecheng-4967 168 13 , , PUNCT fumecheng-4967 168 14 where where SCONJ fumecheng-4967 168 15 a a DET fumecheng-4967 168 16 nucleus nucleus NOUN fumecheng-4967 168 17 appears appear VERB fumecheng-4967 168 18 , , PUNCT fumecheng-4967 168 19 can can AUX fumecheng-4967 168 20 be be AUX fumecheng-4967 168 21 taken take VERB fumecheng-4967 168 22 into into ADP fumecheng-4967 168 23 account account NOUN fumecheng-4967 168 24 by by ADP fumecheng-4967 168 25 assuming assume VERB fumecheng-4967 168 26 that that SCONJ fumecheng-4967 168 27 quantity quantity NOUN fumecheng-4967 168 28 τ τ X fumecheng-4967 168 29 in in ADP fumecheng-4967 168 30 expressions expression NOUN fumecheng-4967 168 31 ( ( PUNCT fumecheng-4967 168 32 9 9 NUM fumecheng-4967 168 33 ) ) PUNCT fumecheng-4967 168 34 is be AUX fumecheng-4967 168 35 a a DET fumecheng-4967 168 36 function function NOUN fumecheng-4967 168 37 of of ADP fumecheng-4967 168 38 position position NOUN fumecheng-4967 168 39 and and CCONJ fumecheng-4967 168 40 time time NOUN fumecheng-4967 168 41 . . PUNCT fumecheng-4967 169 1 the the DET fumecheng-4967 169 2 kinetic kinetic ADJ fumecheng-4967 169 3 equation equation NOUN fumecheng-4967 169 4 for for ADP fumecheng-4967 169 5 the the DET fumecheng-4967 169 6 order order NOUN fumecheng-4967 169 7 parameter parameter NOUN fumecheng-4967 169 8 should should AUX fumecheng-4967 169 9 be be AUX fumecheng-4967 169 10 supplemented supplement VERB fumecheng-4967 169 11 by by ADP fumecheng-4967 169 12 an an DET fumecheng-4967 169 13 equation equation NOUN fumecheng-4967 169 14 which which PRON fumecheng-4967 169 15 describes describe VERB fumecheng-4967 169 16 the the DET fumecheng-4967 169 17 evolution evolution NOUN fumecheng-4967 169 18 of of ADP fumecheng-4967 169 19 τ τ PROPN fumecheng-4967 169 20 = = NOUN fumecheng-4967 169 21 τ(x τ(x NOUN fumecheng-4967 169 22 , , PUNCT fumecheng-4967 169 23 t t PROPN fumecheng-4967 169 24 ) ) PUNCT fumecheng-4967 169 25 . . PUNCT fumecheng-4967 170 1 the the DET fumecheng-4967 170 2 latter latter ADJ fumecheng-4967 170 3 equation equation NOUN fumecheng-4967 170 4 should should AUX fumecheng-4967 170 5 be be AUX fumecheng-4967 170 6 a a DET fumecheng-4967 170 7 heat heat NOUN fumecheng-4967 170 8 - - PUNCT fumecheng-4967 170 9 conduction conduction NOUN fumecheng-4967 170 10 equation equation NOUN fumecheng-4967 170 11 with with ADP fumecheng-4967 170 12 the the DET fumecheng-4967 170 13 heat heat NOUN fumecheng-4967 170 14 removal removal NOUN fumecheng-4967 170 15 and and CCONJ fumecheng-4967 170 16 with with ADP fumecheng-4967 170 17 a a DET fumecheng-4967 170 18 source source NOUN fumecheng-4967 170 19 β[ρ β[ρ PROPN fumecheng-4967 170 20 ] ] PUNCT fumecheng-4967 170 21 , , PUNCT fumecheng-4967 170 22 whose whose DET fumecheng-4967 170 23 intensity intensity NOUN fumecheng-4967 170 24 is be AUX fumecheng-4967 170 25 proportional proportional ADJ fumecheng-4967 170 26 to to ADP fumecheng-4967 170 27 the the DET fumecheng-4967 170 28 rate rate NOUN fumecheng-4967 170 29 of of ADP fumecheng-4967 170 30 change change NOUN fumecheng-4967 170 31 of of ADP fumecheng-4967 170 32 the the DET fumecheng-4967 170 33 free free ADJ fumecheng-4967 170 34 energy energy NOUN fumecheng-4967 170 35 , , PUNCT fumecheng-4967 170 36 i.e. i.e. X fumecheng-4967 170 37 β[ρ]~∂ρ/∂t·δφ β[ρ]~∂ρ/∂t·δφ SYM fumecheng-4967 170 38 / / SYM fumecheng-4967 170 39 δρ δρ NOUN fumecheng-4967 170 40 . . PUNCT fumecheng-4967 171 1 as as ADP fumecheng-4967 171 2 a a DET fumecheng-4967 171 3 result result NOUN fumecheng-4967 171 4 , , PUNCT fumecheng-4967 171 5 we we PRON fumecheng-4967 171 6 have have VERB fumecheng-4967 171 7 the the DET fumecheng-4967 171 8 following follow VERB fumecheng-4967 171 9 system system NOUN fumecheng-4967 171 10 of of ADP fumecheng-4967 171 11 the the DET fumecheng-4967 171 12 connected connected ADJ fumecheng-4967 171 13 equations equation NOUN fumecheng-4967 172 1 [ [ X fumecheng-4967 172 2 7 7 NUM fumecheng-4967 172 3 ] ] NUM fumecheng-4967 172 4 : : PUNCT fumecheng-4967 172 5 ( ( PUNCT fumecheng-4967 172 6 , , PUNCT fumecheng-4967 172 7 ) ) PUNCT fumecheng-4967 172 8 / / PUNCT fumecheng-4967 173 1 [ [ PUNCT fumecheng-4967 173 2 ( ( PUNCT fumecheng-4967 173 3 , , PUNCT fumecheng-4967 173 4 ) ) PUNCT fumecheng-4967 173 5 ] ] PUNCT fumecheng-4967 173 6 / / PUNCT fumecheng-4967 173 7 ( ( PUNCT fumecheng-4967 173 8 , , PUNCT fumecheng-4967 173 9 ) ) PUNCT fumecheng-4967 173 10 ( ( PUNCT fumecheng-4967 173 11 , , PUNCT fumecheng-4967 173 12 ) ) PUNCT fumecheng-4967 173 13 x x SYM fumecheng-4967 174 1 t t NOUN fumecheng-4967 174 2 t t PROPN fumecheng-4967 174 3 x x SYM fumecheng-4967 174 4 t t X fumecheng-4967 174 5 x x SYM fumecheng-4967 174 6 t t NOUN fumecheng-4967 174 7 x x SYM fumecheng-4967 174 8 t t PROPN fumecheng-4967 174 9   ADJ fumecheng-4967 175 1   PROPN fumecheng-4967 175 2   NOUN fumecheng-4967 175 3   PROPN fumecheng-4967 175 4   NOUN fumecheng-4967 175 5   PROPN fumecheng-4967 175 6   ADP fumecheng-4967 175 7   VERB fumecheng-4967 175 8   NOUN fumecheng-4967 175 9 ; ; PUNCT fumecheng-4967 175 10 ( ( PUNCT fumecheng-4967 175 11 13 13 NUM fumecheng-4967 175 12 ) ) PUNCT fumecheng-4967 175 13 ( ( PUNCT fumecheng-4967 175 14 , , PUNCT fumecheng-4967 175 15 ) ) PUNCT fumecheng-4967 175 16 / / SYM fumecheng-4967 175 17 ( ( PUNCT fumecheng-4967 175 18 , , PUNCT fumecheng-4967 175 19 ) ) PUNCT fumecheng-4967 175 20 ( ( PUNCT fumecheng-4967 175 21 , , PUNCT fumecheng-4967 175 22 ) ) PUNCT fumecheng-4967 175 23 / / PUNCT fumecheng-4967 176 1 [ [ PUNCT fumecheng-4967 176 2 ( ( PUNCT fumecheng-4967 176 3 , , PUNCT fumecheng-4967 176 4 ) ) PUNCT fumecheng-4967 176 5 ] ] PUNCT fumecheng-4967 176 6 / / PUNCT fumecheng-4967 176 7 ( ( PUNCT fumecheng-4967 176 8 , , PUNCT fumecheng-4967 176 9 ) ) PUNCT fumecheng-4967 176 10 ( ( PUNCT fumecheng-4967 176 11 , , PUNCT fumecheng-4967 176 12 ) ) PUNCT fumecheng-4967 176 13 x x SYM fumecheng-4967 177 1 t t NOUN fumecheng-4967 177 2 t t PROPN fumecheng-4967 177 3 x x SYM fumecheng-4967 177 4 t t PROPN fumecheng-4967 177 5 x x SYM fumecheng-4967 177 6 t t PROPN fumecheng-4967 177 7 t t PROPN fumecheng-4967 177 8 x x SYM fumecheng-4967 177 9 t t X fumecheng-4967 177 10 x x SYM fumecheng-4967 177 11 t t NOUN fumecheng-4967 177 12 x x SYM fumecheng-4967 177 13 t t PROPN fumecheng-4967 177 14   ADJ fumecheng-4967 177 15   NUM fumecheng-4967 178 1   NOUN fumecheng-4967 179 1   NUM fumecheng-4967 179 2   ADJ fumecheng-4967 179 3   ADJ fumecheng-4967 179 4   PROPN fumecheng-4967 179 5   NOUN fumecheng-4967 179 6   X fumecheng-4967 179 7   VERB fumecheng-4967 179 8   ADP fumecheng-4967 179 9   NUM fumecheng-4967 179 10   ADP fumecheng-4967 179 11   VERB fumecheng-4967 179 12   NOUN fumecheng-4967 179 13 ( ( PUNCT fumecheng-4967 179 14 14 14 NUM fumecheng-4967 179 15 ) ) PUNCT fumecheng-4967 179 16 methods method NOUN fumecheng-4967 179 17 of of ADP fumecheng-4967 179 18 the the DET fumecheng-4967 179 19 pattern pattern NOUN fumecheng-4967 179 20 formation formation NOUN fumecheng-4967 179 21 in in ADP fumecheng-4967 179 22 numerical numerical ADJ fumecheng-4967 179 23 modeling modeling NOUN fumecheng-4967 179 24 of of ADP fumecheng-4967 179 25 biological biological ADJ fumecheng-4967 179 26 problems problem NOUN fumecheng-4967 179 27 225 225 NUM fumecheng-4967 179 28 before before ADP fumecheng-4967 179 29 starting start VERB fumecheng-4967 179 30 discussion discussion NOUN fumecheng-4967 179 31 of of ADP fumecheng-4967 179 32 the the DET fumecheng-4967 179 33 results result NOUN fumecheng-4967 179 34 of of ADP fumecheng-4967 179 35 the the DET fumecheng-4967 179 36 numerical numerical ADJ fumecheng-4967 179 37 experiments experiment NOUN fumecheng-4967 179 38 , , PUNCT fumecheng-4967 179 39 we we PRON fumecheng-4967 179 40 show show VERB fumecheng-4967 179 41 that that SCONJ fumecheng-4967 179 42 with with ADP fumecheng-4967 179 43 some some DET fumecheng-4967 179 44 roughening roughening NOUN fumecheng-4967 179 45 of of ADP fumecheng-4967 179 46 the the DET fumecheng-4967 179 47 model model NOUN fumecheng-4967 179 48 , , PUNCT fumecheng-4967 179 49 the the DET fumecheng-4967 179 50 mechanism mechanism NOUN fumecheng-4967 179 51 under under ADP fumecheng-4967 179 52 consideration consideration NOUN fumecheng-4967 179 53 can can AUX fumecheng-4967 179 54 be be AUX fumecheng-4967 179 55 described describe VERB fumecheng-4967 179 56 in in ADP fumecheng-4967 179 57 terms term NOUN fumecheng-4967 179 58 of of ADP fumecheng-4967 179 59 a a DET fumecheng-4967 179 60 single single ADJ fumecheng-4967 179 61 field field NOUN fumecheng-4967 179 62 variable variable ADJ fumecheng-4967 179 63 ρ(x ρ(x PROPN fumecheng-4967 179 64 , , PUNCT fumecheng-4967 179 65 t t PROPN fumecheng-4967 179 66 ) ) PUNCT fumecheng-4967 179 67 , , PUNCT fumecheng-4967 179 68 which which PRON fumecheng-4967 179 69 evolves evolve VERB fumecheng-4967 179 70 in in ADP fumecheng-4967 179 71 accordance accordance NOUN fumecheng-4967 179 72 with with ADP fumecheng-4967 179 73 an an DET fumecheng-4967 179 74 equation equation NOUN fumecheng-4967 179 75 similar similar ADJ fumecheng-4967 179 76 to to ADP fumecheng-4967 179 77 eq eq PROPN fumecheng-4967 179 78 . . PUNCT fumecheng-4967 180 1 ( ( PUNCT fumecheng-4967 180 2 12 12 NUM fumecheng-4967 180 3 ) ) PUNCT fumecheng-4967 180 4 . . PUNCT fumecheng-4967 181 1 the the DET fumecheng-4967 181 2 physical physical ADJ fumecheng-4967 181 3 arguments argument NOUN fumecheng-4967 181 4 , , PUNCT fumecheng-4967 181 5 which which PRON fumecheng-4967 181 6 lead lead VERB fumecheng-4967 181 7 to to ADP fumecheng-4967 181 8 a a DET fumecheng-4967 181 9 functional functional ADJ fumecheng-4967 181 10 like like ADP fumecheng-4967 181 11 eq eq NOUN fumecheng-4967 181 12 . . PUNCT fumecheng-4967 181 13 ( ( PUNCT fumecheng-4967 181 14 11 11 NUM fumecheng-4967 181 15 ) ) PUNCT fumecheng-4967 181 16 in in ADP fumecheng-4967 181 17 this this DET fumecheng-4967 181 18 case case NOUN fumecheng-4967 181 19 , , PUNCT fumecheng-4967 181 20 too too ADV fumecheng-4967 181 21 , , PUNCT fumecheng-4967 181 22 are be AUX fumecheng-4967 181 23 fairly fairly ADV fumecheng-4967 181 24 simple simple ADJ fumecheng-4967 181 25 . . PUNCT fumecheng-4967 182 1 each each DET fumecheng-4967 182 2 growing grow VERB fumecheng-4967 182 3 domain domain NOUN fumecheng-4967 182 4 of of ADP fumecheng-4967 182 5 the the DET fumecheng-4967 182 6 new new ADJ fumecheng-4967 182 7 phase phase NOUN fumecheng-4967 182 8 creates create VERB fumecheng-4967 182 9 a a DET fumecheng-4967 182 10 non non ADJ fumecheng-4967 182 11 uniform uniform ADJ fumecheng-4967 182 12 temperature temperature NOUN fumecheng-4967 182 13 field field NOUN fumecheng-4967 182 14 τ(x τ(x PROPN fumecheng-4967 182 15 , , PUNCT fumecheng-4967 182 16 t t PROPN fumecheng-4967 182 17 ) ) PUNCT fumecheng-4967 182 18 around around ADP fumecheng-4967 182 19 itself itself PRON fumecheng-4967 182 20 . . PUNCT fumecheng-4967 183 1 owing owe VERB fumecheng-4967 183 2 to to ADP fumecheng-4967 183 3 the the DET fumecheng-4967 183 4 heat heat NOUN fumecheng-4967 183 5 conduction conduction NOUN fumecheng-4967 183 6 , , PUNCT fumecheng-4967 183 7 the the DET fumecheng-4967 183 8 temperature temperature NOUN fumecheng-4967 183 9 at at ADP fumecheng-4967 183 10 other other ADJ fumecheng-4967 183 11 points point NOUN fumecheng-4967 183 12 in in ADP fumecheng-4967 183 13 space space NOUN fumecheng-4967 183 14 deviates deviate VERB fumecheng-4967 183 15 from from ADP fumecheng-4967 183 16 trial trial NOUN fumecheng-4967 183 17 temperature temperature NOUN fumecheng-4967 183 18 altering alter VERB fumecheng-4967 183 19 the the DET fumecheng-4967 183 20 conditions condition NOUN fumecheng-4967 183 21 for for ADP fumecheng-4967 183 22 the the DET fumecheng-4967 183 23 growth growth NOUN fumecheng-4967 183 24 of of ADP fumecheng-4967 183 25 other other ADJ fumecheng-4967 183 26 domains domain NOUN fumecheng-4967 183 27 at at ADP fumecheng-4967 183 28 those those DET fumecheng-4967 183 29 points point NOUN fumecheng-4967 183 30 . . PUNCT fumecheng-4967 184 1 this this PRON fumecheng-4967 184 2 signifies signify VERB fumecheng-4967 184 3 the the DET fumecheng-4967 184 4 appearance appearance NOUN fumecheng-4967 184 5 of of ADP fumecheng-4967 184 6 an an DET fumecheng-4967 184 7 effective effective ADJ fumecheng-4967 184 8 long long ADJ fumecheng-4967 184 9 - - PUNCT fumecheng-4967 184 10 range range NOUN fumecheng-4967 184 11 field field NOUN fumecheng-4967 184 12 accompanying accompany VERB fumecheng-4967 184 13 the the DET fumecheng-4967 184 14 nucleation nucleation NOUN fumecheng-4967 184 15 process process NOUN fumecheng-4967 184 16 in in ADP fumecheng-4967 184 17 the the DET fumecheng-4967 184 18 system system NOUN fumecheng-4967 184 19 . . PUNCT fumecheng-4967 185 1 relating relate VERB fumecheng-4967 185 2 the the DET fumecheng-4967 185 3 variation variation NOUN fumecheng-4967 185 4 of of ADP fumecheng-4967 185 5 the the DET fumecheng-4967 185 6 temperature temperature NOUN fumecheng-4967 185 7 field field NOUN fumecheng-4967 185 8 to to ADP fumecheng-4967 185 9 the the DET fumecheng-4967 185 10 order order NOUN fumecheng-4967 185 11 - - PUNCT fumecheng-4967 185 12 parameter parameter NOUN fumecheng-4967 185 13 field field NOUN fumecheng-4967 185 14 ρ(x ρ(x PROPN fumecheng-4967 185 15 , , PUNCT fumecheng-4967 185 16 t t PROPN fumecheng-4967 185 17 ) ) PUNCT fumecheng-4967 185 18 , , PUNCT fumecheng-4967 185 19 we we PRON fumecheng-4967 185 20 obtain obtain VERB fumecheng-4967 185 21 an an DET fumecheng-4967 185 22 energy energy NOUN fumecheng-4967 185 23 functional functional ADJ fumecheng-4967 185 24 φ[ρ φ[ρ ADV fumecheng-4967 185 25 ] ] PUNCT fumecheng-4967 185 26 like like ADP fumecheng-4967 185 27 that that PRON fumecheng-4967 185 28 in in ADP fumecheng-4967 185 29 eq eq ADP fumecheng-4967 185 30 . . PUNCT fumecheng-4967 186 1 ( ( PUNCT fumecheng-4967 186 2 11 11 NUM fumecheng-4967 186 3 ) ) PUNCT fumecheng-4967 186 4 . . PUNCT fumecheng-4967 187 1 in in ADP fumecheng-4967 187 2 fact fact NOUN fumecheng-4967 187 3 , , PUNCT fumecheng-4967 187 4 when when SCONJ fumecheng-4967 187 5 the the DET fumecheng-4967 187 6 fluctuations fluctuation NOUN fumecheng-4967 187 7 of of ADP fumecheng-4967 187 8 τ(x τ(x PROPN fumecheng-4967 187 9 , , PUNCT fumecheng-4967 187 10 t t PROPN fumecheng-4967 187 11 ) ) PUNCT fumecheng-4967 187 12 are be AUX fumecheng-4967 187 13 " " PUNCT fumecheng-4967 187 14 turned turn VERB fumecheng-4967 187 15 on on ADP fumecheng-4967 187 16 " " PUNCT fumecheng-4967 187 17 in in ADP fumecheng-4967 187 18 a a DET fumecheng-4967 187 19 system system NOUN fumecheng-4967 187 20 with with ADP fumecheng-4967 187 21 a a DET fumecheng-4967 187 22 temperature temperature NOUN fumecheng-4967 187 23 equal equal ADJ fumecheng-4967 187 24 to to ADP fumecheng-4967 187 25 the the DET fumecheng-4967 187 26 heat heat NOUN fumecheng-4967 187 27 - - PUNCT fumecheng-4967 187 28 bath bath NOUN fumecheng-4967 187 29 temperature temperature NOUN fumecheng-4967 187 30 τ0 τ0 NOUN fumecheng-4967 187 31 , , PUNCT fumecheng-4967 187 32 after after ADP fumecheng-4967 187 33 a a DET fumecheng-4967 187 34 unit unit NOUN fumecheng-4967 187 35 of of ADP fumecheng-4967 187 36 time time NOUN fumecheng-4967 187 37 the the DET fumecheng-4967 187 38 mean mean ADJ fumecheng-4967 187 39 value value NOUN fumecheng-4967 187 40 of of ADP fumecheng-4967 187 41 τ(x τ(x PROPN fumecheng-4967 187 42 , , PUNCT fumecheng-4967 187 43 t t PROPN fumecheng-4967 187 44 ) ) PUNCT fumecheng-4967 187 45 deviates deviate VERB fumecheng-4967 187 46 from from ADP fumecheng-4967 187 47 τ0 τ0 NOUN fumecheng-4967 187 48 by by ADP fumecheng-4967 187 49 1 1 NUM fumecheng-4967 187 50 2 2 NUM fumecheng-4967 187 51 0 0 NUM fumecheng-4967 187 52 0 0 NUM fumecheng-4967 187 53 1 1 NUM fumecheng-4967 187 54 1 1 NUM fumecheng-4967 187 55 /dx /dx SYM fumecheng-4967 187 56 t t NOUN fumecheng-4967 187 57 v v NOUN fumecheng-4967 187 58 v v ADP fumecheng-4967 187 59   PROPN fumecheng-4967 188 1   VERB fumecheng-4967 189 1   PROPN fumecheng-4967 189 2   PRON fumecheng-4967 189 3   ADJ fumecheng-4967 189 4   NOUN fumecheng-4967 189 5   PUNCT fumecheng-4967 189 6   VERB fumecheng-4967 189 7   NOUN fumecheng-4967 189 8   NOUN fumecheng-4967 189 9   NOUN fumecheng-4967 189 10 ( ( PUNCT fumecheng-4967 189 11 15 15 NUM fumecheng-4967 189 12 ) ) PUNCT fumecheng-4967 189 13 the the DET fumecheng-4967 189 14 mutual mutual ADJ fumecheng-4967 189 15 influence influence NOUN fumecheng-4967 189 16 of of ADP fumecheng-4967 189 17 the the DET fumecheng-4967 189 18 domains domain NOUN fumecheng-4967 189 19 of of ADP fumecheng-4967 189 20 the the DET fumecheng-4967 189 21 new new ADJ fumecheng-4967 189 22 phase phase NOUN fumecheng-4967 189 23 becomes become VERB fumecheng-4967 189 24 significant significant ADJ fumecheng-4967 189 25 , , PUNCT fumecheng-4967 189 26 when when SCONJ fumecheng-4967 189 27 they they PRON fumecheng-4967 189 28 become become VERB fumecheng-4967 189 29 so so ADV fumecheng-4967 189 30 large large ADJ fumecheng-4967 189 31 ( ( PUNCT fumecheng-4967 189 32 and and CCONJ fumecheng-4967 189 33 this this PRON fumecheng-4967 189 34 is be AUX fumecheng-4967 189 35 seen see VERB fumecheng-4967 189 36 from from ADP fumecheng-4967 189 37 the the DET fumecheng-4967 189 38 results result NOUN fumecheng-4967 189 39 of of ADP fumecheng-4967 189 40 numerical numerical ADJ fumecheng-4967 189 41 experiments experiment NOUN fumecheng-4967 189 42 ) ) PUNCT fumecheng-4967 189 43 that that SCONJ fumecheng-4967 189 44 the the DET fumecheng-4967 189 45 energy energy NOUN fumecheng-4967 189 46 of of ADP fumecheng-4967 189 47 the the DET fumecheng-4967 189 48 domain domain NOUN fumecheng-4967 189 49 boundaries boundary NOUN fumecheng-4967 189 50 between between ADP fumecheng-4967 189 51 the the DET fumecheng-4967 189 52 ordered order VERB fumecheng-4967 189 53 and and CCONJ fumecheng-4967 189 54 unordered unordered ADJ fumecheng-4967 189 55 phases phase NOUN fumecheng-4967 189 56 can can AUX fumecheng-4967 189 57 be be AUX fumecheng-4967 189 58 neglected neglect VERB fumecheng-4967 189 59 . . PUNCT fumecheng-4967 190 1 as as ADP fumecheng-4967 190 2 result result NOUN fumecheng-4967 190 3 , , PUNCT fumecheng-4967 190 4 we we PRON fumecheng-4967 190 5 arrive arrive VERB fumecheng-4967 190 6 at at ADP fumecheng-4967 190 7 a a DET fumecheng-4967 190 8 functional functional ADJ fumecheng-4967 190 9 like like ADP fumecheng-4967 190 10 eq eq NOUN fumecheng-4967 190 11 . . PUNCT fumecheng-4967 191 1 ( ( PUNCT fumecheng-4967 191 2 1 1 NUM fumecheng-4967 191 3 ) ) PUNCT fumecheng-4967 191 4 , , PUNCT fumecheng-4967 191 5 which which PRON fumecheng-4967 191 6 was be AUX fumecheng-4967 191 7 obtained obtain VERB fumecheng-4967 191 8 to to PART fumecheng-4967 191 9 describe describe VERB fumecheng-4967 191 10 striction striction NOUN fumecheng-4967 191 11 effects effect NOUN fumecheng-4967 191 12 in in ADP fumecheng-4967 191 13 the the DET fumecheng-4967 191 14 kinetics kinetic NOUN fumecheng-4967 191 15 of of ADP fumecheng-4967 191 16 a a DET fumecheng-4967 191 17 first first ADJ fumecheng-4967 191 18 - - PUNCT fumecheng-4967 191 19 order order NOUN fumecheng-4967 191 20 phase phase NOUN fumecheng-4967 191 21 transition transition NOUN fumecheng-4967 191 22 . . PUNCT fumecheng-4967 192 1 in in ADP fumecheng-4967 192 2 some some DET fumecheng-4967 192 3 cases case NOUN fumecheng-4967 192 4 , , PUNCT fumecheng-4967 192 5 this this PRON fumecheng-4967 192 6 makes make VERB fumecheng-4967 192 7 it it PRON fumecheng-4967 192 8 possible possible ADJ fumecheng-4967 192 9 , , PUNCT fumecheng-4967 192 10 in in ADP fumecheng-4967 192 11 principle principle NOUN fumecheng-4967 192 12 , , PUNCT fumecheng-4967 192 13 to to PART fumecheng-4967 192 14 disregard disregard VERB fumecheng-4967 192 15 the the DET fumecheng-4967 192 16 specific specific ADJ fumecheng-4967 192 17 mechanism mechanism NOUN fumecheng-4967 192 18 for for ADP fumecheng-4967 192 19 realizing realize VERB fumecheng-4967 192 20 the the DET fumecheng-4967 192 21 long long ADJ fumecheng-4967 192 22 - - PUNCT fumecheng-4967 192 23 range range NOUN fumecheng-4967 192 24 effect effect NOUN fumecheng-4967 192 25 accompanying accompany VERB fumecheng-4967 192 26 the the DET fumecheng-4967 192 27 first first ADJ fumecheng-4967 192 28 - - PUNCT fumecheng-4967 192 29 order order NOUN fumecheng-4967 192 30 phase phase NOUN fumecheng-4967 192 31 transition transition NOUN fumecheng-4967 192 32 and and CCONJ fumecheng-4967 192 33 to to PART fumecheng-4967 192 34 formally formally ADV fumecheng-4967 192 35 analyze analyze VERB fumecheng-4967 192 36 models model NOUN fumecheng-4967 192 37 with with ADP fumecheng-4967 192 38 nonlocalities nonlocalitie NOUN fumecheng-4967 192 39 of of ADP fumecheng-4967 192 40 the the DET fumecheng-4967 192 41 general general ADJ fumecheng-4967 192 42 form form NOUN fumecheng-4967 192 43 . . PUNCT fumecheng-4967 193 1 4 4 X fumecheng-4967 193 2 . . X fumecheng-4967 193 3 large large ADJ fumecheng-4967 193 4 scale scale NOUN fumecheng-4967 193 5 structure structure NOUN fumecheng-4967 193 6 of of ADP fumecheng-4967 193 7 the the DET fumecheng-4967 193 8 fluctuating fluctuate VERB fumecheng-4967 193 9 field field NOUN fumecheng-4967 193 10 . . PUNCT fumecheng-4967 194 1 universality universality NOUN fumecheng-4967 194 2 and and CCONJ fumecheng-4967 194 3 scaling scale VERB fumecheng-4967 194 4 trial trial NOUN fumecheng-4967 194 5 structure structure NOUN fumecheng-4967 194 6 of of ADP fumecheng-4967 194 7 the the DET fumecheng-4967 194 8 energy energy NOUN fumecheng-4967 194 9 functional functional ADJ fumecheng-4967 194 10 has have VERB fumecheng-4967 194 11 direct direct ADJ fumecheng-4967 194 12 relation relation NOUN fumecheng-4967 194 13 to to ADP fumecheng-4967 194 14 the the DET fumecheng-4967 194 15 microscopic microscopic ADJ fumecheng-4967 194 16 interactions interaction NOUN fumecheng-4967 194 17 in in ADP fumecheng-4967 194 18 the the DET fumecheng-4967 194 19 system system NOUN fumecheng-4967 194 20 . . PUNCT fumecheng-4967 195 1 in in ADP fumecheng-4967 195 2 many many ADJ fumecheng-4967 195 3 cases case NOUN fumecheng-4967 195 4 , , PUNCT fumecheng-4967 195 5 it it PRON fumecheng-4967 195 6 can can AUX fumecheng-4967 195 7 be be AUX fumecheng-4967 195 8 even even ADV fumecheng-4967 195 9 analytically analytically ADV fumecheng-4967 195 10 derived derive VERB fumecheng-4967 195 11 from from ADP fumecheng-4967 195 12 the the DET fumecheng-4967 195 13 microscopic microscopic ADJ fumecheng-4967 195 14 theory theory NOUN fumecheng-4967 195 15 . . PUNCT fumecheng-4967 196 1 it it PRON fumecheng-4967 196 2 means mean VERB fumecheng-4967 196 3 that that SCONJ fumecheng-4967 196 4 the the DET fumecheng-4967 196 5 coefficients coefficient NOUN fumecheng-4967 196 6 of of ADP fumecheng-4967 196 7 the the DET fumecheng-4967 196 8 expansions expansion NOUN fumecheng-4967 196 9 used use VERB fumecheng-4967 196 10 in in ADP fumecheng-4967 196 11 the the DET fumecheng-4967 196 12 kinetic kinetic ADJ fumecheng-4967 196 13 equations equation NOUN fumecheng-4967 196 14 above above ADV fumecheng-4967 196 15 have have AUX fumecheng-4967 196 16 well well ADV fumecheng-4967 196 17 defined define VERB fumecheng-4967 196 18 specific specific ADJ fumecheng-4967 196 19 values value NOUN fumecheng-4967 196 20 and and CCONJ fumecheng-4967 196 21 in in ADP fumecheng-4967 196 22 turn turn NOUN fumecheng-4967 196 23 should should AUX fumecheng-4967 196 24 completely completely ADV fumecheng-4967 196 25 determine determine VERB fumecheng-4967 196 26 density density NOUN fumecheng-4967 196 27 distributions distribution NOUN fumecheng-4967 196 28 ρ(x ρ(x PROPN fumecheng-4967 196 29 , , PUNCT fumecheng-4967 196 30 t t PROPN fumecheng-4967 196 31 ) ) PUNCT fumecheng-4967 196 32 and and CCONJ fumecheng-4967 196 33 as as SCONJ fumecheng-4967 196 34 result result VERB fumecheng-4967 196 35 the the DET fumecheng-4967 196 36 structure structure NOUN fumecheng-4967 196 37 of of ADP fumecheng-4967 196 38 the the DET fumecheng-4967 196 39 contact contact NOUN fumecheng-4967 196 40 surface surface NOUN fumecheng-4967 196 41 . . PUNCT fumecheng-4967 197 1 however however ADV fumecheng-4967 197 2 , , PUNCT fumecheng-4967 197 3 it it PRON fumecheng-4967 197 4 is be AUX fumecheng-4967 197 5 well well ADV fumecheng-4967 197 6 known know VERB fumecheng-4967 197 7 that that SCONJ fumecheng-4967 197 8 absolute absolute ADJ fumecheng-4967 197 9 majority majority NOUN fumecheng-4967 197 10 of of ADP fumecheng-4967 197 11 real real ADJ fumecheng-4967 197 12 surfaces surface NOUN fumecheng-4967 197 13 have have VERB fumecheng-4967 197 14 practically practically ADV fumecheng-4967 197 15 universal universal ADJ fumecheng-4967 197 16 ( ( PUNCT fumecheng-4967 197 17 scaling scaling NOUN fumecheng-4967 197 18 ) ) PUNCT fumecheng-4967 197 19 structure structure NOUN fumecheng-4967 197 20 with with ADP fumecheng-4967 197 21 the the DET fumecheng-4967 197 22 power power NOUN fumecheng-4967 197 23 low low ADJ fumecheng-4967 197 24 distribution distribution NOUN fumecheng-4967 197 25 of of ADP fumecheng-4967 197 26 the the DET fumecheng-4967 197 27 relief relief NOUN fumecheng-4967 197 28 . . PUNCT fumecheng-4967 198 1 it it PRON fumecheng-4967 198 2 means mean VERB fumecheng-4967 198 3 that that SCONJ fumecheng-4967 198 4 if if SCONJ fumecheng-4967 198 5 there there PRON fumecheng-4967 198 6 is be VERB fumecheng-4967 198 7 no no DET fumecheng-4967 198 8 special special ADJ fumecheng-4967 198 9 reason reason NOUN fumecheng-4967 198 10 to to PART fumecheng-4967 198 11 produce produce VERB fumecheng-4967 198 12 another another DET fumecheng-4967 198 13 structure structure NOUN fumecheng-4967 198 14 , , PUNCT fumecheng-4967 198 15 it it PRON fumecheng-4967 198 16 should should AUX fumecheng-4967 198 17 appear appear VERB fumecheng-4967 198 18 due due ADJ fumecheng-4967 198 19 to to ADP fumecheng-4967 198 20 universal universal ADJ fumecheng-4967 198 21 kinetic kinetic ADJ fumecheng-4967 198 22 process process NOUN fumecheng-4967 198 23 which which PRON fumecheng-4967 198 24 makes make VERB fumecheng-4967 198 25 difference difference NOUN fumecheng-4967 198 26 in in ADP fumecheng-4967 198 27 the the DET fumecheng-4967 198 28 initial initial ADJ fumecheng-4967 198 29 energy energy NOUN fumecheng-4967 198 30 functional functional ADJ fumecheng-4967 198 31 negligible negligible ADJ fumecheng-4967 198 32 . . PUNCT fumecheng-4967 199 1 as as SCONJ fumecheng-4967 199 2 we we PRON fumecheng-4967 199 3 saw see VERB fumecheng-4967 199 4 in in ADP fumecheng-4967 199 5 the the DET fumecheng-4967 199 6 previous previous ADJ fumecheng-4967 199 7 section section NOUN fumecheng-4967 199 8 , , PUNCT fumecheng-4967 199 9 ordering order VERB fumecheng-4967 199 10 transition transition NOUN fumecheng-4967 199 11 is be AUX fumecheng-4967 199 12 anticipated anticipate VERB fumecheng-4967 199 13 by by ADP fumecheng-4967 199 14 nonlinear nonlinear ADJ fumecheng-4967 199 15 excitations excitation NOUN fumecheng-4967 199 16 , , PUNCT fumecheng-4967 199 17 which which PRON fumecheng-4967 199 18 can can AUX fumecheng-4967 199 19 be be AUX fumecheng-4967 199 20 interpreted interpret VERB fumecheng-4967 199 21 as as ADP fumecheng-4967 199 22 nucleation nucleation NOUN fumecheng-4967 199 23 centers center NOUN fumecheng-4967 199 24 . . PUNCT fumecheng-4967 200 1 the the DET fumecheng-4967 200 2 kinetics kinetic NOUN fumecheng-4967 200 3 of of ADP fumecheng-4967 200 4 the the DET fumecheng-4967 200 5 first first ADJ fumecheng-4967 200 6 - - PUNCT fumecheng-4967 200 7 order order NOUN fumecheng-4967 200 8 phase phase NOUN fumecheng-4967 200 9 transition transition NOUN fumecheng-4967 200 10 in in ADP fumecheng-4967 200 11 different different ADJ fumecheng-4967 200 12 physical physical ADJ fumecheng-4967 200 13 systems system NOUN fumecheng-4967 200 14 has have AUX fumecheng-4967 200 15 been be AUX fumecheng-4967 200 16 the the DET fumecheng-4967 200 17 subject subject NOUN fumecheng-4967 200 18 of of ADP fumecheng-4967 200 19 intensive intensive ADJ fumecheng-4967 200 20 studies study NOUN fumecheng-4967 200 21 . . PUNCT fumecheng-4967 201 1 as as ADP fumecheng-4967 201 2 a a DET fumecheng-4967 201 3 rule rule NOUN fumecheng-4967 201 4 , , PUNCT fumecheng-4967 201 5 the the DET fumecheng-4967 201 6 ordering ordering NOUN fumecheng-4967 201 7 of of ADP fumecheng-4967 201 8 a a DET fumecheng-4967 201 9 metastable metastable ADJ fumecheng-4967 201 10 disordered disorder VERB fumecheng-4967 201 11 phase phase NOUN fumecheng-4967 201 12 is be AUX fumecheng-4967 201 13 due due ADJ fumecheng-4967 201 14 to to ADP fumecheng-4967 201 15 the the DET fumecheng-4967 201 16 fluctuation fluctuation NOUN fumecheng-4967 201 17 production production NOUN fumecheng-4967 201 18 and and CCONJ fumecheng-4967 201 19 finally finally ADV fumecheng-4967 201 20 to to ADP fumecheng-4967 201 21 the the DET fumecheng-4967 201 22 growth growth NOUN fumecheng-4967 201 23 of of ADP fumecheng-4967 201 24 the the DET fumecheng-4967 201 25 nucleus nucleus NOUN fumecheng-4967 201 26 of of ADP fumecheng-4967 201 27 the the DET fumecheng-4967 201 28 stable stable ADJ fumecheng-4967 201 29 phase phase NOUN fumecheng-4967 201 30 . . PUNCT fumecheng-4967 202 1 in in ADP fumecheng-4967 202 2 a a DET fumecheng-4967 202 3 first first ADJ fumecheng-4967 202 4 - - PUNCT fumecheng-4967 202 5 order order NOUN fumecheng-4967 202 6 phase phase NOUN fumecheng-4967 202 7 transition transition NOUN fumecheng-4967 202 8 , , PUNCT fumecheng-4967 202 9 there there PRON fumecheng-4967 202 10 is be VERB fumecheng-4967 202 11 a a DET fumecheng-4967 202 12 change change NOUN fumecheng-4967 202 13 in in ADP fumecheng-4967 202 14 some some DET fumecheng-4967 202 15 order order NOUN fumecheng-4967 202 16 parameter parameter NOUN fumecheng-4967 202 17 between between ADP fumecheng-4967 202 18 these these DET fumecheng-4967 202 19 two two NUM fumecheng-4967 202 20 phases phase NOUN fumecheng-4967 202 21 , , PUNCT fumecheng-4967 202 22 which which PRON fumecheng-4967 202 23 lowers lower VERB fumecheng-4967 202 24 the the DET fumecheng-4967 202 25 free free ADJ fumecheng-4967 202 26 energy energy NOUN fumecheng-4967 202 27 as as ADP fumecheng-4967 202 28 the the DET fumecheng-4967 202 29 new new ADJ fumecheng-4967 202 30 phase phase NOUN fumecheng-4967 202 31 forms form NOUN fumecheng-4967 202 32 . . PUNCT fumecheng-4967 203 1 226 226 NUM fumecheng-4967 203 2 a.e a.e PROPN fumecheng-4967 203 3 . . PROPN fumecheng-4967 203 4 filippov filippov PROPN fumecheng-4967 203 5 , , PUNCT fumecheng-4967 203 6 s.n s.n PROPN fumecheng-4967 203 7 . . PROPN fumecheng-4967 203 8 gorb gorb PROPN fumecheng-4967 203 9 the the DET fumecheng-4967 203 10 corresponding corresponding ADJ fumecheng-4967 203 11 local local ADJ fumecheng-4967 203 12 energy energy NOUN fumecheng-4967 203 13 density density NOUN fumecheng-4967 203 14 f(ρ f(ρ NOUN fumecheng-4967 203 15 ) ) PUNCT fumecheng-4967 203 16 must must AUX fumecheng-4967 203 17 have have VERB fumecheng-4967 203 18 a a DET fumecheng-4967 203 19 metastable metastable ADJ fumecheng-4967 203 20 minimum minimum NOUN fumecheng-4967 203 21 and and CCONJ fumecheng-4967 203 22 be be AUX fumecheng-4967 203 23 energetically energetically ADV fumecheng-4967 203 24 favorable favorable ADJ fumecheng-4967 203 25 . . PUNCT fumecheng-4967 204 1 however however ADV fumecheng-4967 204 2 , , PUNCT fumecheng-4967 204 3 the the DET fumecheng-4967 204 4 free free ADJ fumecheng-4967 204 5 energy energy NOUN fumecheng-4967 204 6 is be AUX fumecheng-4967 204 7 transformed transform VERB fumecheng-4967 204 8 due due ADP fumecheng-4967 204 9 to to ADP fumecheng-4967 204 10 the the DET fumecheng-4967 204 11 fluctuations fluctuation NOUN fumecheng-4967 204 12 . . PUNCT fumecheng-4967 205 1 this this DET fumecheng-4967 205 2 change change NOUN fumecheng-4967 205 3 is be AUX fumecheng-4967 205 4 especially especially ADV fumecheng-4967 205 5 essential essential ADJ fumecheng-4967 205 6 in in ADP fumecheng-4967 205 7 the the DET fumecheng-4967 205 8 critical critical ADJ fumecheng-4967 205 9 region region NOUN fumecheng-4967 205 10 at at ADP fumecheng-4967 205 11 a a DET fumecheng-4967 205 12 second second ADJ fumecheng-4967 205 13 - - PUNCT fumecheng-4967 205 14 order order NOUN fumecheng-4967 205 15 transition transition NOUN fumecheng-4967 205 16 . . PUNCT fumecheng-4967 206 1 it it PRON fumecheng-4967 206 2 is be AUX fumecheng-4967 206 3 well well ADV fumecheng-4967 206 4 known know VERB fumecheng-4967 206 5 from from ADP fumecheng-4967 206 6 the the DET fumecheng-4967 206 7 theory theory NOUN fumecheng-4967 206 8 of of ADP fumecheng-4967 206 9 critical critical ADJ fumecheng-4967 206 10 phenomena phenomenon NOUN fumecheng-4967 206 11 that that SCONJ fumecheng-4967 206 12 the the DET fumecheng-4967 206 13 fluctuations fluctuation NOUN fumecheng-4967 206 14 manifest manifest VERB fumecheng-4967 206 15 themselves themselves PRON fumecheng-4967 206 16 by by ADP fumecheng-4967 206 17 renormalization renormalization NOUN fumecheng-4967 206 18 of of ADP fumecheng-4967 206 19 critical critical ADJ fumecheng-4967 206 20 exponents exponent NOUN fumecheng-4967 206 21 . . PUNCT fumecheng-4967 207 1 but but CCONJ fumecheng-4967 207 2 , , PUNCT fumecheng-4967 207 3 the the DET fumecheng-4967 207 4 renormalization renormalization NOUN fumecheng-4967 207 5 group group NOUN fumecheng-4967 207 6 ( ( PUNCT fumecheng-4967 207 7 rg rg NOUN fumecheng-4967 207 8 ) ) PUNCT fumecheng-4967 207 9 method method NOUN fumecheng-4967 207 10 allows allow VERB fumecheng-4967 207 11 one one NUM fumecheng-4967 207 12 not not PART fumecheng-4967 207 13 only only ADV fumecheng-4967 207 14 to to PART fumecheng-4967 207 15 perform perform VERB fumecheng-4967 207 16 purely purely ADV fumecheng-4967 207 17 numerical numerical ADJ fumecheng-4967 207 18 calculations calculation NOUN fumecheng-4967 207 19 of of ADP fumecheng-4967 207 20 critical critical ADJ fumecheng-4967 207 21 exponents exponent NOUN fumecheng-4967 207 22 , , PUNCT fumecheng-4967 207 23 but but CCONJ fumecheng-4967 207 24 also also ADV fumecheng-4967 207 25 to to PART fumecheng-4967 207 26 predict predict VERB fumecheng-4967 207 27 some some DET fumecheng-4967 207 28 qualitatively qualitatively ADV fumecheng-4967 207 29 new new ADJ fumecheng-4967 207 30 effects effect NOUN fumecheng-4967 207 31 which which PRON fumecheng-4967 207 32 could could AUX fumecheng-4967 207 33 not not PART fumecheng-4967 207 34 be be AUX fumecheng-4967 207 35 obtained obtain VERB fumecheng-4967 207 36 within within ADP fumecheng-4967 207 37 conventional conventional ADJ fumecheng-4967 207 38 approaches approach NOUN fumecheng-4967 207 39 , , PUNCT fumecheng-4967 207 40 e.g. e.g. ADV fumecheng-4967 207 41 , , PUNCT fumecheng-4967 207 42 within within ADP fumecheng-4967 207 43 the the DET fumecheng-4967 207 44 landau landau NOUN fumecheng-4967 207 45 approximation approximation NOUN fumecheng-4967 207 46 , , PUNCT fumecheng-4967 207 47 applied apply VERB fumecheng-4967 207 48 above above ADV fumecheng-4967 207 49 . . PUNCT fumecheng-4967 208 1 among among ADP fumecheng-4967 208 2 them they PRON fumecheng-4967 208 3 , , PUNCT fumecheng-4967 208 4 there there PRON fumecheng-4967 208 5 are be VERB fumecheng-4967 208 6 qualitative qualitative ADJ fumecheng-4967 208 7 effects effect NOUN fumecheng-4967 208 8 , , PUNCT fumecheng-4967 208 9 such such ADJ fumecheng-4967 208 10 as as ADP fumecheng-4967 208 11 the the DET fumecheng-4967 208 12 fluctuation fluctuation NOUN fumecheng-4967 208 13 - - PUNCT fumecheng-4967 208 14 induced induce VERB fumecheng-4967 208 15 first first ADJ fumecheng-4967 208 16 - - PUNCT fumecheng-4967 208 17 order order NOUN fumecheng-4967 208 18 phase phase NOUN fumecheng-4967 208 19 transition transition NOUN fumecheng-4967 208 20 . . PUNCT fumecheng-4967 209 1 this this DET fumecheng-4967 209 2 effect effect NOUN fumecheng-4967 209 3 takes take VERB fumecheng-4967 209 4 place place NOUN fumecheng-4967 209 5 in in ADP fumecheng-4967 209 6 some some DET fumecheng-4967 209 7 anisotropic anisotropic NOUN fumecheng-4967 209 8 systems system NOUN fumecheng-4967 209 9 , , PUNCT fumecheng-4967 209 10 where where SCONJ fumecheng-4967 209 11 the the DET fumecheng-4967 209 12 renormalized renormalize VERB fumecheng-4967 209 13 free free ADJ fumecheng-4967 209 14 energy energy NOUN fumecheng-4967 209 15 f(ρ f(ρ NOUN fumecheng-4967 209 16 ) ) PUNCT fumecheng-4967 209 17 undergoes undergoe NOUN fumecheng-4967 209 18 transformations transformation NOUN fumecheng-4967 209 19 , , PUNCT fumecheng-4967 209 20 which which PRON fumecheng-4967 209 21 are be AUX fumecheng-4967 209 22 typical typical ADJ fumecheng-4967 209 23 for for ADP fumecheng-4967 209 24 the the DET fumecheng-4967 209 25 first first ADJ fumecheng-4967 209 26 - - PUNCT fumecheng-4967 209 27 order order NOUN fumecheng-4967 209 28 phase phase NOUN fumecheng-4967 209 29 transition transition NOUN fumecheng-4967 209 30 . . PUNCT fumecheng-4967 210 1 the the DET fumecheng-4967 210 2 same same ADJ fumecheng-4967 210 3 kind kind NOUN fumecheng-4967 210 4 of of ADP fumecheng-4967 210 5 the the DET fumecheng-4967 210 6 nucleation nucleation NOUN fumecheng-4967 210 7 centers center NOUN fumecheng-4967 210 8 can can AUX fumecheng-4967 210 9 be be AUX fumecheng-4967 210 10 found find VERB fumecheng-4967 210 11 in in ADP fumecheng-4967 210 12 a a DET fumecheng-4967 210 13 fluctuation fluctuation NOUN fumecheng-4967 210 14 - - PUNCT fumecheng-4967 210 15 induced induce VERB fumecheng-4967 210 16 first first ADJ fumecheng-4967 210 17 order order NOUN fumecheng-4967 210 18 transition transition NOUN fumecheng-4967 210 19 . . PUNCT fumecheng-4967 211 1 however however ADV fumecheng-4967 211 2 , , PUNCT fumecheng-4967 211 3 one one PRON fumecheng-4967 211 4 can can AUX fumecheng-4967 211 5 expect expect VERB fumecheng-4967 211 6 that that SCONJ fumecheng-4967 211 7 even even ADV fumecheng-4967 211 8 in in ADP fumecheng-4967 211 9 the the DET fumecheng-4967 211 10 situation situation NOUN fumecheng-4967 211 11 , , PUNCT fumecheng-4967 211 12 when when SCONJ fumecheng-4967 211 13 the the DET fumecheng-4967 211 14 fluctuations fluctuation NOUN fumecheng-4967 211 15 are be AUX fumecheng-4967 211 16 not not PART fumecheng-4967 211 17 strong strong ADJ fumecheng-4967 211 18 enough enough ADV fumecheng-4967 211 19 to to PART fumecheng-4967 211 20 change change VERB fumecheng-4967 211 21 the the DET fumecheng-4967 211 22 transition transition NOUN fumecheng-4967 211 23 order order NOUN fumecheng-4967 211 24 , , PUNCT fumecheng-4967 211 25 they they PRON fumecheng-4967 211 26 manifest manifest VERB fumecheng-4967 211 27 themselves themselves PRON fumecheng-4967 211 28 somehow somehow ADV fumecheng-4967 211 29 . . PUNCT fumecheng-4967 212 1 the the DET fumecheng-4967 212 2 mean mean ADJ fumecheng-4967 212 3 field field NOUN fumecheng-4967 212 4 model model NOUN fumecheng-4967 212 5 is be AUX fumecheng-4967 212 6 very very ADV fumecheng-4967 212 7 convenient convenient ADJ fumecheng-4967 212 8 for for ADP fumecheng-4967 212 9 analytical analytical ADJ fumecheng-4967 212 10 study study NOUN fumecheng-4967 212 11 , , PUNCT fumecheng-4967 212 12 but but CCONJ fumecheng-4967 212 13 it it PRON fumecheng-4967 212 14 reduces reduce VERB fumecheng-4967 212 15 the the DET fumecheng-4967 212 16 fluctuation fluctuation NOUN fumecheng-4967 212 17 interaction interaction NOUN fumecheng-4967 212 18 , , PUNCT fumecheng-4967 212 19 and and CCONJ fumecheng-4967 212 20 it it PRON fumecheng-4967 212 21 is be AUX fumecheng-4967 212 22 impossible impossible ADJ fumecheng-4967 212 23 to to PART fumecheng-4967 212 24 control control VERB fumecheng-4967 212 25 a a DET fumecheng-4967 212 26 correction correction NOUN fumecheng-4967 212 27 which which PRON fumecheng-4967 212 28 should should AUX fumecheng-4967 212 29 be be AUX fumecheng-4967 212 30 done do VERB fumecheng-4967 212 31 to to ADP fumecheng-4967 212 32 the the DET fumecheng-4967 212 33 free free ADJ fumecheng-4967 212 34 energy energy NOUN fumecheng-4967 212 35 with with ADP fumecheng-4967 212 36 account account NOUN fumecheng-4967 212 37 of of ADP fumecheng-4967 212 38 the the DET fumecheng-4967 212 39 neglected neglect VERB fumecheng-4967 212 40 fluctuations fluctuation NOUN fumecheng-4967 212 41 [ [ X fumecheng-4967 212 42 8 8 NUM fumecheng-4967 212 43 ] ] PUNCT fumecheng-4967 212 44 . . PUNCT fumecheng-4967 213 1 a a DET fumecheng-4967 213 2 more more ADV fumecheng-4967 213 3 correct correct ADJ fumecheng-4967 213 4 approach approach NOUN fumecheng-4967 213 5 was be AUX fumecheng-4967 213 6 developed develop VERB fumecheng-4967 213 7 almost almost ADV fumecheng-4967 213 8 50 50 NUM fumecheng-4967 213 9 years year NOUN fumecheng-4967 213 10 ago ago ADV fumecheng-4967 213 11 . . PUNCT fumecheng-4967 214 1 it it PRON fumecheng-4967 214 2 states state VERB fumecheng-4967 214 3 that that SCONJ fumecheng-4967 214 4 the the DET fumecheng-4967 214 5 fluctuations fluctuation NOUN fumecheng-4967 214 6 renormalize renormalize VERB fumecheng-4967 214 7 energy energy NOUN fumecheng-4967 214 8 functional functional ADJ fumecheng-4967 214 9 φ[ρ(x φ[ρ(x NUM fumecheng-4967 214 10 , , PUNCT fumecheng-4967 214 11 t t PROPN fumecheng-4967 214 12 ) ) PUNCT fumecheng-4967 214 13 ] ] PUNCT fumecheng-4967 214 14 according accord VERB fumecheng-4967 214 15 to to ADP fumecheng-4967 214 16 so so ADV fumecheng-4967 214 17 - - PUNCT fumecheng-4967 214 18 called call VERB fumecheng-4967 214 19 renormalization renormalization NOUN fumecheng-4967 214 20 group group NOUN fumecheng-4967 214 21 ( ( PUNCT fumecheng-4967 214 22 rg rg NOUN fumecheng-4967 214 23 ) ) PUNCT fumecheng-4967 214 24 equation equation NOUN fumecheng-4967 214 25 ˆ/ ˆ/ ADP fumecheng-4967 214 26 l l PROPN fumecheng-4967 214 27 r r PROPN fumecheng-4967 214 28   ADJ fumecheng-4967 214 29   ADJ fumecheng-4967 214 30   PROPN fumecheng-4967 214 31 . . PUNCT fumecheng-4967 215 1 here here ADV fumecheng-4967 215 2 we we PRON fumecheng-4967 215 3 do do AUX fumecheng-4967 215 4 not not PART fumecheng-4967 215 5 need need VERB fumecheng-4967 215 6 the the DET fumecheng-4967 215 7 complex complex ADJ fumecheng-4967 215 8 exact exact ADJ fumecheng-4967 215 9 form form NOUN fumecheng-4967 215 10 of of ADP fumecheng-4967 215 11 the the DET fumecheng-4967 215 12 rg rg NOUN fumecheng-4967 215 13 equation equation NOUN fumecheng-4967 215 14 and and CCONJ fumecheng-4967 215 15 use use VERB fumecheng-4967 215 16 its its PRON fumecheng-4967 215 17 simplified simplified ADJ fumecheng-4967 215 18 approximate approximate ADJ fumecheng-4967 215 19 version version NOUN fumecheng-4967 215 20 : : PUNCT fumecheng-4967 215 21 2 2 NUM fumecheng-4967 215 22 ( ( PUNCT fumecheng-4967 215 23 ) ) PUNCT fumecheng-4967 215 24 ˆ ˆ NOUN fumecheng-4967 215 25 [ [ X fumecheng-4967 215 26 ( ( PUNCT fumecheng-4967 215 27 2 2 NUM fumecheng-4967 215 28 ) ) PUNCT fumecheng-4967 215 29 ( ( PUNCT fumecheng-4967 215 30 ) ) PUNCT fumecheng-4967 215 31 ] ] X fumecheng-4967 215 32 ' ' PUNCT fumecheng-4967 215 33 2 2 NUM fumecheng-4967 215 34 ( ( PUNCT fumecheng-4967 215 35 ) ) PUNCT fumecheng-4967 215 36 ( ( PUNCT fumecheng-4967 215 37 ) ) PUNCT fumecheng-4967 215 38 ( ( PUNCT fumecheng-4967 215 39 ' ' PUNCT fumecheng-4967 215 40 ) ) PUNCT fumecheng-4967 215 41 ( ( PUNCT fumecheng-4967 215 42 ) ) PUNCT fumecheng-4967 215 43 ( ( PUNCT fumecheng-4967 215 44 ' ' NUM fumecheng-4967 215 45 ) ) PUNCT fumecheng-4967 216 1 d d PUNCT fumecheng-4967 217 1 d d NOUN fumecheng-4967 217 2 r r NOUN fumecheng-4967 217 3 r r NOUN fumecheng-4967 217 4 r r NOUN fumecheng-4967 217 5 d d NOUN fumecheng-4967 217 6 r r NOUN fumecheng-4967 218 1 d d NOUN fumecheng-4967 218 2 r r NOUN fumecheng-4967 218 3 r r NOUN fumecheng-4967 218 4 d d NOUN fumecheng-4967 218 5 r r NOUN fumecheng-4967 218 6 r r NOUN fumecheng-4967 218 7 r r NOUN fumecheng-4967 218 8 r r NOUN fumecheng-4967 218 9 r r NOUN fumecheng-4967 218 10 r r NOUN fumecheng-4967 218 11   NOUN fumecheng-4967 218 12   VERB fumecheng-4967 218 13   NOUN fumecheng-4967 219 1   NOUN fumecheng-4967 219 2   NOUN fumecheng-4967 219 3   NOUN fumecheng-4967 219 4   NUM fumecheng-4967 219 5   PROPN fumecheng-4967 219 6   PROPN fumecheng-4967 219 7   PROPN fumecheng-4967 219 8   PROPN fumecheng-4967 219 9   ADV fumecheng-4967 219 10   NOUN fumecheng-4967 219 11   PUNCT fumecheng-4967 219 12   NOUN fumecheng-4967 219 13   VERB fumecheng-4967 219 14   NOUN fumecheng-4967 219 15   NUM fumecheng-4967 219 16   NOUN fumecheng-4967 219 17   ADJ fumecheng-4967 219 18   NOUN fumecheng-4967 219 19   X fumecheng-4967 219 20   PUNCT fumecheng-4967 219 21   ADP fumecheng-4967 219 22   NUM fumecheng-4967 219 23   NUM fumecheng-4967 219 24   PROPN fumecheng-4967 219 25   NUM fumecheng-4967 219 26   ADP fumecheng-4967 219 27   NUM fumecheng-4967 219 28   NUM fumecheng-4967 219 29   NUM fumecheng-4967 219 30   PROPN fumecheng-4967 219 31   PROPN fumecheng-4967 219 32 ( ( PUNCT fumecheng-4967 219 33 16 16 NUM fumecheng-4967 219 34 ) ) PUNCT fumecheng-4967 219 35 where where SCONJ fumecheng-4967 219 36 d d NOUN fumecheng-4967 219 37 is be AUX fumecheng-4967 219 38 the the DET fumecheng-4967 219 39 space space NOUN fumecheng-4967 219 40 dimensionality dimensionality NOUN fumecheng-4967 219 41 . . PUNCT fumecheng-4967 220 1 the the DET fumecheng-4967 220 2 first first ADJ fumecheng-4967 220 3 term term NOUN fumecheng-4967 220 4 in in ADP fumecheng-4967 220 5 eq eq ADP fumecheng-4967 220 6 . . PUNCT fumecheng-4967 221 1 ( ( PUNCT fumecheng-4967 221 2 16 16 NUM fumecheng-4967 221 3 ) ) PUNCT fumecheng-4967 221 4 corresponds correspond VERB fumecheng-4967 221 5 to to ADP fumecheng-4967 221 6 a a DET fumecheng-4967 221 7 simple simple ADJ fumecheng-4967 221 8 scale scale NOUN fumecheng-4967 221 9 transformation transformation NOUN fumecheng-4967 221 10 of of ADP fumecheng-4967 221 11 the the DET fumecheng-4967 221 12 density density NOUN fumecheng-4967 221 13 distribution distribution NOUN fumecheng-4967 221 14 ρ(x ρ(x PROPN fumecheng-4967 221 15 , , PUNCT fumecheng-4967 221 16 t t PROPN fumecheng-4967 221 17 ) ) PUNCT fumecheng-4967 221 18 and and CCONJ fumecheng-4967 221 19 the the DET fumecheng-4967 221 20 second second ADJ fumecheng-4967 221 21 term term NOUN fumecheng-4967 221 22 appears appear VERB fumecheng-4967 221 23 due due ADJ fumecheng-4967 221 24 to to ADP fumecheng-4967 221 25 the the DET fumecheng-4967 221 26 integration integration NOUN fumecheng-4967 221 27 over over ADP fumecheng-4967 221 28 internal internal ADJ fumecheng-4967 221 29 fluctuations fluctuation NOUN fumecheng-4967 221 30 inside inside ADP fumecheng-4967 221 31 small small ADJ fumecheng-4967 221 32 regions region NOUN fumecheng-4967 221 33 after after ADP fumecheng-4967 221 34 scale scale NOUN fumecheng-4967 221 35 transformations transformation NOUN fumecheng-4967 221 36 . . PUNCT fumecheng-4967 222 1 according accord VERB fumecheng-4967 222 2 to to ADP fumecheng-4967 222 3 the the DET fumecheng-4967 222 4 general general ADJ fumecheng-4967 222 5 rg rg PROPN fumecheng-4967 222 6 hypothesis hypothesis NOUN fumecheng-4967 222 7 in in ADP fumecheng-4967 222 8 critical critical ADJ fumecheng-4967 222 9 point point NOUN fumecheng-4967 222 10 of of ADP fumecheng-4967 222 11 the the DET fumecheng-4967 222 12 phase phase NOUN fumecheng-4967 222 13 transition transition NOUN fumecheng-4967 222 14 ( ( PUNCT fumecheng-4967 222 15 exactly exactly ADV fumecheng-4967 222 16 , , PUNCT fumecheng-4967 222 17 where where SCONJ fumecheng-4967 222 18 the the DET fumecheng-4967 222 19 ordering ordering NOUN fumecheng-4967 222 20 of of ADP fumecheng-4967 222 21 ρ(x ρ(x PROPN fumecheng-4967 222 22 , , PUNCT fumecheng-4967 222 23 t t PROPN fumecheng-4967 222 24 ) ) PUNCT fumecheng-4967 222 25 takes take VERB fumecheng-4967 222 26 place place NOUN fumecheng-4967 222 27 ) ) PUNCT fumecheng-4967 222 28 the the DET fumecheng-4967 222 29 functional functional ADJ fumecheng-4967 222 30 φ→φ φ→φ NOUN fumecheng-4967 222 31 * * PUNCT fumecheng-4967 222 32 tends tend VERB fumecheng-4967 222 33 to to ADP fumecheng-4967 222 34 the the DET fumecheng-4967 222 35 fixed fixed ADJ fumecheng-4967 222 36 point point NOUN fumecheng-4967 222 37 * * PUNCT fumecheng-4967 223 1 * * PUNCT fumecheng-4967 223 2 ˆ/ ˆ/ ADP fumecheng-4967 223 3 0l 0l X fumecheng-4967 223 4 r r PROPN fumecheng-4967 223 5   PROPN fumecheng-4967 223 6   NUM fumecheng-4967 223 7   NUM fumecheng-4967 223 8   INTJ fumecheng-4967 223 9 . . PUNCT fumecheng-4967 224 1 let let VERB fumecheng-4967 224 2 us we PRON fumecheng-4967 224 3 study study VERB fumecheng-4967 224 4 now now ADV fumecheng-4967 224 5 the the DET fumecheng-4967 224 6 time time NOUN fumecheng-4967 224 7 - - PUNCT fumecheng-4967 224 8 space space NOUN fumecheng-4967 224 9 evolution evolution NOUN fumecheng-4967 224 10 of of ADP fumecheng-4967 224 11 fluctuating fluctuate VERB fumecheng-4967 224 12 density density NOUN fumecheng-4967 224 13 ρ(x ρ(x PROPN fumecheng-4967 224 14 , , PUNCT fumecheng-4967 224 15 t t PROPN fumecheng-4967 224 16 ) ) PUNCT fumecheng-4967 224 17 in in ADP fumecheng-4967 224 18 this this DET fumecheng-4967 224 19 state state NOUN fumecheng-4967 224 20 . . PUNCT fumecheng-4967 225 1 we we PRON fumecheng-4967 225 2 plan plan VERB fumecheng-4967 225 3 to to PART fumecheng-4967 225 4 show show VERB fumecheng-4967 225 5 that that SCONJ fumecheng-4967 225 6 ρ(x ρ(x NOUN fumecheng-4967 225 7 , , PUNCT fumecheng-4967 225 8 t t PROPN fumecheng-4967 225 9 ) ) PUNCT fumecheng-4967 225 10 produces produce VERB fumecheng-4967 225 11 a a DET fumecheng-4967 225 12 well well ADV fumecheng-4967 225 13 - - PUNCT fumecheng-4967 225 14 pronounced pronounce VERB fumecheng-4967 225 15 large large ADJ fumecheng-4967 225 16 - - PUNCT fumecheng-4967 225 17 scale scale NOUN fumecheng-4967 225 18 structure structure NOUN fumecheng-4967 225 19 in in ADP fumecheng-4967 225 20 spite spite NOUN fumecheng-4967 225 21 of of ADP fumecheng-4967 225 22 its its PRON fumecheng-4967 225 23 scale scale NOUN fumecheng-4967 225 24 invariance invariance NOUN fumecheng-4967 225 25 on on ADP fumecheng-4967 225 26 average average ADJ fumecheng-4967 225 27 . . PUNCT fumecheng-4967 226 1 as as SCONJ fumecheng-4967 226 2 always always ADV fumecheng-4967 226 3 kinetic kinetic ADJ fumecheng-4967 226 4 equation equation NOUN fumecheng-4967 226 5 can can AUX fumecheng-4967 226 6 be be AUX fumecheng-4967 226 7 written write VERB fumecheng-4967 226 8 in in ADP fumecheng-4967 226 9 the the DET fumecheng-4967 226 10 form form NOUN fumecheng-4967 226 11 : : PUNCT fumecheng-4967 226 12 ∂ρ/∂t=−γδφ*[ρ]/δρ+δ ∂ρ/∂t=−γδφ*[ρ]/δρ+δ PROPN fumecheng-4967 226 13 . . PUNCT fumecheng-4967 227 1 at at ADP fumecheng-4967 227 2 every every DET fumecheng-4967 227 3 time time NOUN fumecheng-4967 227 4 moment moment NOUN fumecheng-4967 227 5 , , PUNCT fumecheng-4967 227 6 average average ADJ fumecheng-4967 227 7 probability probability NOUN fumecheng-4967 227 8 w= > X fumecheng-4967 227 11 to to PART fumecheng-4967 227 12 find find VERB fumecheng-4967 227 13 density density NOUN fumecheng-4967 227 14 distribution distribution NOUN fumecheng-4967 227 15 ρ(x ρ(x NOUN fumecheng-4967 227 16 , , PUNCT fumecheng-4967 227 17 t t PROPN fumecheng-4967 227 18 ) ) PUNCT fumecheng-4967 227 19 is be AUX fumecheng-4967 227 20 determined determine VERB fumecheng-4967 227 21 by by ADP fumecheng-4967 227 22 functional functional ADJ fumecheng-4967 227 23 w[ρ]=exp(−φ[ρ w[ρ]=exp(−φ[ρ NOUN fumecheng-4967 227 24 ] ] PUNCT fumecheng-4967 227 25 ) ) PUNCT fumecheng-4967 227 26 . . PUNCT fumecheng-4967 228 1 this this DET fumecheng-4967 228 2 probability probability NOUN fumecheng-4967 228 3 develops develop VERB fumecheng-4967 228 4 with with ADP fumecheng-4967 228 5 time time NOUN fumecheng-4967 228 6 according accord VERB fumecheng-4967 228 7 to to ADP fumecheng-4967 228 8 the the DET fumecheng-4967 228 9 equation equation NOUN fumecheng-4967 228 10 : : PUNCT fumecheng-4967 228 11 [ [ PUNCT fumecheng-4967 228 12 ] ] X fumecheng-4967 228 13 / / PUNCT fumecheng-4967 228 14 /d /d PUNCT fumecheng-4967 228 15 w w PROPN fumecheng-4967 228 16 w w PROPN fumecheng-4967 228 17 t t PROPN fumecheng-4967 229 1 d d X fumecheng-4967 229 2 r r NOUN fumecheng-4967 229 3 t t NUM fumecheng-4967 229 4   ADJ fumecheng-4967 229 5   ADJ fumecheng-4967 229 6   ADJ fumecheng-4967 229 7   ADJ fumecheng-4967 229 8   PROPN fumecheng-4967 229 9   NUM fumecheng-4967 229 10   NOUN fumecheng-4967 229 11   ADP fumecheng-4967 229 12   VERB fumecheng-4967 229 13 . . PUNCT fumecheng-4967 230 1 ( ( PUNCT fumecheng-4967 230 2 17 17 NUM fumecheng-4967 230 3 ) ) PUNCT fumecheng-4967 230 4 by by ADP fumecheng-4967 230 5 combining combine VERB fumecheng-4967 230 6 eq eq ADP fumecheng-4967 230 7 . . PUNCT fumecheng-4967 231 1 ( ( PUNCT fumecheng-4967 231 2 16 16 NUM fumecheng-4967 231 3 ) ) PUNCT fumecheng-4967 231 4 with with ADP fumecheng-4967 231 5 condition condition NOUN fumecheng-4967 231 6 * * NOUN fumecheng-4967 231 7 ˆ ˆ ADJ fumecheng-4967 231 8 0r 0r PROPN fumecheng-4967 231 9   PROPN fumecheng-4967 231 10 and and CCONJ fumecheng-4967 231 11 ∂ρ/∂t=−γδφ*[ρ]/δρ+δ ∂ρ/∂t=−γδφ*[ρ]/δρ+δ PROPN fumecheng-4967 231 12 , , PUNCT fumecheng-4967 231 13 one one PRON fumecheng-4967 231 14 can can AUX fumecheng-4967 231 15 obtain obtain VERB fumecheng-4967 231 16 that that PRON fumecheng-4967 231 17 in in ADP fumecheng-4967 231 18 the the DET fumecheng-4967 231 19 critical critical ADJ fumecheng-4967 231 20 point point NOUN fumecheng-4967 231 21 time time NOUN fumecheng-4967 231 22 the the DET fumecheng-4967 231 23 evolution evolution NOUN fumecheng-4967 231 24 of of ADP fumecheng-4967 231 25 probability probability NOUN fumecheng-4967 231 26 w= > X fumecheng-4967 231 29 is be AUX fumecheng-4967 231 30 reduced reduce VERB fumecheng-4967 231 31 to to ADP fumecheng-4967 231 32 the the DET fumecheng-4967 231 33 simple simple ADJ fumecheng-4967 231 34 scale scale NOUN fumecheng-4967 231 35 transformation transformation NOUN fumecheng-4967 231 36 : : PUNCT fumecheng-4967 232 1 * * PUNCT fumecheng-4967 232 2 / / PUNCT fumecheng-4967 233 1 [ [ PUNCT fumecheng-4967 233 2 ] ] X fumecheng-4967 233 3 [ [ X fumecheng-4967 233 4 ( ( PUNCT fumecheng-4967 233 5 2 2 NUM fumecheng-4967 233 6 ) ) PUNCT fumecheng-4967 233 7 ] ] PUNCT fumecheng-4967 234 1 2 2 NUM fumecheng-4967 234 2 d d X fumecheng-4967 234 3 rw rw PROPN fumecheng-4967 234 4 t t PROPN fumecheng-4967 234 5 w w PROPN fumecheng-4967 234 6 d d NOUN fumecheng-4967 234 7 r r NOUN fumecheng-4967 234 8 d d NOUN fumecheng-4967 234 9 r r NOUN fumecheng-4967 234 10   PROPN fumecheng-4967 234 11   ADJ fumecheng-4967 234 12   ADJ fumecheng-4967 234 13   ADJ fumecheng-4967 234 14   NOUN fumecheng-4967 234 15   PUNCT fumecheng-4967 234 16   NOUN fumecheng-4967 234 17   PROPN fumecheng-4967 234 18   ADP fumecheng-4967 234 19   NUM fumecheng-4967 234 20   NOUN fumecheng-4967 234 21   ADP fumecheng-4967 234 22   PROPN fumecheng-4967 234 23 ( ( PUNCT fumecheng-4967 234 24 18 18 NUM fumecheng-4967 234 25 ) ) PUNCT fumecheng-4967 234 26 methods method NOUN fumecheng-4967 234 27 of of ADP fumecheng-4967 234 28 the the DET fumecheng-4967 234 29 pattern pattern NOUN fumecheng-4967 234 30 formation formation NOUN fumecheng-4967 234 31 in in ADP fumecheng-4967 234 32 numerical numerical ADJ fumecheng-4967 234 33 modeling modeling NOUN fumecheng-4967 234 34 of of ADP fumecheng-4967 234 35 biological biological ADJ fumecheng-4967 234 36 problems problem NOUN fumecheng-4967 235 1 227 227 NUM fumecheng-4967 235 2 physically physically ADV fumecheng-4967 235 3 it it PRON fumecheng-4967 235 4 means mean VERB fumecheng-4967 235 5 the the DET fumecheng-4967 235 6 following following NOUN fumecheng-4967 235 7 : : PUNCT fumecheng-4967 235 8 at at ADP fumecheng-4967 235 9 the the DET fumecheng-4967 235 10 point point NOUN fumecheng-4967 235 11 of of ADP fumecheng-4967 235 12 the the DET fumecheng-4967 235 13 transition transition NOUN fumecheng-4967 235 14 energy energy NOUN fumecheng-4967 235 15 , , PUNCT fumecheng-4967 235 16 the the DET fumecheng-4967 235 17 functional functional ADJ fumecheng-4967 235 18 becomes become VERB fumecheng-4967 235 19 the the DET fumecheng-4967 235 20 universal universal ADJ fumecheng-4967 235 21 one one NOUN fumecheng-4967 235 22 φ→φ φ→φ NUM fumecheng-4967 235 23 * * PUNCT fumecheng-4967 235 24 . . PUNCT fumecheng-4967 236 1 the the DET fumecheng-4967 236 2 kinetic kinetic ADJ fumecheng-4967 236 3 equation equation NOUN fumecheng-4967 236 4 based base VERB fumecheng-4967 236 5 on on ADP fumecheng-4967 236 6 this this DET fumecheng-4967 236 7 functional functional ADJ fumecheng-4967 236 8 produces produce NOUN fumecheng-4967 236 9 with with ADP fumecheng-4967 236 10 time time NOUN fumecheng-4967 236 11 new new ADJ fumecheng-4967 236 12 realizations realization NOUN fumecheng-4967 236 13 of of ADP fumecheng-4967 236 14 ρ(r ρ(r PROPN fumecheng-4967 236 15 , , PUNCT fumecheng-4967 236 16 t t PROPN fumecheng-4967 236 17 ) ) PUNCT fumecheng-4967 236 18 with with ADP fumecheng-4967 236 19 the the DET fumecheng-4967 236 20 same same ADJ fumecheng-4967 236 21 statistical statistical ADJ fumecheng-4967 236 22 properties property NOUN fumecheng-4967 236 23 , , PUNCT fumecheng-4967 236 24 but but CCONJ fumecheng-4967 236 25 larger large ADJ fumecheng-4967 236 26 scales scale NOUN fumecheng-4967 236 27 . . PUNCT fumecheng-4967 237 1 in in ADP fumecheng-4967 237 2 the the DET fumecheng-4967 237 3 limit limit NOUN fumecheng-4967 237 4 t→∞ t→∞ ADP fumecheng-4967 237 5 , , PUNCT fumecheng-4967 237 6 the the DET fumecheng-4967 237 7 structure structure NOUN fumecheng-4967 237 8 becomes become VERB fumecheng-4967 237 9 scale scale NOUN fumecheng-4967 237 10 invariant invariant ADJ fumecheng-4967 237 11 . . PUNCT fumecheng-4967 238 1 this this DET fumecheng-4967 238 2 structure structure NOUN fumecheng-4967 238 3 is be AUX fumecheng-4967 238 4 generally generally ADV fumecheng-4967 238 5 similar similar ADJ fumecheng-4967 238 6 to to ADP fumecheng-4967 238 7 that that PRON fumecheng-4967 238 8 found find VERB fumecheng-4967 238 9 in in ADP fumecheng-4967 238 10 the the DET fumecheng-4967 238 11 intermediate intermediate ADJ fumecheng-4967 238 12 stage stage NOUN fumecheng-4967 238 13 of of ADP fumecheng-4967 238 14 the the DET fumecheng-4967 238 15 nucleation nucleation NOUN fumecheng-4967 238 16 process process NOUN fumecheng-4967 238 17 at at ADP fumecheng-4967 238 18 firstorder firstorder NOUN fumecheng-4967 238 19 phase phase NOUN fumecheng-4967 238 20 transitions transition NOUN fumecheng-4967 238 21 , , PUNCT fumecheng-4967 238 22 but but CCONJ fumecheng-4967 238 23 it it PRON fumecheng-4967 238 24 never never ADV fumecheng-4967 238 25 finishes finish VERB fumecheng-4967 238 26 in in ADP fumecheng-4967 238 27 static static ADJ fumecheng-4967 238 28 ordering ordering NOUN fumecheng-4967 238 29 . . PUNCT fumecheng-4967 239 1 to to PART fumecheng-4967 239 2 calculate calculate VERB fumecheng-4967 239 3 practically practically ADV fumecheng-4967 239 4 some some DET fumecheng-4967 239 5 particular particular ADJ fumecheng-4967 239 6 realization realization NOUN fumecheng-4967 239 7 of of ADP fumecheng-4967 239 8 the the DET fumecheng-4967 239 9 density density NOUN fumecheng-4967 239 10 in in ADP fumecheng-4967 239 11 the the DET fumecheng-4967 239 12 critical critical ADJ fumecheng-4967 239 13 point point NOUN fumecheng-4967 239 14 , , PUNCT fumecheng-4967 239 15 one one PRON fumecheng-4967 239 16 can can AUX fumecheng-4967 239 17 solve solve VERB fumecheng-4967 239 18 numerically numerically ADV fumecheng-4967 239 19 equation equation NOUN fumecheng-4967 239 20 ∂ρ/∂t=−γδφ*[ρ]/δρ+δ ∂ρ/∂t=−γδφ*[ρ]/δρ+δ PROPN fumecheng-4967 239 21 with with ADP fumecheng-4967 239 22 the the DET fumecheng-4967 239 23 energy energy NOUN fumecheng-4967 239 24 density density NOUN fumecheng-4967 239 25 found find VERB fumecheng-4967 239 26 from from ADP fumecheng-4967 239 27 the the DET fumecheng-4967 239 28 rg rg PROPN fumecheng-4967 239 29 equation equation NOUN fumecheng-4967 239 30 in in ADP fumecheng-4967 239 31 its its PRON fumecheng-4967 239 32 local local ADJ fumecheng-4967 239 33 approximation approximation NOUN fumecheng-4967 239 34 : : PUNCT fumecheng-4967 239 35 2 2 NUM fumecheng-4967 239 36 [ [ PUNCT fumecheng-4967 239 37 ( ( PUNCT fumecheng-4967 239 38 ) ) PUNCT fumecheng-4967 239 39 ] ] PUNCT fumecheng-4967 240 1 [ [ PUNCT fumecheng-4967 240 2 ( ( PUNCT fumecheng-4967 240 3 ) ) PUNCT fumecheng-4967 240 4 ( ( PUNCT fumecheng-4967 240 5 ) ) PUNCT fumecheng-4967 240 6 ] ] PUNCT fumecheng-4967 240 7 2 2 NUM fumecheng-4967 240 8 c c NOUN fumecheng-4967 240 9 x x X fumecheng-4967 240 10 dx dx PROPN fumecheng-4967 240 11 f f PROPN fumecheng-4967 240 12   PUNCT fumecheng-4967 240 13   PROPN fumecheng-4967 240 14   AUX fumecheng-4967 240 15   ADP fumecheng-4967 240 16   X fumecheng-4967 240 17 , , PUNCT fumecheng-4967 240 18 ( ( PUNCT fumecheng-4967 240 19 19 19 NUM fumecheng-4967 240 20 ) ) PUNCT fumecheng-4967 240 21 where where SCONJ fumecheng-4967 240 22 ( ( PUNCT fumecheng-4967 240 23 ) ) PUNCT fumecheng-4967 240 24 f f PROPN fumecheng-4967 240 25   NOUN fumecheng-4967 240 26 is be AUX fumecheng-4967 240 27 normalized normalize VERB fumecheng-4967 240 28 to to ADP fumecheng-4967 240 29 the the DET fumecheng-4967 240 30 critical critical ADJ fumecheng-4967 240 31 temperature temperature NOUN fumecheng-4967 240 32 * * PUNCT fumecheng-4967 240 33 2 2 NUM fumecheng-4967 240 34 ( ( PUNCT fumecheng-4967 240 35 ) ) PUNCT fumecheng-4967 240 36 ( ( PUNCT fumecheng-4967 240 37 0)f 0)f PROPN fumecheng-4967 240 38 f f PROPN fumecheng-4967 240 39 f f PROPN fumecheng-4967 240 40   PROPN fumecheng-4967 240 41   PROPN fumecheng-4967 240 42   PROPN fumecheng-4967 240 43   NOUN fumecheng-4967 240 44   ADV fumecheng-4967 240 45   ADP fumecheng-4967 240 46 solution solution NOUN fumecheng-4967 240 47 of of ADP fumecheng-4967 240 48 the the DET fumecheng-4967 240 49 local local ADJ fumecheng-4967 240 50 version version NOUN fumecheng-4967 240 51 of of ADP fumecheng-4967 240 52 rg rg PRON fumecheng-4967 240 53 equation equation NOUN fumecheng-4967 240 54 * * PUNCT fumecheng-4967 241 1 ˆ ˆ X fumecheng-4967 241 2 0r 0r PROPN fumecheng-4967 241 3   NUM fumecheng-4967 241 4 : : PUNCT fumecheng-4967 241 5 22 22 NUM fumecheng-4967 241 6 2 2 NUM fumecheng-4967 241 7 2ˆ 2ˆ NOUN fumecheng-4967 241 8 0 0 NUM fumecheng-4967 241 9 2 2 NUM fumecheng-4967 242 1 d d NOUN fumecheng-4967 242 2 f f X fumecheng-4967 242 3 f f PROPN fumecheng-4967 242 4 f f PROPN fumecheng-4967 242 5 rf rf PROPN fumecheng-4967 242 6 df df PROPN fumecheng-4967 242 7   NOUN fumecheng-4967 242 8   VERB fumecheng-4967 242 9   ADJ fumecheng-4967 242 10   ADJ fumecheng-4967 242 11   PROPN fumecheng-4967 242 12   PROPN fumecheng-4967 242 13   PROPN fumecheng-4967 242 14   VERB fumecheng-4967 242 15   X fumecheng-4967 242 16   PUNCT fumecheng-4967 242 17   PROPN fumecheng-4967 242 18   PROPN fumecheng-4967 242 19   PROPN fumecheng-4967 242 20   PROPN fumecheng-4967 242 21   NOUN fumecheng-4967 242 22   ADV fumecheng-4967 242 23   ADP fumecheng-4967 242 24   PROPN fumecheng-4967 242 25 ( ( PUNCT fumecheng-4967 242 26 20 20 NUM fumecheng-4967 242 27 ) ) PUNCT fumecheng-4967 242 28 despite despite SCONJ fumecheng-4967 242 29 of of ADP fumecheng-4967 242 30 its its PRON fumecheng-4967 242 31 visual visual ADJ fumecheng-4967 242 32 simplicity simplicity NOUN fumecheng-4967 242 33 , , PUNCT fumecheng-4967 242 34 eq eq NOUN fumecheng-4967 242 35 . . PUNCT fumecheng-4967 242 36 ( ( PUNCT fumecheng-4967 242 37 20 20 NUM fumecheng-4967 242 38 ) ) PUNCT fumecheng-4967 242 39 is be AUX fumecheng-4967 242 40 nonlinear nonlinear ADJ fumecheng-4967 242 41 and and CCONJ fumecheng-4967 242 42 can can AUX fumecheng-4967 242 43 not not PART fumecheng-4967 242 44 be be AUX fumecheng-4967 242 45 solved solve VERB fumecheng-4967 242 46 analytically analytically ADV fumecheng-4967 242 47 . . PUNCT fumecheng-4967 243 1 but but CCONJ fumecheng-4967 243 2 , , PUNCT fumecheng-4967 243 3 in in ADP fumecheng-4967 243 4 contrast contrast NOUN fumecheng-4967 243 5 to to ADP fumecheng-4967 243 6 functional functional ADJ fumecheng-4967 243 7 equation equation NOUN fumecheng-4967 243 8 * * PUNCT fumecheng-4967 243 9 ˆ ˆ X fumecheng-4967 243 10 0r 0r PROPN fumecheng-4967 244 1   ADJ fumecheng-4967 244 2 it it PRON fumecheng-4967 244 3 is be AUX fumecheng-4967 244 4 already already ADV fumecheng-4967 244 5 an an DET fumecheng-4967 244 6 “ " PUNCT fumecheng-4967 244 7 ordinary ordinary ADJ fumecheng-4967 244 8 ” " PUNCT fumecheng-4967 244 9 differential differential ADJ fumecheng-4967 244 10 equation equation NOUN fumecheng-4967 244 11 and and CCONJ fumecheng-4967 244 12 it it PRON fumecheng-4967 244 13 is be AUX fumecheng-4967 244 14 easy easy ADJ fumecheng-4967 244 15 to to PART fumecheng-4967 244 16 find find VERB fumecheng-4967 244 17 physical physical ADJ fumecheng-4967 244 18 branch branch NOUN fumecheng-4967 245 1 f f PROPN fumecheng-4967 246 1 * * PUNCT fumecheng-4967 246 2 of of ADP fumecheng-4967 246 3 its its PRON fumecheng-4967 246 4 solution solution NOUN fumecheng-4967 246 5 * * PUNCT fumecheng-4967 246 6 ˆ ˆ X fumecheng-4967 246 7 0rf 0rf NOUN fumecheng-4967 247 1   ADJ fumecheng-4967 247 2 numerically numerically ADV fumecheng-4967 247 3 with with ADP fumecheng-4967 247 4 a a DET fumecheng-4967 247 5 very very ADV fumecheng-4967 247 6 high high ADJ fumecheng-4967 247 7 accuracy accuracy NOUN fumecheng-4967 247 8 . . PUNCT fumecheng-4967 248 1 discrete discrete ADJ fumecheng-4967 248 2 data data NOUN fumecheng-4967 248 3 array array NOUN fumecheng-4967 249 1 f f PROPN fumecheng-4967 249 2 * * PUNCT fumecheng-4967 249 3 ( ( PUNCT fumecheng-4967 249 4 ρk ρk NOUN fumecheng-4967 249 5 ) ) PUNCT fumecheng-4967 249 6 has have VERB fumecheng-4967 249 7 big big ADJ fumecheng-4967 249 8 enough enough ADJ fumecheng-4967 249 9 number number NOUN fumecheng-4967 249 10 n≫1 n≫1 PROPN fumecheng-4967 249 11 of of ADP fumecheng-4967 249 12 points points PROPN fumecheng-4967 249 13 k=1,2 k=1,2 PROPN fumecheng-4967 249 14 … … SYM fumecheng-4967 249 15 n n CCONJ fumecheng-4967 249 16 , , PUNCT fumecheng-4967 249 17 where where SCONJ fumecheng-4967 249 18 each each DET fumecheng-4967 249 19 value value NOUN fumecheng-4967 249 20 of of ADP fumecheng-4967 249 21 { { PUNCT fumecheng-4967 249 22 ρk ρk NOUN fumecheng-4967 249 23 } } PUNCT fumecheng-4967 249 24 defines define VERB fumecheng-4967 249 25 unique unique ADJ fumecheng-4967 249 26 value value NOUN fumecheng-4967 249 27 of of ADP fumecheng-4967 249 28 { { PUNCT fumecheng-4967 249 29 f f PROPN fumecheng-4967 249 30 * * PUNCT fumecheng-4967 249 31 k k NOUN fumecheng-4967 249 32 } } PUNCT fumecheng-4967 249 33 . . PUNCT fumecheng-4967 250 1 with with ADP fumecheng-4967 250 2 a a DET fumecheng-4967 250 3 good good ADJ fumecheng-4967 250 4 accuracy accuracy NOUN fumecheng-4967 250 5 , , PUNCT fumecheng-4967 250 6 it it PRON fumecheng-4967 250 7 can can AUX fumecheng-4967 250 8 be be AUX fumecheng-4967 250 9 used use VERB fumecheng-4967 250 10 in in ADP fumecheng-4967 250 11 the the DET fumecheng-4967 250 12 kinetic kinetic ADJ fumecheng-4967 250 13 equation equation NOUN fumecheng-4967 250 14 : : PUNCT fumecheng-4967 251 1 * * PUNCT fumecheng-4967 251 2 / / SYM fumecheng-4967 251 3 [ [ PUNCT fumecheng-4967 251 4 / / SYM fumecheng-4967 251 5 ] ] X fumecheng-4967 251 6 t t X fumecheng-4967 251 7 c c PROPN fumecheng-4967 251 8 f f NOUN fumecheng-4967 251 9   PROPN fumecheng-4967 252 1   PROPN fumecheng-4967 252 2   PROPN fumecheng-4967 252 3   NOUN fumecheng-4967 252 4   VERB fumecheng-4967 252 5   ADJ fumecheng-4967 252 6   PRON fumecheng-4967 252 7   NUM fumecheng-4967 252 8   ADP fumecheng-4967 252 9   ADP fumecheng-4967 252 10   X fumecheng-4967 252 11 ( ( PUNCT fumecheng-4967 252 12 21 21 NUM fumecheng-4967 252 13 ) ) PUNCT fumecheng-4967 252 14 instead instead ADV fumecheng-4967 252 15 of of ADP fumecheng-4967 252 16 the the DET fumecheng-4967 252 17 analytic analytic ADJ fumecheng-4967 252 18 formulae formulae NOUN fumecheng-4967 252 19 for for ADP fumecheng-4967 252 20 the the DET fumecheng-4967 252 21 energy energy NOUN fumecheng-4967 252 22 , , PUNCT fumecheng-4967 252 23 otherwise otherwise ADV fumecheng-4967 252 24 normally normally ADV fumecheng-4967 252 25 used use VERB fumecheng-4967 252 26 before before ADV fumecheng-4967 252 27 . . PUNCT fumecheng-4967 253 1 repeating repeat VERB fumecheng-4967 253 2 the the DET fumecheng-4967 253 3 simulation simulation NOUN fumecheng-4967 253 4 with with ADP fumecheng-4967 253 5 random random ADJ fumecheng-4967 253 6 initial initial ADJ fumecheng-4967 253 7 conditions condition NOUN fumecheng-4967 253 8 and and CCONJ fumecheng-4967 253 9 with with ADP fumecheng-4967 253 10 the the DET fumecheng-4967 253 11 random random ADJ fumecheng-4967 253 12 timedependent timedependent NOUN fumecheng-4967 253 13 noise noise NOUN fumecheng-4967 253 14 < < X fumecheng-4967 253 15 δ(r δ(r NOUN fumecheng-4967 253 16 , , PUNCT fumecheng-4967 253 17 t)>=0 t)>=0 NOUN fumecheng-4967 253 18 , , PUNCT fumecheng-4967 253 19 < < X fumecheng-4967 253 20 δ(r δ(r NOUN fumecheng-4967 253 21 , , PUNCT fumecheng-4967 253 22 t)δ(r´,t´)>=dζδ(r t)δ(r´,t´)>=dζδ(r NOUN fumecheng-4967 253 23 - - PUNCT fumecheng-4967 253 24 r´)δ(t r´)δ(t VERB fumecheng-4967 253 25 - - PUNCT fumecheng-4967 253 26 t t NOUN fumecheng-4967 253 27 ´ ´ NOUN fumecheng-4967 253 28 ) ) PUNCT fumecheng-4967 253 29 after after ADP fumecheng-4967 253 30 long long ADJ fumecheng-4967 253 31 - - PUNCT fumecheng-4967 253 32 time time NOUN fumecheng-4967 253 33 runs run NOUN fumecheng-4967 253 34 , , PUNCT fumecheng-4967 253 35 we we PRON fumecheng-4967 253 36 can can AUX fumecheng-4967 253 37 get get VERB fumecheng-4967 253 38 unlimited unlimited ADJ fumecheng-4967 253 39 number number NOUN fumecheng-4967 253 40 of of ADP fumecheng-4967 253 41 the the DET fumecheng-4967 253 42 realizations realization NOUN fumecheng-4967 253 43 ρ(r ρ(r PROPN fumecheng-4967 253 44 , , PUNCT fumecheng-4967 253 45 t t PROPN fumecheng-4967 253 46 ) ) PUNCT fumecheng-4967 253 47 . . PUNCT fumecheng-4967 254 1 direct direct ADJ fumecheng-4967 254 2 observations observation NOUN fumecheng-4967 254 3 of of ADP fumecheng-4967 254 4 the the DET fumecheng-4967 254 5 simulation simulation NOUN fumecheng-4967 254 6 results result NOUN fumecheng-4967 254 7 show show VERB fumecheng-4967 254 8 that that SCONJ fumecheng-4967 254 9 every every DET fumecheng-4967 254 10 instant instant ADJ fumecheng-4967 254 11 density density NOUN fumecheng-4967 254 12 distribution distribution NOUN fumecheng-4967 254 13 ρ(r ρ(r PROPN fumecheng-4967 254 14 , , PUNCT fumecheng-4967 254 15 t t PROPN fumecheng-4967 254 16 ) ) PUNCT fumecheng-4967 254 17 contains contain VERB fumecheng-4967 254 18 many many ADJ fumecheng-4967 254 19 nuclei nucleus NOUN fumecheng-4967 254 20 of of ADP fumecheng-4967 254 21 different different ADJ fumecheng-4967 254 22 size size NOUN fumecheng-4967 254 23 . . PUNCT fumecheng-4967 255 1 then then ADV fumecheng-4967 255 2 , , PUNCT fumecheng-4967 255 3 the the DET fumecheng-4967 255 4 wider wide ADJ fumecheng-4967 255 5 particular particular ADJ fumecheng-4967 255 6 maximums maximum NOUN fumecheng-4967 255 7 of of ADP fumecheng-4967 255 8 density density NOUN fumecheng-4967 255 9 are be AUX fumecheng-4967 255 10 formed form VERB fumecheng-4967 255 11 , , PUNCT fumecheng-4967 255 12 the the DET fumecheng-4967 255 13 longer long ADJ fumecheng-4967 255 14 time time NOUN fumecheng-4967 255 15 they they PRON fumecheng-4967 255 16 survive survive VERB fumecheng-4967 255 17 in in ADP fumecheng-4967 255 18 the the DET fumecheng-4967 255 19 general general ADJ fumecheng-4967 255 20 landscape landscape NOUN fumecheng-4967 255 21 . . PUNCT fumecheng-4967 256 1 it it PRON fumecheng-4967 256 2 means mean VERB fumecheng-4967 256 3 that that SCONJ fumecheng-4967 256 4 at at ADP fumecheng-4967 256 5 large large ADJ fumecheng-4967 256 6 scales scale NOUN fumecheng-4967 256 7 the the DET fumecheng-4967 256 8 total total ADJ fumecheng-4967 256 9 process process NOUN fumecheng-4967 256 10 of of ADP fumecheng-4967 256 11 transformation transformation NOUN fumecheng-4967 256 12 becomes become VERB fumecheng-4967 256 13 slower slow ADJ fumecheng-4967 256 14 and and CCONJ fumecheng-4967 256 15 slower slow ADJ fumecheng-4967 256 16 . . PUNCT fumecheng-4967 257 1 besides besides SCONJ fumecheng-4967 257 2 , , PUNCT fumecheng-4967 257 3 stronger strong ADJ fumecheng-4967 257 4 correlation correlation NOUN fumecheng-4967 257 5 between between ADP fumecheng-4967 257 6 the the DET fumecheng-4967 257 7 densities density NOUN fumecheng-4967 257 8 in in ADP fumecheng-4967 257 9 different different ADJ fumecheng-4967 257 10 spatial spatial ADJ fumecheng-4967 257 11 positions position NOUN fumecheng-4967 257 12 appears appear VERB fumecheng-4967 257 13 . . PUNCT fumecheng-4967 258 1 in in ADP fumecheng-4967 258 2 an an DET fumecheng-4967 258 3 extremely extremely ADV fumecheng-4967 258 4 long long ADJ fumecheng-4967 258 5 run run NOUN fumecheng-4967 258 6 limit limit NOUN fumecheng-4967 258 7 ( ( PUNCT fumecheng-4967 258 8 when when SCONJ fumecheng-4967 258 9 t→∞ t→∞ NUM fumecheng-4967 258 10 ) ) PUNCT fumecheng-4967 258 11 , , PUNCT fumecheng-4967 258 12 density density NOUN fumecheng-4967 258 13 distribution distribution NOUN fumecheng-4967 258 14 ρ(r ρ(r PROPN fumecheng-4967 258 15 , , PUNCT fumecheng-4967 258 16 t t PROPN fumecheng-4967 258 17 ) ) PUNCT fumecheng-4967 258 18 tends tend VERB fumecheng-4967 258 19 to to ADP fumecheng-4967 258 20 the the DET fumecheng-4967 258 21 expected expect VERB fumecheng-4967 258 22 scale scale NOUN fumecheng-4967 258 23 invariant invariant ADJ fumecheng-4967 258 24 structure structure NOUN fumecheng-4967 258 25 . . PUNCT fumecheng-4967 259 1 one one PRON fumecheng-4967 259 2 can can AUX fumecheng-4967 259 3 calculate calculate VERB fumecheng-4967 259 4 correlation correlation NOUN fumecheng-4967 259 5 function function NOUN fumecheng-4967 259 6 g(rr g(rr NOUN fumecheng-4967 259 7 ´ ´ NOUN fumecheng-4967 259 8 ) ) PUNCT fumecheng-4967 260 1 = = SYM fumecheng-4967 260 2 < < X fumecheng-4967 260 3 ρ(r ρ(r PROPN fumecheng-4967 260 4 , , PUNCT fumecheng-4967 260 5 t)ρ(r´,t t)ρ(r´,t NOUN fumecheng-4967 260 6 ´ ´ NOUN fumecheng-4967 260 7 ) ) PUNCT fumecheng-4967 260 8 > > X fumecheng-4967 260 9 at at ADP fumecheng-4967 260 10 the the DET fumecheng-4967 260 11 fixed fix VERB fumecheng-4967 260 12 time time NOUN fumecheng-4967 260 13 moment moment NOUN fumecheng-4967 260 14 t t NOUN fumecheng-4967 260 15 and and CCONJ fumecheng-4967 260 16 find find VERB fumecheng-4967 260 17 this this DET fumecheng-4967 260 18 scaling scale VERB fumecheng-4967 260 19 correlation correlation NOUN fumecheng-4967 260 20 function function NOUN fumecheng-4967 260 21 . . PUNCT fumecheng-4967 261 1 it it PRON fumecheng-4967 261 2 means mean VERB fumecheng-4967 261 3 that that SCONJ fumecheng-4967 261 4 g(rr´)=<ρ(r g(rr´)=<ρ(r PROPN fumecheng-4967 261 5 , , PUNCT fumecheng-4967 261 6 t)ρ(r´,t´)~1/|rr´| t)ρ(r´,t´)~1/|rr´| NUM fumecheng-4967 261 7 β β NOUN fumecheng-4967 261 8 depends depend VERB fumecheng-4967 261 9 as as ADP fumecheng-4967 261 10 a a DET fumecheng-4967 261 11 power power NOUN fumecheng-4967 261 12 function function NOUN fumecheng-4967 261 13 on on ADP fumecheng-4967 261 14 distance distance NOUN fumecheng-4967 261 15 |rr´| |rr´| NOUN fumecheng-4967 261 16 between between ADP fumecheng-4967 261 17 the the DET fumecheng-4967 261 18 points point NOUN fumecheng-4967 261 19 . . PUNCT fumecheng-4967 262 1 this this DET fumecheng-4967 262 2 quite quite ADV fumecheng-4967 262 3 general general ADJ fumecheng-4967 262 4 result result NOUN fumecheng-4967 262 5 favors favor VERB fumecheng-4967 262 6 to to ADP fumecheng-4967 262 7 the the DET fumecheng-4967 262 8 common common ADJ fumecheng-4967 262 9 observation observation NOUN fumecheng-4967 262 10 that that SCONJ fumecheng-4967 262 11 in in ADP fumecheng-4967 262 12 many many ADJ fumecheng-4967 262 13 cases case NOUN fumecheng-4967 262 14 , , PUNCT fumecheng-4967 262 15 irrespective irrespective ADV fumecheng-4967 262 16 of of ADP fumecheng-4967 262 17 the the DET fumecheng-4967 262 18 specific specific ADJ fumecheng-4967 262 19 features feature NOUN fumecheng-4967 262 20 of of ADP fumecheng-4967 262 21 the the DET fumecheng-4967 262 22 system system NOUN fumecheng-4967 262 23 under under ADP fumecheng-4967 262 24 investigation investigation NOUN fumecheng-4967 262 25 , , PUNCT fumecheng-4967 262 26 the the DET fumecheng-4967 262 27 evolution evolution NOUN fumecheng-4967 262 28 of of ADP fumecheng-4967 262 29 the the DET fumecheng-4967 262 30 surface surface NOUN fumecheng-4967 262 31 layer layer NOUN fumecheng-4967 262 32 proceeds proceed VERB fumecheng-4967 262 33 in in ADP fumecheng-4967 262 34 a a DET fumecheng-4967 262 35 fairly fairly ADV fumecheng-4967 262 36 universal universal ADJ fumecheng-4967 262 37 manner manner NOUN fumecheng-4967 262 38 . . PUNCT fumecheng-4967 263 1 228 228 NUM fumecheng-4967 263 2 a.e a.e PROPN fumecheng-4967 263 3 . . PROPN fumecheng-4967 263 4 filippov filippov PROPN fumecheng-4967 263 5 , , PUNCT fumecheng-4967 263 6 s.n s.n PROPN fumecheng-4967 263 7 . . PROPN fumecheng-4967 263 8 gorb gorb PROPN fumecheng-4967 263 9 5 5 NUM fumecheng-4967 263 10 . . PUNCT fumecheng-4967 264 1 chemical chemical ADJ fumecheng-4967 264 2 appearance appearance NOUN fumecheng-4967 264 3 of of ADP fumecheng-4967 264 4 fractal fractal ADJ fumecheng-4967 264 5 surfaces surface NOUN fumecheng-4967 264 6 one one NUM fumecheng-4967 264 7 more more ADJ fumecheng-4967 264 8 example example NOUN fumecheng-4967 264 9 of of ADP fumecheng-4967 264 10 automatic automatic ADJ fumecheng-4967 264 11 generation generation NOUN fumecheng-4967 264 12 of of ADP fumecheng-4967 264 13 fractal fractal ADJ fumecheng-4967 264 14 surfaces surface NOUN fumecheng-4967 264 15 comes come VERB fumecheng-4967 264 16 from from ADP fumecheng-4967 264 17 the the DET fumecheng-4967 264 18 case case NOUN fumecheng-4967 264 19 , , PUNCT fumecheng-4967 264 20 where where SCONJ fumecheng-4967 264 21 in in ADP fumecheng-4967 264 22 the the DET fumecheng-4967 264 23 immediate immediate ADJ fumecheng-4967 264 24 vicinity vicinity NOUN fumecheng-4967 264 25 of of ADP fumecheng-4967 264 26 the the DET fumecheng-4967 264 27 smooth smooth ADJ fumecheng-4967 264 28 flat flat ADJ fumecheng-4967 264 29 interface interface NOUN fumecheng-4967 264 30 of of ADP fumecheng-4967 264 31 the the DET fumecheng-4967 264 32 two two NUM fumecheng-4967 264 33 media medium NOUN fumecheng-4967 264 34 in in ADP fumecheng-4967 264 35 contact contact NOUN fumecheng-4967 264 36 , , PUNCT fumecheng-4967 264 37 a a DET fumecheng-4967 264 38 dense dense ADJ fumecheng-4967 264 39 layer layer NOUN fumecheng-4967 264 40 of of ADP fumecheng-4967 264 41 one one NUM fumecheng-4967 264 42 or or CCONJ fumecheng-4967 264 43 more more ADJ fumecheng-4967 264 44 reaction reaction NOUN fumecheng-4967 264 45 products product NOUN fumecheng-4967 264 46 emerges emerge VERB fumecheng-4967 264 47 , , PUNCT fumecheng-4967 264 48 as as ADP fumecheng-4967 264 49 a a DET fumecheng-4967 264 50 result result NOUN fumecheng-4967 264 51 of of ADP fumecheng-4967 264 52 a a DET fumecheng-4967 264 53 chemical chemical NOUN fumecheng-4967 264 54 reaction reaction NOUN fumecheng-4967 264 55 . . PUNCT fumecheng-4967 265 1 it it PRON fumecheng-4967 265 2 was be AUX fumecheng-4967 265 3 observed observe VERB fumecheng-4967 265 4 that that SCONJ fumecheng-4967 265 5 in in ADP fumecheng-4967 265 6 the the DET fumecheng-4967 265 7 process process NOUN fumecheng-4967 265 8 of of ADP fumecheng-4967 265 9 growing grow VERB fumecheng-4967 265 10 this this DET fumecheng-4967 265 11 layer layer NOUN fumecheng-4967 265 12 becomes become VERB fumecheng-4967 265 13 more more ADV fumecheng-4967 265 14 and and CCONJ fumecheng-4967 265 15 more more ADV fumecheng-4967 265 16 porous porous ADJ fumecheng-4967 265 17 and and CCONJ fumecheng-4967 265 18 rough rough ADJ fumecheng-4967 265 19 . . PUNCT fumecheng-4967 266 1 gradually gradually ADV fumecheng-4967 266 2 , , PUNCT fumecheng-4967 266 3 an an DET fumecheng-4967 266 4 essentially essentially ADV fumecheng-4967 266 5 inhomogeneous inhomogeneous ADJ fumecheng-4967 266 6 but but CCONJ fumecheng-4967 266 7 , , PUNCT fumecheng-4967 266 8 as as ADP fumecheng-4967 266 9 a a DET fumecheng-4967 266 10 rule rule NOUN fumecheng-4967 266 11 , , PUNCT fumecheng-4967 266 12 scale scale NOUN fumecheng-4967 266 13 invariant invariant ADJ fumecheng-4967 266 14 structure structure NOUN fumecheng-4967 266 15 is be AUX fumecheng-4967 266 16 formed form VERB fumecheng-4967 266 17 , , PUNCT fumecheng-4967 266 18 and and CCONJ fumecheng-4967 266 19 the the DET fumecheng-4967 266 20 laws law NOUN fumecheng-4967 266 21 governing govern VERB fumecheng-4967 266 22 the the DET fumecheng-4967 266 23 growth growth NOUN fumecheng-4967 266 24 of of ADP fumecheng-4967 266 25 this this DET fumecheng-4967 266 26 structure structure NOUN fumecheng-4967 266 27 are be AUX fumecheng-4967 266 28 characterized characterize VERB fumecheng-4967 266 29 by by ADP fumecheng-4967 266 30 fractal fractal ADJ fumecheng-4967 266 31 dimension dimension NOUN fumecheng-4967 266 32 and and CCONJ fumecheng-4967 266 33 growth growth NOUN fumecheng-4967 266 34 exponent exponent NOUN fumecheng-4967 267 1 [ [ X fumecheng-4967 267 2 9 9 NUM fumecheng-4967 267 3 ] ] PUNCT fumecheng-4967 267 4 . . PUNCT fumecheng-4967 268 1 in in ADP fumecheng-4967 268 2 addition addition NOUN fumecheng-4967 268 3 to to ADP fumecheng-4967 268 4 arousing arouse VERB fumecheng-4967 268 5 purely purely ADV fumecheng-4967 268 6 scientific scientific ADJ fumecheng-4967 268 7 interest interest NOUN fumecheng-4967 268 8 , , PUNCT fumecheng-4967 268 9 the the DET fumecheng-4967 268 10 study study NOUN fumecheng-4967 268 11 of of ADP fumecheng-4967 268 12 corrosion corrosion NOUN fumecheng-4967 268 13 - - PUNCT fumecheng-4967 268 14 front front NOUN fumecheng-4967 268 15 growth growth NOUN fumecheng-4967 268 16 attracts attract VERB fumecheng-4967 268 17 attention attention NOUN fumecheng-4967 268 18 because because SCONJ fumecheng-4967 268 19 of of ADP fumecheng-4967 268 20 its its PRON fumecheng-4967 268 21 importance importance NOUN fumecheng-4967 268 22 from from ADP fumecheng-4967 268 23 the the DET fumecheng-4967 268 24 standpoint standpoint NOUN fumecheng-4967 268 25 of of ADP fumecheng-4967 268 26 practice practice NOUN fumecheng-4967 268 27 , , PUNCT fumecheng-4967 268 28 since since SCONJ fumecheng-4967 268 29 in in ADP fumecheng-4967 268 30 some some DET fumecheng-4967 268 31 applications application NOUN fumecheng-4967 268 32 the the DET fumecheng-4967 268 33 problem problem NOUN fumecheng-4967 268 34 is be AUX fumecheng-4967 268 35 closely closely ADV fumecheng-4967 268 36 linked link VERB fumecheng-4967 268 37 to to ADP fumecheng-4967 268 38 that that PRON fumecheng-4967 268 39 of of ADP fumecheng-4967 268 40 raising raise VERB fumecheng-4967 268 41 the the DET fumecheng-4967 268 42 efficiency efficiency NOUN fumecheng-4967 268 43 of of ADP fumecheng-4967 268 44 electric electric ADJ fumecheng-4967 268 45 batteries battery NOUN fumecheng-4967 268 46 . . PUNCT fumecheng-4967 269 1 for for ADP fumecheng-4967 269 2 instance instance NOUN fumecheng-4967 269 3 , , PUNCT fumecheng-4967 269 4 when when SCONJ fumecheng-4967 269 5 a a DET fumecheng-4967 269 6 lithium lithium NOUN fumecheng-4967 269 7 anode anode NOUN fumecheng-4967 269 8 is be AUX fumecheng-4967 269 9 placed place VERB fumecheng-4967 269 10 into into ADP fumecheng-4967 269 11 an an DET fumecheng-4967 269 12 electrolyte electrolyte NOUN fumecheng-4967 269 13 containing contain VERB fumecheng-4967 269 14 socl2 socl2 NOUN fumecheng-4967 269 15 as as ADP fumecheng-4967 269 16 an an DET fumecheng-4967 269 17 additive additive NOUN fumecheng-4967 269 18 , , PUNCT fumecheng-4967 269 19 due due ADP fumecheng-4967 269 20 to to ADP fumecheng-4967 269 21 the the DET fumecheng-4967 269 22 exceptionally exceptionally ADV fumecheng-4967 269 23 high high ADJ fumecheng-4967 269 24 reactivity reactivity NOUN fumecheng-4967 269 25 of of ADP fumecheng-4967 269 26 lithium lithium NOUN fumecheng-4967 269 27 , , PUNCT fumecheng-4967 269 28 a a DET fumecheng-4967 269 29 porous porous ADJ fumecheng-4967 269 30 twocomponent twocomponent NOUN fumecheng-4967 269 31 layer layer NOUN fumecheng-4967 269 32 of of ADP fumecheng-4967 269 33 licl licl PROPN fumecheng-4967 269 34 and and CCONJ fumecheng-4967 269 35 so2 so2 PROPN fumecheng-4967 269 36 is be AUX fumecheng-4967 269 37 formed form VERB fumecheng-4967 269 38 at at ADP fumecheng-4967 269 39 the the DET fumecheng-4967 269 40 surface surface NOUN fumecheng-4967 269 41 of of ADP fumecheng-4967 269 42 the the DET fumecheng-4967 269 43 anode anode NOUN fumecheng-4967 269 44 . . PUNCT fumecheng-4967 270 1 the the DET fumecheng-4967 270 2 presence presence NOUN fumecheng-4967 270 3 of of ADP fumecheng-4967 270 4 such such DET fumecheng-4967 270 5 a a DET fumecheng-4967 270 6 layer layer NOUN fumecheng-4967 270 7 leads lead VERB fumecheng-4967 270 8 to to ADP fumecheng-4967 270 9 what what PRON fumecheng-4967 270 10 is be AUX fumecheng-4967 270 11 known know VERB fumecheng-4967 270 12 as as ADP fumecheng-4967 270 13 a a DET fumecheng-4967 270 14 lag lag NOUN fumecheng-4967 270 15 effect effect NOUN fumecheng-4967 270 16 , , PUNCT fumecheng-4967 270 17 when when SCONJ fumecheng-4967 270 18 the the DET fumecheng-4967 270 19 element element NOUN fumecheng-4967 270 20 is be AUX fumecheng-4967 270 21 stored store VERB fumecheng-4967 270 22 for for ADP fumecheng-4967 270 23 a a DET fumecheng-4967 270 24 long long ADJ fumecheng-4967 270 25 time time NOUN fumecheng-4967 270 26 . . PUNCT fumecheng-4967 271 1 micrographs micrograph NOUN fumecheng-4967 271 2 of of ADP fumecheng-4967 271 3 the the DET fumecheng-4967 271 4 surface surface NOUN fumecheng-4967 271 5 layer layer NOUN fumecheng-4967 271 6 show show VERB fumecheng-4967 271 7 that that SCONJ fumecheng-4967 271 8 the the DET fumecheng-4967 271 9 layer layer NOUN fumecheng-4967 271 10 can can AUX fumecheng-4967 271 11 be be AUX fumecheng-4967 271 12 considered consider VERB fumecheng-4967 271 13 as as ADP fumecheng-4967 271 14 a a DET fumecheng-4967 271 15 combination combination NOUN fumecheng-4967 271 16 of of ADP fumecheng-4967 271 17 a a DET fumecheng-4967 271 18 relatively relatively ADV fumecheng-4967 271 19 dense dense ADJ fumecheng-4967 271 20 initial initial ADJ fumecheng-4967 271 21 layer layer NOUN fumecheng-4967 271 22 with with ADP fumecheng-4967 271 23 a a DET fumecheng-4967 271 24 subsequent subsequent ADJ fumecheng-4967 271 25 transition transition NOUN fumecheng-4967 271 26 to to ADP fumecheng-4967 271 27 a a DET fumecheng-4967 271 28 fractal fractal ADJ fumecheng-4967 271 29 structure structure NOUN fumecheng-4967 271 30 with with ADP fumecheng-4967 271 31 an an DET fumecheng-4967 271 32 ever ever ADV fumecheng-4967 271 33 increasing increase VERB fumecheng-4967 271 34 porosity porosity NOUN fumecheng-4967 271 35 . . PUNCT fumecheng-4967 272 1 the the DET fumecheng-4967 272 2 highly highly ADV fumecheng-4967 272 3 universal universal ADJ fumecheng-4967 272 4 properties property NOUN fumecheng-4967 272 5 manifested manifest VERB fumecheng-4967 272 6 by by ADP fumecheng-4967 272 7 different different ADJ fumecheng-4967 272 8 systems system NOUN fumecheng-4967 272 9 suggest suggest VERB fumecheng-4967 272 10 that that SCONJ fumecheng-4967 272 11 one one PRON fumecheng-4967 272 12 can can AUX fumecheng-4967 272 13 use use VERB fumecheng-4967 272 14 universal universal ADJ fumecheng-4967 272 15 growth growth NOUN fumecheng-4967 272 16 models model NOUN fumecheng-4967 272 17 based base VERB fumecheng-4967 272 18 on on ADP fumecheng-4967 272 19 a a DET fumecheng-4967 272 20 combination combination NOUN fumecheng-4967 272 21 of of ADP fumecheng-4967 272 22 the the DET fumecheng-4967 272 23 ideas idea NOUN fumecheng-4967 272 24 of of ADP fumecheng-4967 272 25 continuum continuum ADJ fumecheng-4967 272 26 field field NOUN fumecheng-4967 272 27 theory theory NOUN fumecheng-4967 272 28 and and CCONJ fumecheng-4967 272 29 kinetic kinetic ADJ fumecheng-4967 272 30 equations equation NOUN fumecheng-4967 272 31 with with ADP fumecheng-4967 272 32 a a DET fumecheng-4967 272 33 random random ADJ fumecheng-4967 272 34 source source NOUN fumecheng-4967 272 35 . . PUNCT fumecheng-4967 273 1 being be AUX fumecheng-4967 273 2 fairly fairly ADV fumecheng-4967 273 3 common common ADJ fumecheng-4967 273 4 in in ADP fumecheng-4967 273 5 the the DET fumecheng-4967 273 6 theory theory NOUN fumecheng-4967 273 7 of of ADP fumecheng-4967 273 8 phase phase NOUN fumecheng-4967 273 9 separation separation NOUN fumecheng-4967 273 10 and and CCONJ fumecheng-4967 273 11 fluctuation fluctuation NOUN fumecheng-4967 273 12 phenomena phenomenon NOUN fumecheng-4967 273 13 in in ADP fumecheng-4967 273 14 phase phase NOUN fumecheng-4967 273 15 transitions transition NOUN fumecheng-4967 273 16 , , PUNCT fumecheng-4967 273 17 the the DET fumecheng-4967 273 18 kinetic kinetic ADJ fumecheng-4967 273 19 equations equation NOUN fumecheng-4967 273 20 with with ADP fumecheng-4967 273 21 a a DET fumecheng-4967 273 22 source source NOUN fumecheng-4967 273 23 of of ADP fumecheng-4967 273 24 noise noise NOUN fumecheng-4967 273 25 should should AUX fumecheng-4967 273 26 be be AUX fumecheng-4967 273 27 used use VERB fumecheng-4967 273 28 cautiously cautiously ADV fumecheng-4967 273 29 in in ADP fumecheng-4967 273 30 describing describe VERB fumecheng-4967 273 31 front front ADJ fumecheng-4967 273 32 growth growth NOUN fumecheng-4967 273 33 , , PUNCT fumecheng-4967 273 34 the the DET fumecheng-4967 273 35 reason reason NOUN fumecheng-4967 273 36 being be AUX fumecheng-4967 273 37 that that SCONJ fumecheng-4967 273 38 , , PUNCT fumecheng-4967 273 39 in in ADP fumecheng-4967 273 40 contrast contrast NOUN fumecheng-4967 273 41 to to ADP fumecheng-4967 273 42 phase phase NOUN fumecheng-4967 273 43 transitions transition NOUN fumecheng-4967 273 44 , , PUNCT fumecheng-4967 273 45 where where SCONJ fumecheng-4967 273 46 generation generation NOUN fumecheng-4967 273 47 of of ADP fumecheng-4967 273 48 the the DET fumecheng-4967 273 49 order order NOUN fumecheng-4967 273 50 parameter parameter NOUN fumecheng-4967 273 51 occurs occur VERB fumecheng-4967 273 52 in in ADP fumecheng-4967 273 53 the the DET fumecheng-4967 273 54 bulk bulk NOUN fumecheng-4967 273 55 of of ADP fumecheng-4967 273 56 the the DET fumecheng-4967 273 57 system system NOUN fumecheng-4967 273 58 , , PUNCT fumecheng-4967 273 59 a a DET fumecheng-4967 273 60 random random ADJ fumecheng-4967 273 61 source source NOUN fumecheng-4967 273 62 can can AUX fumecheng-4967 273 63 not not PART fumecheng-4967 273 64 be be AUX fumecheng-4967 273 65 considered consider VERB fumecheng-4967 273 66 additive additive ADJ fumecheng-4967 273 67 . . PUNCT fumecheng-4967 274 1 the the DET fumecheng-4967 274 2 generation generation NOUN fumecheng-4967 274 3 of of ADP fumecheng-4967 274 4 a a DET fumecheng-4967 274 5 finite finite ADJ fumecheng-4967 274 6 density density NOUN fumecheng-4967 274 7 of of ADP fumecheng-4967 274 8 components component NOUN fumecheng-4967 274 9 forming form VERB fumecheng-4967 274 10 the the DET fumecheng-4967 274 11 front front NOUN fumecheng-4967 274 12 occurs occur VERB fumecheng-4967 274 13 only only ADV fumecheng-4967 274 14 in in ADP fumecheng-4967 274 15 the the DET fumecheng-4967 274 16 immediate immediate ADJ fumecheng-4967 274 17 vicinity vicinity NOUN fumecheng-4967 274 18 of of ADP fumecheng-4967 274 19 the the DET fumecheng-4967 274 20 already already ADV fumecheng-4967 274 21 existing exist VERB fumecheng-4967 274 22 boundary boundary NOUN fumecheng-4967 274 23 . . PUNCT fumecheng-4967 275 1 this this PRON fumecheng-4967 275 2 means mean VERB fumecheng-4967 275 3 that that SCONJ fumecheng-4967 275 4 in in ADP fumecheng-4967 275 5 the the DET fumecheng-4967 275 6 case case NOUN fumecheng-4967 275 7 at at ADP fumecheng-4967 275 8 hand hand NOUN fumecheng-4967 275 9 the the DET fumecheng-4967 275 10 corresponding correspond VERB fumecheng-4967 275 11 source source NOUN fumecheng-4967 275 12 in in ADP fumecheng-4967 275 13 the the DET fumecheng-4967 275 14 equation equation NOUN fumecheng-4967 275 15 must must AUX fumecheng-4967 275 16 be be AUX fumecheng-4967 275 17 multiplicative multiplicative ADJ fumecheng-4967 275 18 i.e. i.e. X fumecheng-4967 275 19 , , PUNCT fumecheng-4967 275 20 at at ADP fumecheng-4967 275 21 least least ADJ fumecheng-4967 275 22 contain contain VERB fumecheng-4967 275 23 the the DET fumecheng-4967 275 24 density density NOUN fumecheng-4967 275 25 as as ADP fumecheng-4967 275 26 a a DET fumecheng-4967 275 27 factor factor NOUN fumecheng-4967 275 28 . . PUNCT fumecheng-4967 276 1 however however ADV fumecheng-4967 276 2 , , PUNCT fumecheng-4967 276 3 in in ADP fumecheng-4967 276 4 recent recent ADJ fumecheng-4967 276 5 publications publication NOUN fumecheng-4967 276 6 , , PUNCT fumecheng-4967 276 7 devoted devote VERB fumecheng-4967 276 8 to to ADP fumecheng-4967 276 9 theoretical theoretical ADJ fumecheng-4967 276 10 studies study NOUN fumecheng-4967 276 11 of of ADP fumecheng-4967 276 12 phase phase NOUN fumecheng-4967 276 13 diagrams diagram NOUN fumecheng-4967 276 14 and and CCONJ fumecheng-4967 276 15 transitions transition NOUN fumecheng-4967 276 16 in in ADP fumecheng-4967 276 17 systems system NOUN fumecheng-4967 276 18 with with ADP fumecheng-4967 276 19 multiplicative multiplicative ADJ fumecheng-4967 276 20 noise noise NOUN fumecheng-4967 276 21 , , PUNCT fumecheng-4967 276 22 it it PRON fumecheng-4967 276 23 was be AUX fumecheng-4967 276 24 noted note VERB fumecheng-4967 276 25 that that SCONJ fumecheng-4967 276 26 the the DET fumecheng-4967 276 27 presence presence NOUN fumecheng-4967 276 28 of of ADP fumecheng-4967 276 29 such such ADJ fumecheng-4967 276 30 strong strong ADJ fumecheng-4967 276 31 noise noise NOUN fumecheng-4967 276 32 can can AUX fumecheng-4967 276 33 have have VERB fumecheng-4967 276 34 a a DET fumecheng-4967 276 35 dramatic dramatic ADJ fumecheng-4967 276 36 effect effect NOUN fumecheng-4967 276 37 on on ADP fumecheng-4967 276 38 the the DET fumecheng-4967 276 39 ordered order VERB fumecheng-4967 276 40 structure structure NOUN fumecheng-4967 276 41 and and CCONJ fumecheng-4967 276 42 on on ADP fumecheng-4967 276 43 the the DET fumecheng-4967 276 44 phase phase NOUN fumecheng-4967 276 45 diagram diagram NOUN fumecheng-4967 276 46 , , PUNCT fumecheng-4967 276 47 and and CCONJ fumecheng-4967 276 48 may may AUX fumecheng-4967 276 49 lead lead VERB fumecheng-4967 276 50 to to ADP fumecheng-4967 276 51 the the DET fumecheng-4967 276 52 emergence emergence NOUN fumecheng-4967 276 53 of of ADP fumecheng-4967 276 54 new new ADJ fumecheng-4967 276 55 nontrivial nontrivial ADJ fumecheng-4967 276 56 phases phase NOUN fumecheng-4967 276 57 . . PUNCT fumecheng-4967 277 1 in in ADP fumecheng-4967 277 2 our our PRON fumecheng-4967 277 3 case case NOUN fumecheng-4967 277 4 , , PUNCT fumecheng-4967 277 5 this this PRON fumecheng-4967 277 6 means mean VERB fumecheng-4967 277 7 that that SCONJ fumecheng-4967 277 8 the the DET fumecheng-4967 277 9 model model NOUN fumecheng-4967 277 10 equation equation NOUN fumecheng-4967 277 11 should should AUX fumecheng-4967 277 12 be be AUX fumecheng-4967 277 13 written write VERB fumecheng-4967 277 14 in in ADP fumecheng-4967 277 15 such such DET fumecheng-4967 277 16 a a DET fumecheng-4967 277 17 way way NOUN fumecheng-4967 277 18 so so SCONJ fumecheng-4967 277 19 as as SCONJ fumecheng-4967 277 20 to to PART fumecheng-4967 277 21 exclude exclude VERB fumecheng-4967 277 22 additional additional ADJ fumecheng-4967 277 23 difficulties difficulty NOUN fumecheng-4967 277 24 associated associate VERB fumecheng-4967 277 25 with with ADP fumecheng-4967 277 26 this this DET fumecheng-4967 277 27 noise noise NOUN fumecheng-4967 277 28 . . PUNCT fumecheng-4967 278 1 from from ADP fumecheng-4967 278 2 an an DET fumecheng-4967 278 3 experimental experimental ADJ fumecheng-4967 278 4 standpoint standpoint NOUN fumecheng-4967 278 5 , , PUNCT fumecheng-4967 278 6 the the DET fumecheng-4967 278 7 study study NOUN fumecheng-4967 278 8 of of ADP fumecheng-4967 278 9 fractal fractal ADJ fumecheng-4967 278 10 corrosion corrosion NOUN fumecheng-4967 278 11 structures structure NOUN fumecheng-4967 278 12 is be AUX fumecheng-4967 278 13 convenient convenient ADJ fumecheng-4967 278 14 since since SCONJ fumecheng-4967 278 15 the the DET fumecheng-4967 278 16 corrosion corrosion NOUN fumecheng-4967 278 17 front front NOUN fumecheng-4967 278 18 is be AUX fumecheng-4967 278 19 observed observe VERB fumecheng-4967 278 20 directly directly ADV fumecheng-4967 278 21 in in ADP fumecheng-4967 278 22 micrographs micrograph NOUN fumecheng-4967 278 23 and and CCONJ fumecheng-4967 278 24 the the DET fumecheng-4967 278 25 corresponding correspond VERB fumecheng-4967 278 26 two two NUM fumecheng-4967 278 27 dimensional dimensional ADJ fumecheng-4967 278 28 distributions distribution NOUN fumecheng-4967 278 29 of of ADP fumecheng-4967 278 30 density density NOUN fumecheng-4967 278 31 can can AUX fumecheng-4967 278 32 be be AUX fumecheng-4967 278 33 studied study VERB fumecheng-4967 278 34 explicitly explicitly ADV fumecheng-4967 278 35 . . PUNCT fumecheng-4967 279 1 at at ADP fumecheng-4967 279 2 the the DET fumecheng-4967 279 3 same same ADJ fumecheng-4967 279 4 time time NOUN fumecheng-4967 279 5 , , PUNCT fumecheng-4967 279 6 the the DET fumecheng-4967 279 7 processes process NOUN fumecheng-4967 279 8 involved involve VERB fumecheng-4967 279 9 are be AUX fumecheng-4967 279 10 very very ADV fumecheng-4967 279 11 complex complex ADJ fumecheng-4967 279 12 , , PUNCT fumecheng-4967 279 13 and and CCONJ fumecheng-4967 279 14 notwithstanding notwithstanding ADP fumecheng-4967 279 15 the the DET fumecheng-4967 279 16 continuing continue VERB fumecheng-4967 279 17 efforts effort NOUN fumecheng-4967 279 18 , , PUNCT fumecheng-4967 279 19 the the DET fumecheng-4967 279 20 theoretical theoretical ADJ fumecheng-4967 279 21 models model NOUN fumecheng-4967 279 22 still still ADV fumecheng-4967 279 23 remain remain VERB fumecheng-4967 279 24 extremely extremely ADV fumecheng-4967 279 25 simple simple ADJ fumecheng-4967 279 26 , , PUNCT fumecheng-4967 279 27 although although SCONJ fumecheng-4967 279 28 they they PRON fumecheng-4967 279 29 presuppose presuppose VERB fumecheng-4967 279 30 a a DET fumecheng-4967 279 31 numerical numerical ADJ fumecheng-4967 279 32 analysis analysis NOUN fumecheng-4967 279 33 of of ADP fumecheng-4967 279 34 the the DET fumecheng-4967 279 35 kinetic kinetic ADJ fumecheng-4967 279 36 equations equation NOUN fumecheng-4967 279 37 . . PUNCT fumecheng-4967 280 1 usually usually ADV fumecheng-4967 280 2 , , PUNCT fumecheng-4967 280 3 only only ADV fumecheng-4967 280 4 the the DET fumecheng-4967 280 5 density density NOUN fumecheng-4967 280 6 of of ADP fumecheng-4967 280 7 a a DET fumecheng-4967 280 8 single single ADJ fumecheng-4967 280 9 distributed distribute VERB fumecheng-4967 280 10 quantity quantity NOUN fumecheng-4967 280 11 that that PRON fumecheng-4967 280 12 is be AUX fumecheng-4967 280 13 considered consider VERB fumecheng-4967 280 14 the the DET fumecheng-4967 280 15 most most ADV fumecheng-4967 280 16 important important ADJ fumecheng-4967 280 17 in in ADP fumecheng-4967 280 18 each each DET fumecheng-4967 280 19 specific specific ADJ fumecheng-4967 280 20 case case NOUN fumecheng-4967 280 21 is be AUX fumecheng-4967 280 22 involved involve VERB fumecheng-4967 280 23 . . PUNCT fumecheng-4967 281 1 this this PRON fumecheng-4967 281 2 is be AUX fumecheng-4967 281 3 generally generally ADV fumecheng-4967 281 4 not not PART fumecheng-4967 281 5 the the DET fumecheng-4967 281 6 case case NOUN fumecheng-4967 281 7 in in ADP fumecheng-4967 281 8 physicochemical physicochemical ADJ fumecheng-4967 281 9 processes process NOUN fumecheng-4967 281 10 , , PUNCT fumecheng-4967 281 11 since since SCONJ fumecheng-4967 281 12 usually usually ADV fumecheng-4967 281 13 two two NUM fumecheng-4967 281 14 or or CCONJ fumecheng-4967 281 15 more more ADJ fumecheng-4967 281 16 components component NOUN fumecheng-4967 281 17 participate participate VERB fumecheng-4967 281 18 in in ADP fumecheng-4967 281 19 the the DET fumecheng-4967 281 20 reactions reaction NOUN fumecheng-4967 281 21 . . PUNCT fumecheng-4967 282 1 no no ADV fumecheng-4967 282 2 matter matter ADV fumecheng-4967 282 3 how how SCONJ fumecheng-4967 282 4 subtle subtle ADJ fumecheng-4967 282 5 the the DET fumecheng-4967 282 6 description description NOUN fumecheng-4967 282 7 of of ADP fumecheng-4967 282 8 a a DET fumecheng-4967 282 9 system system NOUN fumecheng-4967 282 10 by by ADP fumecheng-4967 282 11 the the DET fumecheng-4967 282 12 single single ADJ fumecheng-4967 282 13 - - PUNCT fumecheng-4967 282 14 component component NOUN fumecheng-4967 282 15 approach approach NOUN fumecheng-4967 282 16 is be AUX fumecheng-4967 282 17 , , PUNCT fumecheng-4967 282 18 it it PRON fumecheng-4967 282 19 is be AUX fumecheng-4967 282 20 sufficient sufficient ADJ fumecheng-4967 282 21 to to PART fumecheng-4967 282 22 replace replace VERB fumecheng-4967 282 23 the the DET fumecheng-4967 282 24 study study NOUN fumecheng-4967 282 25 of of ADP fumecheng-4967 282 26 the the DET fumecheng-4967 282 27 system system NOUN fumecheng-4967 282 28 by by ADP fumecheng-4967 282 29 an an DET fumecheng-4967 282 30 analysis analysis NOUN fumecheng-4967 282 31 of of ADP fumecheng-4967 282 32 purely purely ADV fumecheng-4967 282 33 theoretical theoretical ADJ fumecheng-4967 282 34 models model NOUN fumecheng-4967 282 35 . . PUNCT fumecheng-4967 283 1 given give VERB fumecheng-4967 283 2 contemporary contemporary ADJ fumecheng-4967 283 3 computer computer NOUN fumecheng-4967 283 4 modeling modeling NOUN fumecheng-4967 283 5 methods method NOUN fumecheng-4967 283 6 of of ADP fumecheng-4967 283 7 the the DET fumecheng-4967 283 8 pattern pattern NOUN fumecheng-4967 283 9 formation formation NOUN fumecheng-4967 283 10 in in ADP fumecheng-4967 283 11 numerical numerical ADJ fumecheng-4967 283 12 modeling modeling NOUN fumecheng-4967 283 13 of of ADP fumecheng-4967 283 14 biological biological ADJ fumecheng-4967 283 15 problems problem NOUN fumecheng-4967 283 16 229 229 NUM fumecheng-4967 283 17 techniques technique NOUN fumecheng-4967 283 18 , , PUNCT fumecheng-4967 283 19 any any DET fumecheng-4967 283 20 attempt attempt NOUN fumecheng-4967 283 21 to to PART fumecheng-4967 283 22 reduce reduce VERB fumecheng-4967 283 23 the the DET fumecheng-4967 283 24 problem problem NOUN fumecheng-4967 283 25 to to ADP fumecheng-4967 283 26 a a DET fumecheng-4967 283 27 single single ADJ fumecheng-4967 283 28 equation equation NOUN fumecheng-4967 283 29 is be AUX fumecheng-4967 283 30 more more ADJ fumecheng-4967 283 31 a a DET fumecheng-4967 283 32 tribute tribute NOUN fumecheng-4967 283 33 to to ADP fumecheng-4967 283 34 the the DET fumecheng-4967 283 35 analytic analytic ADJ fumecheng-4967 283 36 tradition tradition NOUN fumecheng-4967 283 37 than than ADP fumecheng-4967 283 38 a a DET fumecheng-4967 283 39 real real ADJ fumecheng-4967 283 40 necessity necessity NOUN fumecheng-4967 283 41 . . PUNCT fumecheng-4967 284 1 here here ADV fumecheng-4967 284 2 we we PRON fumecheng-4967 284 3 will will AUX fumecheng-4967 284 4 demonstrate demonstrate VERB fumecheng-4967 284 5 the the DET fumecheng-4967 284 6 feasibility feasibility NOUN fumecheng-4967 284 7 of of ADP fumecheng-4967 284 8 moving move VERB fumecheng-4967 284 9 in in ADP fumecheng-4967 284 10 this this DET fumecheng-4967 284 11 direction direction NOUN fumecheng-4967 284 12 by by ADP fumecheng-4967 284 13 the the DET fumecheng-4967 284 14 example example NOUN fumecheng-4967 284 15 of of ADP fumecheng-4967 284 16 a a DET fumecheng-4967 284 17 two two NUM fumecheng-4967 284 18 - - PUNCT fumecheng-4967 284 19 component component NOUN fumecheng-4967 284 20 model model NOUN fumecheng-4967 284 21 formulated formulate VERB fumecheng-4967 284 22 for for ADP fumecheng-4967 284 23 the the DET fumecheng-4967 284 24 description description NOUN fumecheng-4967 284 25 of of ADP fumecheng-4967 284 26 growth growth NOUN fumecheng-4967 284 27 and and CCONJ fumecheng-4967 284 28 corrosion corrosion NOUN fumecheng-4967 284 29 of of ADP fumecheng-4967 284 30 a a DET fumecheng-4967 284 31 broad broad ADJ fumecheng-4967 284 32 class class NOUN fumecheng-4967 284 33 of of ADP fumecheng-4967 284 34 porous porous ADJ fumecheng-4967 284 35 surface surface NOUN fumecheng-4967 284 36 layers layer NOUN fumecheng-4967 284 37 initiated initiate VERB fumecheng-4967 284 38 by by ADP fumecheng-4967 284 39 chemical chemical ADJ fumecheng-4967 284 40 reactions reaction NOUN fumecheng-4967 284 41 . . PUNCT fumecheng-4967 285 1 below below ADP fumecheng-4967 285 2 we we PRON fumecheng-4967 285 3 examine examine VERB fumecheng-4967 285 4 the the DET fumecheng-4967 285 5 simplest simple ADJ fumecheng-4967 285 6 two two NUM fumecheng-4967 285 7 - - PUNCT fumecheng-4967 285 8 component component NOUN fumecheng-4967 285 9 case case NOUN fumecheng-4967 285 10 , , PUNCT fumecheng-4967 285 11 assuming assume VERB fumecheng-4967 285 12 , , PUNCT fumecheng-4967 285 13 as as ADP fumecheng-4967 285 14 an an DET fumecheng-4967 285 15 example example NOUN fumecheng-4967 285 16 , , PUNCT fumecheng-4967 285 17 that that SCONJ fumecheng-4967 285 18 we we PRON fumecheng-4967 285 19 are be AUX fumecheng-4967 285 20 dealing deal VERB fumecheng-4967 285 21 with with ADP fumecheng-4967 285 22 chemical chemical ADJ fumecheng-4967 285 23 reactions reaction NOUN fumecheng-4967 285 24 that that PRON fumecheng-4967 285 25 proceed proceed VERB fumecheng-4967 285 26 in in ADP fumecheng-4967 285 27 a a DET fumecheng-4967 285 28 system system NOUN fumecheng-4967 285 29 with with ADP fumecheng-4967 285 30 a a DET fumecheng-4967 285 31 contaminated contaminate VERB fumecheng-4967 285 32 lithium lithium NOUN fumecheng-4967 285 33 anode anode NOUN fumecheng-4967 285 34 . . PUNCT fumecheng-4967 286 1 the the DET fumecheng-4967 286 2 complete complete ADJ fumecheng-4967 286 3 picture picture NOUN fumecheng-4967 286 4 of of ADP fumecheng-4967 286 5 the the DET fumecheng-4967 286 6 reactions reaction NOUN fumecheng-4967 286 7 in in ADP fumecheng-4967 286 8 such such DET fumecheng-4967 286 9 a a DET fumecheng-4967 286 10 system system NOUN fumecheng-4967 286 11 is be AUX fumecheng-4967 286 12 fairly fairly ADV fumecheng-4967 286 13 complicated complicated ADJ fumecheng-4967 286 14 and and CCONJ fumecheng-4967 286 15 can can AUX fumecheng-4967 286 16 be be AUX fumecheng-4967 286 17 expressed express VERB fumecheng-4967 286 18 as as SCONJ fumecheng-4967 286 19 follows follow VERB fumecheng-4967 286 20 : : PUNCT fumecheng-4967 286 21 li→li li→li ADJ fumecheng-4967 286 22 + + CCONJ fumecheng-4967 287 1 + + ADJ fumecheng-4967 287 2 e e NOUN fumecheng-4967 287 3 , , PUNCT fumecheng-4967 287 4 4li 4li ADJ fumecheng-4967 287 5 + + CCONJ fumecheng-4967 287 6 +4e +4e NUM fumecheng-4967 287 7 +2socl2→4licl+so2+s +2socl2→4licl+so2+s NOUN fumecheng-4967 287 8 . . PUNCT fumecheng-4967 288 1 actually actually ADV fumecheng-4967 288 2 , , PUNCT fumecheng-4967 288 3 we we PRON fumecheng-4967 288 4 are be AUX fumecheng-4967 288 5 interested interested ADJ fumecheng-4967 288 6 only only ADV fumecheng-4967 288 7 in in ADP fumecheng-4967 288 8 the the DET fumecheng-4967 288 9 formation formation NOUN fumecheng-4967 288 10 of of ADP fumecheng-4967 288 11 a a DET fumecheng-4967 288 12 front front NOUN fumecheng-4967 288 13 consisting consist VERB fumecheng-4967 288 14 of of ADP fumecheng-4967 288 15 lithium lithium NOUN fumecheng-4967 288 16 chloride chloride NOUN fumecheng-4967 288 17 licl licl NOUN fumecheng-4967 288 18 contaminated contaminate VERB fumecheng-4967 288 19 by by ADP fumecheng-4967 288 20 the the DET fumecheng-4967 288 21 reaction reaction NOUN fumecheng-4967 288 22 product product NOUN fumecheng-4967 288 23 so2 so2 PROPN fumecheng-4967 288 24 that that PRON fumecheng-4967 288 25 concentrates concentrate VERB fumecheng-4967 288 26 near near ADP fumecheng-4967 288 27 the the DET fumecheng-4967 288 28 surface surface NOUN fumecheng-4967 288 29 . . PUNCT fumecheng-4967 289 1 bearing bear VERB fumecheng-4967 289 2 all all DET fumecheng-4967 289 3 this this PRON fumecheng-4967 289 4 in in ADP fumecheng-4967 289 5 mind mind NOUN fumecheng-4967 289 6 , , PUNCT fumecheng-4967 289 7 we we PRON fumecheng-4967 289 8 can can AUX fumecheng-4967 289 9 interpret interpret VERB fumecheng-4967 289 10 the the DET fumecheng-4967 289 11 bare bare ADJ fumecheng-4967 289 12 equation equation NOUN fumecheng-4967 289 13 9 9 NUM fumecheng-4967 289 14 as as ADP fumecheng-4967 289 15 an an DET fumecheng-4967 289 16 initial initial ADJ fumecheng-4967 289 17 equation equation NOUN fumecheng-4967 289 18 for for ADP fumecheng-4967 289 19 the the DET fumecheng-4967 289 20 evolution evolution NOUN fumecheng-4967 289 21 of of ADP fumecheng-4967 289 22 the the DET fumecheng-4967 289 23 density density NOUN fumecheng-4967 289 24 of of ADP fumecheng-4967 289 25 licl licl NUM fumecheng-4967 289 26 which which PRON fumecheng-4967 289 27 we we PRON fumecheng-4967 289 28 denote denote VERB fumecheng-4967 289 29 by by ADP fumecheng-4967 289 30 ρ1(r ρ1(r PROPN fumecheng-4967 289 31 , , PUNCT fumecheng-4967 289 32 t t PROPN fumecheng-4967 289 33 ) ) PUNCT fumecheng-4967 289 34 . . PUNCT fumecheng-4967 290 1 the the DET fumecheng-4967 290 2 corresponding corresponding ADJ fumecheng-4967 290 3 coefficients coefficient NOUN fumecheng-4967 290 4 and and CCONJ fumecheng-4967 290 5 the the DET fumecheng-4967 290 6 source source NOUN fumecheng-4967 290 7 of of ADP fumecheng-4967 290 8 noise noise NOUN fumecheng-4967 290 9 will will AUX fumecheng-4967 290 10 be be AUX fumecheng-4967 290 11 labeled label VERB fumecheng-4967 290 12 by by ADP fumecheng-4967 290 13 the the DET fumecheng-4967 290 14 index index NOUN fumecheng-4967 290 15 “ " PUNCT fumecheng-4967 290 16 1 1 NUM fumecheng-4967 290 17 ” " PUNCT fumecheng-4967 290 18 . . PUNCT fumecheng-4967 291 1 by by ADP fumecheng-4967 291 2 ρ2(r ρ2(r PROPN fumecheng-4967 291 3 , , PUNCT fumecheng-4967 291 4 t t PROPN fumecheng-4967 291 5 ) ) PUNCT fumecheng-4967 291 6 we we PRON fumecheng-4967 291 7 denote denote VERB fumecheng-4967 291 8 the the DET fumecheng-4967 291 9 density density NOUN fumecheng-4967 291 10 of of ADP fumecheng-4967 291 11 so2 so2 PROPN fumecheng-4967 291 12 . . PUNCT fumecheng-4967 292 1 we we PRON fumecheng-4967 292 2 model model VERB fumecheng-4967 292 3 the the DET fumecheng-4967 292 4 local local ADJ fumecheng-4967 292 5 repulsion repulsion NOUN fumecheng-4967 292 6 of of ADP fumecheng-4967 292 7 the the DET fumecheng-4967 292 8 reaction reaction NOUN fumecheng-4967 292 9 of of ADP fumecheng-4967 292 10 the the DET fumecheng-4967 292 11 products product NOUN fumecheng-4967 292 12 licl licl VERB fumecheng-4967 292 13 and and CCONJ fumecheng-4967 292 14 so2 so2 PROPN fumecheng-4967 292 15 by by ADP fumecheng-4967 292 16 a a DET fumecheng-4967 292 17 fixed fix VERB fumecheng-4967 292 18 - - PUNCT fumecheng-4967 292 19 sign sign NOUN fumecheng-4967 292 20 additional additional ADJ fumecheng-4967 292 21 term term NOUN fumecheng-4967 292 22 in in ADP fumecheng-4967 292 23 the the DET fumecheng-4967 292 24 effective effective ADJ fumecheng-4967 292 25 energy energy NOUN fumecheng-4967 292 26 of of ADP fumecheng-4967 292 27 the the DET fumecheng-4967 292 28 system system NOUN fumecheng-4967 292 29 , , PUNCT fumecheng-4967 292 30 v12(ρ1,ρ2 v12(ρ1,ρ2 NOUN fumecheng-4967 292 31 ) ) PUNCT fumecheng-4967 292 32 , , PUNCT fumecheng-4967 292 33 which which PRON fumecheng-4967 292 34 in in ADP fumecheng-4967 292 35 the the DET fumecheng-4967 292 36 lowest low ADJ fumecheng-4967 292 37 order order NOUN fumecheng-4967 292 38 that that PRON fumecheng-4967 292 39 can can AUX fumecheng-4967 292 40 be be AUX fumecheng-4967 292 41 written write VERB fumecheng-4967 292 42 v12(ρ1,ρ2)=bρ v12(ρ1,ρ2)=bρ ADP fumecheng-4967 292 43 2 2 NUM fumecheng-4967 292 44 1ρ 1ρ NOUN fumecheng-4967 292 45 2 2 NUM fumecheng-4967 292 46 2/2 2/2 NUM fumecheng-4967 292 47 . . PUNCT fumecheng-4967 293 1 equation equation NOUN fumecheng-4967 293 2 of of ADP fumecheng-4967 293 3 motion motion NOUN fumecheng-4967 293 4 for for ADP fumecheng-4967 293 5 the the DET fumecheng-4967 293 6 first first ADJ fumecheng-4967 293 7 density density NOUN fumecheng-4967 293 8 becomes become VERB fumecheng-4967 293 9 ∂ρ/∂t=−γ[c1δρ1+ρ1(1−ρ1)][c1+δ1(r ∂ρ/∂t=−γ[c1δρ1+ρ1(1−ρ1)][c1+δ1(r NOUN fumecheng-4967 293 10 , , PUNCT fumecheng-4967 293 11 t)]bρ1ρ t)]bρ1ρ NOUN fumecheng-4967 293 12 2 2 NUM fumecheng-4967 293 13 2 2 NUM fumecheng-4967 293 14 . . PUNCT fumecheng-4967 294 1 this this DET fumecheng-4967 294 2 equation equation NOUN fumecheng-4967 294 3 must must AUX fumecheng-4967 294 4 be be AUX fumecheng-4967 294 5 augmented augment VERB fumecheng-4967 294 6 with with ADP fumecheng-4967 294 7 an an DET fumecheng-4967 294 8 equation equation NOUN fumecheng-4967 294 9 describing describe VERB fumecheng-4967 294 10 the the DET fumecheng-4967 294 11 evolution evolution NOUN fumecheng-4967 294 12 of of ADP fumecheng-4967 294 13 the the DET fumecheng-4967 294 14 second second ADJ fumecheng-4967 294 15 component component NOUN fumecheng-4967 294 16 , , PUNCT fumecheng-4967 294 17 ρ2 ρ2 NOUN fumecheng-4967 294 18 . . PUNCT fumecheng-4967 295 1 the the DET fumecheng-4967 295 2 second second ADJ fumecheng-4967 295 3 component component NOUN fumecheng-4967 295 4 ρ2 ρ2 NOUN fumecheng-4967 295 5 , , PUNCT fumecheng-4967 295 6 just just ADV fumecheng-4967 295 7 like like ADP fumecheng-4967 295 8 the the DET fumecheng-4967 295 9 first first ADJ fumecheng-4967 295 10 one one NUM fumecheng-4967 295 11 , , PUNCT fumecheng-4967 295 12 is be AUX fumecheng-4967 295 13 generated generate VERB fumecheng-4967 295 14 as as ADP fumecheng-4967 295 15 a a DET fumecheng-4967 295 16 result result NOUN fumecheng-4967 295 17 of of ADP fumecheng-4967 295 18 the the DET fumecheng-4967 295 19 same same ADJ fumecheng-4967 295 20 reactions reaction NOUN fumecheng-4967 295 21 near near ADP fumecheng-4967 295 22 the the DET fumecheng-4967 295 23 free free ADJ fumecheng-4967 295 24 ( ( PUNCT fumecheng-4967 295 25 not not PART fumecheng-4967 295 26 contaminated contaminate VERB fumecheng-4967 295 27 by by ADP fumecheng-4967 295 28 so2 so2 PROPN fumecheng-4967 295 29 ) ) PUNCT fumecheng-4967 295 30 licl licl VERB fumecheng-4967 295 31 surface surface NOUN fumecheng-4967 295 32 . . PUNCT fumecheng-4967 296 1 this this PRON fumecheng-4967 296 2 means mean VERB fumecheng-4967 296 3 that that SCONJ fumecheng-4967 296 4 for for ADP fumecheng-4967 296 5 ρ2 ρ2 NOUN fumecheng-4967 296 6 , , PUNCT fumecheng-4967 296 7 we we PRON fumecheng-4967 296 8 must must AUX fumecheng-4967 296 9 use use VERB fumecheng-4967 296 10 the the DET fumecheng-4967 296 11 same same ADJ fumecheng-4967 296 12 generating generating NOUN fumecheng-4967 296 13 term term NOUN fumecheng-4967 296 14 ρ1(1−ρ1 ρ1(1−ρ1 PROPN fumecheng-4967 296 15 ) ) PUNCT fumecheng-4967 296 16 as as ADP fumecheng-4967 296 17 for for ADP fumecheng-4967 296 18 ρ1 ρ1 NOUN fumecheng-4967 296 19 : : PUNCT fumecheng-4967 296 20 2 2 NUM fumecheng-4967 296 21 1 1 NUM fumecheng-4967 296 22 2 2 NUM fumecheng-4967 296 23 2 2 NUM fumecheng-4967 296 24 1 1 NUM fumecheng-4967 296 25 1 1 NUM fumecheng-4967 296 26 2 2 NUM fumecheng-4967 296 27 2 2 NUM fumecheng-4967 296 28 2 2 NUM fumecheng-4967 296 29 1 1 NUM fumecheng-4967 296 30 2/ 2/ NUM fumecheng-4967 296 31 [ [ PUNCT fumecheng-4967 296 32 ( ( PUNCT fumecheng-4967 296 33 1 1 NUM fumecheng-4967 296 34 ) ) PUNCT fumecheng-4967 296 35 ] ] PUNCT fumecheng-4967 296 36 [ [ PUNCT fumecheng-4967 296 37 ( ( PUNCT fumecheng-4967 296 38 , , PUNCT fumecheng-4967 296 39 ) ) PUNCT fumecheng-4967 296 40 ] ] PUNCT fumecheng-4967 296 41 ( ( PUNCT fumecheng-4967 296 42 ) ) PUNCT fumecheng-4967 296 43 .t .t PROPN fumecheng-4967 297 1 c c NOUN fumecheng-4967 297 2 c c NOUN fumecheng-4967 297 3 r r NOUN fumecheng-4967 297 4 t t PROPN fumecheng-4967 297 5 b b PROPN fumecheng-4967 297 6 f f PROPN fumecheng-4967 297 7   NOUN fumecheng-4967 297 8   PROPN fumecheng-4967 297 9   PROPN fumecheng-4967 297 10   NOUN fumecheng-4967 297 11   VERB fumecheng-4967 297 12   PROPN fumecheng-4967 297 13   VERB fumecheng-4967 297 14   VERB fumecheng-4967 297 15   PRON fumecheng-4967 297 16   NUM fumecheng-4967 297 17   ADP fumecheng-4967 297 18   ADP fumecheng-4967 297 19   ADP fumecheng-4967 297 20   PROPN fumecheng-4967 297 21   ADP fumecheng-4967 297 22   ADP fumecheng-4967 297 23   NOUN fumecheng-4967 297 24 here here ADV fumecheng-4967 297 25 we we PRON fumecheng-4967 297 26 have have AUX fumecheng-4967 297 27 allowed allow VERB fumecheng-4967 297 28 for for ADP fumecheng-4967 297 29 the the DET fumecheng-4967 297 30 fact fact NOUN fumecheng-4967 297 31 that that SCONJ fumecheng-4967 297 32 although although SCONJ fumecheng-4967 297 33 both both DET fumecheng-4967 297 34 densities density NOUN fumecheng-4967 297 35 , , PUNCT fumecheng-4967 297 36 ρ1 ρ1 NOUN fumecheng-4967 297 37 and and CCONJ fumecheng-4967 297 38 ρ2 ρ2 NOUN fumecheng-4967 297 39 , , PUNCT fumecheng-4967 297 40 emerge emerge VERB fumecheng-4967 297 41 as as ADP fumecheng-4967 297 42 a a DET fumecheng-4967 297 43 result result NOUN fumecheng-4967 297 44 of of ADP fumecheng-4967 297 45 the the DET fumecheng-4967 297 46 same same ADJ fumecheng-4967 297 47 reaction reaction NOUN fumecheng-4967 297 48 , , PUNCT fumecheng-4967 297 49 the the DET fumecheng-4967 297 50 rate rate NOUN fumecheng-4967 297 51 of of ADP fumecheng-4967 297 52 formation formation NOUN fumecheng-4967 297 53 of of ADP fumecheng-4967 297 54 the the DET fumecheng-4967 297 55 dense dense ADJ fumecheng-4967 297 56 components component NOUN fumecheng-4967 297 57 in in ADP fumecheng-4967 297 58 r r NOUN fumecheng-4967 297 59 ρ1 ρ1 NOUN fumecheng-4967 297 60 and and CCONJ fumecheng-4967 297 61 ρ2 ρ2 NOUN fumecheng-4967 297 62 may may AUX fumecheng-4967 297 63 differ differ VERB fumecheng-4967 297 64 , , PUNCT fumecheng-4967 297 65 so so SCONJ fumecheng-4967 297 66 that that SCONJ fumecheng-4967 297 67 generally generally ADV fumecheng-4967 297 68 c1≠c2 c1≠c2 VERB fumecheng-4967 297 69 . . PUNCT fumecheng-4967 298 1 obviously obviously ADV fumecheng-4967 298 2 , , PUNCT fumecheng-4967 298 3 the the DET fumecheng-4967 298 4 terms term NOUN fumecheng-4967 298 5 linear linear VERB fumecheng-4967 298 6 in in ADP fumecheng-4967 298 7 ρ2 ρ2 NOUN fumecheng-4967 298 8 can can AUX fumecheng-4967 298 9 not not PART fumecheng-4967 298 10 ensure ensure VERB fumecheng-4967 298 11 that that SCONJ fumecheng-4967 298 12 the the DET fumecheng-4967 298 13 increase increase NOUN fumecheng-4967 298 14 in in ADP fumecheng-4967 298 15 ρ2 ρ2 NOUN fumecheng-4967 298 16 is be AUX fumecheng-4967 298 17 stopped stop VERB fumecheng-4967 298 18 and and CCONJ fumecheng-4967 298 19 is be AUX fumecheng-4967 298 20 stabilized stabilize VERB fumecheng-4967 298 21 ρ2→1 ρ2→1 ADV fumecheng-4967 298 22 in in ADP fumecheng-4967 298 23 the the DET fumecheng-4967 298 24 static static ADJ fumecheng-4967 298 25 limit limit NOUN fumecheng-4967 298 26 . . PUNCT fumecheng-4967 299 1 we we PRON fumecheng-4967 299 2 must must AUX fumecheng-4967 299 3 also also ADV fumecheng-4967 299 4 bear bear VERB fumecheng-4967 299 5 in in ADP fumecheng-4967 299 6 mind mind NOUN fumecheng-4967 299 7 that that SCONJ fumecheng-4967 299 8 far far ADV fumecheng-4967 299 9 from from ADP fumecheng-4967 299 10 the the DET fumecheng-4967 299 11 front front NOUN fumecheng-4967 299 12 , , PUNCT fumecheng-4967 299 13 there there PRON fumecheng-4967 299 14 is be VERB fumecheng-4967 299 15 no no DET fumecheng-4967 299 16 spontaneous spontaneous ADJ fumecheng-4967 299 17 generation generation NOUN fumecheng-4967 299 18 of of ADP fumecheng-4967 299 19 ρ2 ρ2 NOUN fumecheng-4967 299 20 , , PUNCT fumecheng-4967 299 21 and and CCONJ fumecheng-4967 299 22 hence hence ADV fumecheng-4967 299 23 the the DET fumecheng-4967 299 24 effective effective ADJ fumecheng-4967 299 25 energy energy NOUN fumecheng-4967 299 26 v2(ρ v2(ρ NOUN fumecheng-4967 299 27 2 2 NUM fumecheng-4967 299 28 2)=bρ 2)=bρ NUM fumecheng-4967 299 29 2 2 NUM fumecheng-4967 299 30 2(1−ρ 2(1−ρ NUM fumecheng-4967 299 31 2 2 NUM fumecheng-4967 299 32 2 2 NUM fumecheng-4967 299 33 ) ) PUNCT fumecheng-4967 299 34 , , PUNCT fumecheng-4967 299 35 whose whose DET fumecheng-4967 299 36 variation variation NOUN fumecheng-4967 299 37 yields yield VERB fumecheng-4967 299 38 the the DET fumecheng-4967 299 39 combination combination NOUN fumecheng-4967 299 40 proportional proportional ADJ fumecheng-4967 299 41 to to ADP fumecheng-4967 299 42 the the DET fumecheng-4967 299 43 function function NOUN fumecheng-4967 299 44 f(ρ2)=ρ2(0.5−ρ2 f(ρ2)=ρ2(0.5−ρ2 PROPN fumecheng-4967 299 45 ) ) PUNCT fumecheng-4967 299 46 ( ( PUNCT fumecheng-4967 299 47 1−ρ2 1−ρ2 NUM fumecheng-4967 299 48 ) ) PUNCT fumecheng-4967 299 49 . . PUNCT fumecheng-4967 300 1 it it PRON fumecheng-4967 300 2 contains contain VERB fumecheng-4967 300 3 a a DET fumecheng-4967 300 4 barrier barrier NOUN fumecheng-4967 300 5 that that PRON fumecheng-4967 300 6 separates separate VERB fumecheng-4967 300 7 the the DET fumecheng-4967 300 8 two two NUM fumecheng-4967 300 9 similar similar ADJ fumecheng-4967 300 10 minima minima NOUN fumecheng-4967 300 11 at at ADP fumecheng-4967 300 12 ρ2=0 ρ2=0 PROPN fumecheng-4967 300 13 and and CCONJ fumecheng-4967 300 14 ρ2=1 ρ2=1 PROPN fumecheng-4967 300 15 . . PUNCT fumecheng-4967 301 1 it it PRON fumecheng-4967 301 2 can can AUX fumecheng-4967 301 3 be be AUX fumecheng-4967 301 4 shown show VERB fumecheng-4967 301 5 that that SCONJ fumecheng-4967 301 6 in in ADP fumecheng-4967 301 7 the the DET fumecheng-4967 301 8 continuum continuum ADJ fumecheng-4967 301 9 approximation approximation NOUN fumecheng-4967 301 10 , , PUNCT fumecheng-4967 301 11 with with ADP fumecheng-4967 301 12 only only ADV fumecheng-4967 301 13 the the DET fumecheng-4967 301 14 lowest low ADJ fumecheng-4967 301 15 harmonics harmonic NOUN fumecheng-4967 301 16 in in ADP fumecheng-4967 301 17 the the DET fumecheng-4967 301 18 energy energy NOUN fumecheng-4967 301 19 ( ( PUNCT fumecheng-4967 301 20 and and CCONJ fumecheng-4967 301 21 hence hence ADV fumecheng-4967 301 22 laplasian laplasian ADJ fumecheng-4967 301 23 terms term NOUN fumecheng-4967 301 24 δρ1,2 δρ1,2 VERB fumecheng-4967 301 25 written write VERB fumecheng-4967 301 26 in in ADP fumecheng-4967 301 27 the the DET fumecheng-4967 301 28 equations equation NOUN fumecheng-4967 301 29 ) ) PUNCT fumecheng-4967 301 30 , , PUNCT fumecheng-4967 301 31 one one PRON fumecheng-4967 301 32 has have VERB fumecheng-4967 301 33 to to PART fumecheng-4967 301 34 add add VERB fumecheng-4967 301 35 generation generation NOUN fumecheng-4967 301 36 terms term NOUN fumecheng-4967 301 37 with with ADP fumecheng-4967 301 38 the the DET fumecheng-4967 301 39 step step NOUN fumecheng-4967 301 40 - - PUNCT fumecheng-4967 301 41 function function NOUN fumecheng-4967 301 42 cut cut NOUN fumecheng-4967 301 43 - - PUNCT fumecheng-4967 301 44 off off ADP fumecheng-4967 301 45 factor factor NOUN fumecheng-4967 302 1 | | ADV fumecheng-4967 302 2 ' ' PUNCT fumecheng-4967 302 3 | | ADV fumecheng-4967 302 4 ( ( PUNCT fumecheng-4967 302 5 ' ' PUNCT fumecheng-4967 302 6 ( ( PUNCT fumecheng-4967 302 7 ' ' NUM fumecheng-4967 302 8 ) ) PUNCT fumecheng-4967 302 9 ) ) PUNCT fumecheng-4967 303 1 r r NOUN fumecheng-4967 303 2 r r NOUN fumecheng-4967 303 3 dr dr PROPN fumecheng-4967 303 4 r r PROPN fumecheng-4967 303 5 a a DET fumecheng-4967 303 6   NOUN fumecheng-4967 303 7   PROPN fumecheng-4967 304 1   PROPN fumecheng-4967 304 2   NOUN fumecheng-4967 304 3   NOUN fumecheng-4967 304 4   PROPN fumecheng-4967 304 5   NOUN fumecheng-4967 304 6   NOUN fumecheng-4967 304 7 . . PUNCT fumecheng-4967 305 1 it it PRON fumecheng-4967 305 2 turns turn VERB fumecheng-4967 305 3 on on ADP fumecheng-4967 305 4 the the DET fumecheng-4967 305 5 generation generation NOUN fumecheng-4967 305 6 , , PUNCT fumecheng-4967 305 7 when when SCONJ fumecheng-4967 305 8 the the DET fumecheng-4967 305 9 density density NOUN fumecheng-4967 305 10 in in ADP fumecheng-4967 305 11 some some DET fumecheng-4967 305 12 neighborhood neighborhood NOUN fumecheng-4967 305 13 |r |r NOUN fumecheng-4967 305 14 - - PUNCT fumecheng-4967 305 15 r´|<σ r´|<σ NOUN fumecheng-4967 305 16 exceeds exceed VERB fumecheng-4967 305 17 critical critical ADJ fumecheng-4967 305 18 threshold threshold NOUN fumecheng-4967 305 19 a. a. NOUN fumecheng-4967 305 20 in in ADP fumecheng-4967 305 21 other other ADJ fumecheng-4967 305 22 words word NOUN fumecheng-4967 305 23 , , PUNCT fumecheng-4967 305 24 θ→1 θ→1 ADV fumecheng-4967 305 25 when when SCONJ fumecheng-4967 305 26 ' ' PUNCT fumecheng-4967 305 27 ' ' PUNCT fumecheng-4967 305 28 ( ( PUNCT fumecheng-4967 305 29 ' ' NUM fumecheng-4967 305 30 ) ) PUNCT fumecheng-4967 305 31 r r NOUN fumecheng-4967 305 32 r r NOUN fumecheng-4967 305 33 dr dr PROPN fumecheng-4967 305 34 r r PROPN fumecheng-4967 305 35 a a DET fumecheng-4967 305 36   PROPN fumecheng-4967 305 37   PROPN fumecheng-4967 305 38   PROPN fumecheng-4967 305 39   PROPN fumecheng-4967 305 40   NOUN fumecheng-4967 305 41 and and CCONJ fumecheng-4967 305 42 θ→0 θ→0 X fumecheng-4967 305 43 in in ADP fumecheng-4967 305 44 the the DET fumecheng-4967 305 45 opposite opposite ADJ fumecheng-4967 305 46 limit limit NOUN fumecheng-4967 305 47 . . PUNCT fumecheng-4967 306 1 finally finally ADV fumecheng-4967 306 2 kinetic kinetic ADJ fumecheng-4967 306 3 equations equation NOUN fumecheng-4967 306 4 take take VERB fumecheng-4967 306 5 the the DET fumecheng-4967 306 6 form form NOUN fumecheng-4967 306 7 : : PUNCT fumecheng-4967 306 8 2 2 NUM fumecheng-4967 306 9 1 1 NUM fumecheng-4967 306 10 1 1 NUM fumecheng-4967 306 11 1 1 NUM fumecheng-4967 306 12 1 1 NUM fumecheng-4967 306 13 1 1 NUM fumecheng-4967 306 14 1 1 NUM fumecheng-4967 306 15 1 1 NUM fumecheng-4967 306 16 1 1 NUM fumecheng-4967 306 17 2/ 2/ NUM fumecheng-4967 306 18 [ [ PUNCT fumecheng-4967 306 19 ( ( PUNCT fumecheng-4967 306 20 1 1 NUM fumecheng-4967 306 21 ) ) PUNCT fumecheng-4967 306 22 ] ] PUNCT fumecheng-4967 306 23 [ [ PUNCT fumecheng-4967 306 24 ( ( PUNCT fumecheng-4967 306 25 , , PUNCT fumecheng-4967 306 26 ) ) PUNCT fumecheng-4967 306 27 ] ] PUNCT fumecheng-4967 307 1 t t X fumecheng-4967 307 2 c c NOUN fumecheng-4967 307 3 c c NOUN fumecheng-4967 307 4 r r PROPN fumecheng-4967 307 5 t t PROPN fumecheng-4967 307 6 b b PROPN fumecheng-4967 307 7   PROPN fumecheng-4967 307 8   PRON fumecheng-4967 307 9   NOUN fumecheng-4967 307 10   PROPN fumecheng-4967 307 11   PROPN fumecheng-4967 307 12   VERB fumecheng-4967 307 13   NUM fumecheng-4967 307 14   NUM fumecheng-4967 307 15   ADP fumecheng-4967 307 16   ADP fumecheng-4967 307 17   ADP fumecheng-4967 307 18   PROPN fumecheng-4967 307 19   ADP fumecheng-4967 307 20   X fumecheng-4967 307 21 ( ( PUNCT fumecheng-4967 307 22 22 22 NUM fumecheng-4967 307 23 ) ) SYM fumecheng-4967 307 24 2 2 NUM fumecheng-4967 307 25 1 1 NUM fumecheng-4967 307 26 2 2 NUM fumecheng-4967 307 27 2 2 NUM fumecheng-4967 307 28 1 1 NUM fumecheng-4967 307 29 1 1 NUM fumecheng-4967 307 30 2 2 NUM fumecheng-4967 307 31 2 2 NUM fumecheng-4967 307 32 2 2 NUM fumecheng-4967 307 33 1 1 NUM fumecheng-4967 307 34 2 2 NUM fumecheng-4967 307 35 2 2 NUM fumecheng-4967 307 36 2/ 2/ NUM fumecheng-4967 307 37 [ [ PUNCT fumecheng-4967 307 38 ( ( PUNCT fumecheng-4967 307 39 1 1 NUM fumecheng-4967 307 40 ) ) PUNCT fumecheng-4967 307 41 ] ] PUNCT fumecheng-4967 307 42 [ [ PUNCT fumecheng-4967 307 43 ( ( PUNCT fumecheng-4967 307 44 , , PUNCT fumecheng-4967 307 45 ) ) PUNCT fumecheng-4967 307 46 ] ] PUNCT fumecheng-4967 307 47 ( ( PUNCT fumecheng-4967 307 48 0.5 0.5 NUM fumecheng-4967 307 49 ) ) PUNCT fumecheng-4967 307 50 ( ( PUNCT fumecheng-4967 307 51 1 1 X fumecheng-4967 307 52 ) ) PUNCT fumecheng-4967 307 53 t t NOUN fumecheng-4967 307 54 c c NOUN fumecheng-4967 307 55 c c NOUN fumecheng-4967 307 56 r r PROPN fumecheng-4967 307 57 t t PROPN fumecheng-4967 307 58 b b PROPN fumecheng-4967 307 59   PROPN fumecheng-4967 307 60   PRON fumecheng-4967 307 61   NOUN fumecheng-4967 307 62   VERB fumecheng-4967 307 63   PROPN fumecheng-4967 307 64   PUNCT fumecheng-4967 307 65   VERB fumecheng-4967 307 66   PROPN fumecheng-4967 307 67   PROPN fumecheng-4967 307 68   PROPN fumecheng-4967 307 69   NUM fumecheng-4967 307 70   ADP fumecheng-4967 307 71   ADP fumecheng-4967 307 72   ADP fumecheng-4967 307 73   PROPN fumecheng-4967 307 74   ADP fumecheng-4967 307 75   X fumecheng-4967 307 76   X fumecheng-4967 307 77   X fumecheng-4967 307 78   NOUN fumecheng-4967 307 79 . . PUNCT fumecheng-4967 308 1 in in ADP fumecheng-4967 308 2 purely purely ADV fumecheng-4967 308 3 local local ADJ fumecheng-4967 308 4 approximation approximation NOUN fumecheng-4967 308 5 , , PUNCT fumecheng-4967 308 6 the the DET fumecheng-4967 308 7 system system NOUN fumecheng-4967 308 8 eq eq ADJ fumecheng-4967 308 9 . . PUNCT fumecheng-4967 309 1 ( ( PUNCT fumecheng-4967 309 2 22 22 NUM fumecheng-4967 309 3 ) ) PUNCT fumecheng-4967 309 4 can can AUX fumecheng-4967 309 5 be be AUX fumecheng-4967 309 6 reduced reduce VERB fumecheng-4967 309 7 to to ADP fumecheng-4967 309 8 the the DET fumecheng-4967 309 9 form form NOUN fumecheng-4967 309 10 of of ADP fumecheng-4967 309 11 ordinary ordinary ADJ fumecheng-4967 309 12 differential differential ADJ fumecheng-4967 309 13 equations equation NOUN fumecheng-4967 309 14 : : PUNCT fumecheng-4967 309 15 230 230 NUM fumecheng-4967 309 16 a.e a.e PROPN fumecheng-4967 309 17 . . PROPN fumecheng-4967 309 18 filippov filippov PROPN fumecheng-4967 309 19 , , PUNCT fumecheng-4967 309 20 s.n s.n PROPN fumecheng-4967 309 21 . . PROPN fumecheng-4967 309 22 gorb gorb PROPN fumecheng-4967 309 23 2 2 NUM fumecheng-4967 309 24 1 1 NUM fumecheng-4967 309 25 1 1 NUM fumecheng-4967 309 26 1 1 NUM fumecheng-4967 309 27 1 1 NUM fumecheng-4967 309 28 1 1 NUM fumecheng-4967 309 29 1 1 NUM fumecheng-4967 309 30 2/ 2/ NUM fumecheng-4967 309 31 ( ( PUNCT fumecheng-4967 309 32 1 1 NUM fumecheng-4967 309 33 ) ) PUNCT fumecheng-4967 309 34 [ [ PUNCT fumecheng-4967 309 35 ( ( PUNCT fumecheng-4967 309 36 , , PUNCT fumecheng-4967 309 37 ) ) PUNCT fumecheng-4967 310 1 ] ] X fumecheng-4967 310 2 t t X fumecheng-4967 310 3 c c NOUN fumecheng-4967 310 4 r r NOUN fumecheng-4967 310 5 t t PROPN fumecheng-4967 310 6 b b PROPN fumecheng-4967 310 7   PROPN fumecheng-4967 310 8   PROPN fumecheng-4967 310 9   PROPN fumecheng-4967 310 10   CCONJ fumecheng-4967 310 11   PUNCT fumecheng-4967 310 12   ADP fumecheng-4967 310 13   ADP fumecheng-4967 310 14   PROPN fumecheng-4967 310 15   ADP fumecheng-4967 310 16   X fumecheng-4967 310 17 ( ( PUNCT fumecheng-4967 310 18 23 23 NUM fumecheng-4967 310 19 ) ) SYM fumecheng-4967 310 20 2 2 NUM fumecheng-4967 310 21 1 1 NUM fumecheng-4967 310 22 1 1 NUM fumecheng-4967 310 23 1 1 NUM fumecheng-4967 310 24 2 2 NUM fumecheng-4967 310 25 2 2 NUM fumecheng-4967 310 26 2 2 NUM fumecheng-4967 310 27 1 1 NUM fumecheng-4967 310 28 2 2 NUM fumecheng-4967 310 29 2 2 NUM fumecheng-4967 310 30 2/ 2/ NUM fumecheng-4967 310 31 ( ( PUNCT fumecheng-4967 310 32 1 1 NUM fumecheng-4967 310 33 ) ) PUNCT fumecheng-4967 310 34 [ [ PUNCT fumecheng-4967 310 35 ( ( PUNCT fumecheng-4967 310 36 , , PUNCT fumecheng-4967 310 37 ) ) PUNCT fumecheng-4967 310 38 ] ] PUNCT fumecheng-4967 310 39 ( ( PUNCT fumecheng-4967 310 40 0.5 0.5 NUM fumecheng-4967 310 41 ) ) PUNCT fumecheng-4967 310 42 ( ( PUNCT fumecheng-4967 310 43 1 1 X fumecheng-4967 310 44 ) ) PUNCT fumecheng-4967 310 45 t t NOUN fumecheng-4967 310 46 c c NOUN fumecheng-4967 310 47 r r NOUN fumecheng-4967 310 48 t t PROPN fumecheng-4967 310 49 b b PROPN fumecheng-4967 310 50   PROPN fumecheng-4967 311 1   PROPN fumecheng-4967 311 2   PROPN fumecheng-4967 311 3   VERB fumecheng-4967 311 4   VERB fumecheng-4967 311 5   PROPN fumecheng-4967 311 6   PROPN fumecheng-4967 311 7   PROPN fumecheng-4967 311 8   ADV fumecheng-4967 311 9   ADP fumecheng-4967 311 10   PROPN fumecheng-4967 311 11   ADP fumecheng-4967 311 12   X fumecheng-4967 311 13   X fumecheng-4967 311 14   X fumecheng-4967 311 15   NOUN fumecheng-4967 311 16 . . PUNCT fumecheng-4967 312 1 here here ADV fumecheng-4967 312 2 the the DET fumecheng-4967 312 3 scale scale NOUN fumecheng-4967 312 4 of of ADP fumecheng-4967 312 5 time time NOUN fumecheng-4967 312 6 is be AUX fumecheng-4967 312 7 normalized normalize VERB fumecheng-4967 312 8 to to ADP fumecheng-4967 312 9 γ=1 γ=1 PROPN fumecheng-4967 312 10 . . PUNCT fumecheng-4967 313 1 the the DET fumecheng-4967 313 2 global global ADJ fumecheng-4967 313 3 structure structure NOUN fumecheng-4967 313 4 of of ADP fumecheng-4967 313 5 the the DET fumecheng-4967 313 6 phase phase NOUN fumecheng-4967 313 7 portrait portrait NOUN fumecheng-4967 313 8 is be AUX fumecheng-4967 313 9 depicted depict VERB fumecheng-4967 313 10 in in ADP fumecheng-4967 313 11 fig fig NOUN fumecheng-4967 313 12 . . PUNCT fumecheng-4967 314 1 3 3 NUM fumecheng-4967 314 2 which which PRON fumecheng-4967 314 3 presents present VERB fumecheng-4967 314 4 a a DET fumecheng-4967 314 5 physically physically ADV fumecheng-4967 314 6 interesting interesting ADJ fumecheng-4967 314 7 realization realization NOUN fumecheng-4967 314 8 of of ADP fumecheng-4967 314 9 the the DET fumecheng-4967 314 10 portrait portrait NOUN fumecheng-4967 314 11 . . PUNCT fumecheng-4967 315 1 the the DET fumecheng-4967 315 2 local local ADJ fumecheng-4967 315 3 system system NOUN fumecheng-4967 315 4 of of ADP fumecheng-4967 315 5 equations equation NOUN fumecheng-4967 315 6 eq eq ADP fumecheng-4967 315 7 . . PUNCT fumecheng-4967 316 1 ( ( PUNCT fumecheng-4967 316 2 23 23 NUM fumecheng-4967 316 3 ) ) PUNCT fumecheng-4967 316 4 actually actually ADV fumecheng-4967 316 5 describes describe VERB fumecheng-4967 316 6 the the DET fumecheng-4967 316 7 evolution evolution NOUN fumecheng-4967 316 8 of of ADP fumecheng-4967 316 9 the the DET fumecheng-4967 316 10 densities density NOUN fumecheng-4967 316 11 at at ADP fumecheng-4967 316 12 each each DET fumecheng-4967 316 13 point point NOUN fumecheng-4967 316 14 in in ADP fumecheng-4967 316 15 space space NOUN fumecheng-4967 316 16 without without ADP fumecheng-4967 316 17 allowing allow VERB fumecheng-4967 316 18 for for ADP fumecheng-4967 316 19 interaction interaction NOUN fumecheng-4967 316 20 between between ADP fumecheng-4967 316 21 different different ADJ fumecheng-4967 316 22 points point NOUN fumecheng-4967 316 23 . . PUNCT fumecheng-4967 317 1 in in ADP fumecheng-4967 317 2 this this DET fumecheng-4967 317 3 approximation approximation NOUN fumecheng-4967 317 4 , , PUNCT fumecheng-4967 317 5 the the DET fumecheng-4967 317 6 interaction interaction NOUN fumecheng-4967 317 7 is be AUX fumecheng-4967 317 8 taken take VERB fumecheng-4967 317 9 into into ADP fumecheng-4967 317 10 account account NOUN fumecheng-4967 317 11 only only ADV fumecheng-4967 317 12 via via ADP fumecheng-4967 317 13 the the DET fumecheng-4967 317 14 initial initial ADJ fumecheng-4967 317 15 conditions condition NOUN fumecheng-4967 317 16 . . PUNCT fumecheng-4967 318 1 specifically specifically ADV fumecheng-4967 318 2 , , PUNCT fumecheng-4967 318 3 as as SCONJ fumecheng-4967 318 4 the the DET fumecheng-4967 318 5 front front NOUN fumecheng-4967 318 6 arrives arrive VERB fumecheng-4967 318 7 at at ADP fumecheng-4967 318 8 a a DET fumecheng-4967 318 9 point point NOUN fumecheng-4967 318 10 in in ADP fumecheng-4967 318 11 space space NOUN fumecheng-4967 318 12 , , PUNCT fumecheng-4967 318 13 both both DET fumecheng-4967 318 14 densities density NOUN fumecheng-4967 318 15 ρ1 ρ1 NOUN fumecheng-4967 318 16 and and CCONJ fumecheng-4967 318 17 ρ2 ρ2 NOUN fumecheng-4967 318 18 begin begin VERB fumecheng-4967 318 19 to to PART fumecheng-4967 318 20 be be AUX fumecheng-4967 318 21 generated generate VERB fumecheng-4967 318 22 at at ADP fumecheng-4967 318 23 that that DET fumecheng-4967 318 24 point point NOUN fumecheng-4967 318 25 , , PUNCT fumecheng-4967 318 26 so so SCONJ fumecheng-4967 318 27 that that SCONJ fumecheng-4967 318 28 the the DET fumecheng-4967 318 29 physical physical ADJ fumecheng-4967 318 30 scenario scenario NOUN fumecheng-4967 318 31 in in ADP fumecheng-4967 318 32 the the DET fumecheng-4967 318 33 phase phase NOUN fumecheng-4967 318 34 portrait portrait NOUN fumecheng-4967 318 35 in in ADP fumecheng-4967 318 36 fig fig NOUN fumecheng-4967 318 37 . . PUNCT fumecheng-4967 319 1 5 5 NUM fumecheng-4967 319 2 corresponds correspond NOUN fumecheng-4967 319 3 to to ADP fumecheng-4967 319 4 the the DET fumecheng-4967 319 5 trajectories trajectory NOUN fumecheng-4967 319 6 that that PRON fumecheng-4967 319 7 emerge emerge VERB fumecheng-4967 319 8 in in ADP fumecheng-4967 319 9 the the DET fumecheng-4967 319 10 neighborhood neighborhood NOUN fumecheng-4967 319 11 of of ADP fumecheng-4967 319 12 the the DET fumecheng-4967 319 13 trivial trivial ADJ fumecheng-4967 319 14 point point NOUN fumecheng-4967 319 15 ρ1 ρ1 NOUN fumecheng-4967 319 16 = = SYM fumecheng-4967 319 17 ρ2=0 ρ2=0 PROPN fumecheng-4967 319 18 . . PUNCT fumecheng-4967 320 1 fig fig NOUN fumecheng-4967 320 2 . . PUNCT fumecheng-4967 321 1 5 5 NUM fumecheng-4967 321 2 phase phase NOUN fumecheng-4967 321 3 portrait portrait NOUN fumecheng-4967 321 4 of of ADP fumecheng-4967 321 5 local local ADJ fumecheng-4967 321 6 version version NOUN fumecheng-4967 321 7 of of ADP fumecheng-4967 321 8 the the DET fumecheng-4967 321 9 kinetic kinetic ADJ fumecheng-4967 321 10 equations equation NOUN fumecheng-4967 321 11 describing describe VERB fumecheng-4967 321 12 growth growth NOUN fumecheng-4967 321 13 of of ADP fumecheng-4967 321 14 porous porous ADJ fumecheng-4967 321 15 surface surface NOUN fumecheng-4967 321 16 . . PUNCT fumecheng-4967 322 1 fixed fix VERB fumecheng-4967 322 2 points point NOUN fumecheng-4967 322 3 corresponding correspond VERB fumecheng-4967 322 4 to to ADP fumecheng-4967 322 5 possible possible ADJ fumecheng-4967 322 6 combinations combination NOUN fumecheng-4967 322 7 of of ADP fumecheng-4967 322 8 local local ADJ fumecheng-4967 322 9 densities density NOUN fumecheng-4967 322 10 are be AUX fumecheng-4967 322 11 marked mark VERB fumecheng-4967 322 12 by by ADP fumecheng-4967 322 13 red red ADJ fumecheng-4967 322 14 color color NOUN fumecheng-4967 322 15 . . PUNCT fumecheng-4967 323 1 two two NUM fumecheng-4967 323 2 well well ADV fumecheng-4967 323 3 pronounced pronounce VERB fumecheng-4967 323 4 “ " PUNCT fumecheng-4967 323 5 large large ADJ fumecheng-4967 323 6 rivers river NOUN fumecheng-4967 323 7 ” " PUNCT fumecheng-4967 323 8 leading lead VERB fumecheng-4967 323 9 to to ADP fumecheng-4967 323 10 the the DET fumecheng-4967 323 11 static static ADJ fumecheng-4967 323 12 final final ADJ fumecheng-4967 323 13 configurations configuration NOUN fumecheng-4967 323 14 are be AUX fumecheng-4967 323 15 shown show VERB fumecheng-4967 323 16 by by ADP fumecheng-4967 323 17 the the DET fumecheng-4967 323 18 blue blue ADJ fumecheng-4967 323 19 lines line NOUN fumecheng-4967 323 20 . . PUNCT fumecheng-4967 324 1 cloud cloud NOUN fumecheng-4967 324 2 of of ADP fumecheng-4967 324 3 small small ADJ fumecheng-4967 324 4 gray gray ADJ fumecheng-4967 324 5 points point NOUN fumecheng-4967 324 6 represents represent VERB fumecheng-4967 324 7 instant instant ADJ fumecheng-4967 324 8 realizations realization NOUN fumecheng-4967 324 9 of of ADP fumecheng-4967 324 10 the the DET fumecheng-4967 324 11 densities density NOUN fumecheng-4967 324 12 numerically numerically ADV fumecheng-4967 324 13 found find VERB fumecheng-4967 324 14 for for ADP fumecheng-4967 324 15 the the DET fumecheng-4967 324 16 exact exact ADJ fumecheng-4967 324 17 nonlocal nonlocal ADJ fumecheng-4967 324 18 equations equation NOUN fumecheng-4967 324 19 . . PUNCT fumecheng-4967 325 1 the the DET fumecheng-4967 325 2 separatrix separatrix NOUN fumecheng-4967 325 3 connecting connect VERB fumecheng-4967 325 4 this this DET fumecheng-4967 325 5 point point NOUN fumecheng-4967 325 6 and and CCONJ fumecheng-4967 325 7 the the DET fumecheng-4967 325 8 saddle saddle NOUN fumecheng-4967 325 9 point point NOUN fumecheng-4967 325 10 divides divide VERB fumecheng-4967 325 11 plane plane NOUN fumecheng-4967 325 12 { { PUNCT fumecheng-4967 325 13 ρ1,ρ2 ρ1,ρ2 PROPN fumecheng-4967 325 14 } } PUNCT fumecheng-4967 325 15 into into ADP fumecheng-4967 325 16 attracting attract VERB fumecheng-4967 325 17 basins basin NOUN fumecheng-4967 325 18 for for ADP fumecheng-4967 325 19 the the DET fumecheng-4967 325 20 two two NUM fumecheng-4967 325 21 stable stable ADJ fumecheng-4967 325 22 directly directly ADV fumecheng-4967 325 23 seen see VERB fumecheng-4967 325 24 fixed fix VERB fumecheng-4967 325 25 points point NOUN fumecheng-4967 325 26 . . PUNCT fumecheng-4967 326 1 studying study VERB fumecheng-4967 326 2 the the DET fumecheng-4967 326 3 behavior behavior NOUN fumecheng-4967 326 4 of of ADP fumecheng-4967 326 5 the the DET fumecheng-4967 326 6 trajectories trajectory NOUN fumecheng-4967 326 7 that that PRON fumecheng-4967 326 8 start start VERB fumecheng-4967 326 9 near near ADP fumecheng-4967 326 10 the the DET fumecheng-4967 326 11 separatrix separatrix NOUN fumecheng-4967 326 12 , , PUNCT fumecheng-4967 326 13 we we PRON fumecheng-4967 326 14 can can AUX fumecheng-4967 326 15 predict predict VERB fumecheng-4967 326 16 several several ADJ fumecheng-4967 326 17 results result NOUN fumecheng-4967 326 18 of of ADP fumecheng-4967 326 19 numerical numerical ADJ fumecheng-4967 326 20 modeling modeling NOUN fumecheng-4967 326 21 of of ADP fumecheng-4967 326 22 the the DET fumecheng-4967 326 23 complete complete ADJ fumecheng-4967 326 24 equations equation NOUN fumecheng-4967 326 25 and and CCONJ fumecheng-4967 326 26 , , PUNCT fumecheng-4967 326 27 in in ADP fumecheng-4967 326 28 the the DET fumecheng-4967 326 29 final final ADJ fumecheng-4967 326 30 analysis analysis NOUN fumecheng-4967 326 31 , , PUNCT fumecheng-4967 326 32 the the DET fumecheng-4967 326 33 properties property NOUN fumecheng-4967 326 34 of of ADP fumecheng-4967 326 35 real real ADJ fumecheng-4967 326 36 systems system NOUN fumecheng-4967 326 37 . . PUNCT fumecheng-4967 327 1 in in ADP fumecheng-4967 327 2 particular particular ADJ fumecheng-4967 327 3 , , PUNCT fumecheng-4967 327 4 we we PRON fumecheng-4967 327 5 can can AUX fumecheng-4967 327 6 easily easily ADV fumecheng-4967 327 7 predict predict VERB fumecheng-4967 327 8 the the DET fumecheng-4967 327 9 role role NOUN fumecheng-4967 327 10 of of ADP fumecheng-4967 327 11 the the DET fumecheng-4967 327 12 source source NOUN fumecheng-4967 327 13 of of ADP fumecheng-4967 327 14 noise noise NOUN fumecheng-4967 327 15 . . PUNCT fumecheng-4967 328 1 if if SCONJ fumecheng-4967 328 2 the the DET fumecheng-4967 328 3 noise noise NOUN fumecheng-4967 328 4 is be AUX fumecheng-4967 328 5 strong strong ADJ fumecheng-4967 328 6 , , PUNCT fumecheng-4967 328 7 the the DET fumecheng-4967 328 8 phase phase NOUN fumecheng-4967 328 9 trajectories trajectory NOUN fumecheng-4967 328 10 can can AUX fumecheng-4967 328 11 pass pass VERB fumecheng-4967 328 12 both both PRON fumecheng-4967 328 13 above above ADP fumecheng-4967 328 14 and and CCONJ fumecheng-4967 328 15 below below ADP fumecheng-4967 328 16 the the DET fumecheng-4967 328 17 separatrix separatrix NOUN fumecheng-4967 328 18 , , PUNCT fumecheng-4967 328 19 irrespective irrespective ADV fumecheng-4967 328 20 of of ADP fumecheng-4967 328 21 the the DET fumecheng-4967 328 22 scenario scenario NOUN fumecheng-4967 328 23 according accord VERB fumecheng-4967 328 24 to to ADP fumecheng-4967 328 25 which which PRON fumecheng-4967 328 26 the the DET fumecheng-4967 328 27 front front NOUN fumecheng-4967 328 28 arrives arrive VERB fumecheng-4967 328 29 at at ADP fumecheng-4967 328 30 the the DET fumecheng-4967 328 31 given give VERB fumecheng-4967 328 32 point point NOUN fumecheng-4967 328 33 . . PUNCT fumecheng-4967 329 1 within within ADP fumecheng-4967 329 2 a a DET fumecheng-4967 329 3 certain certain ADJ fumecheng-4967 329 4 time time NOUN fumecheng-4967 329 5 interval interval NOUN fumecheng-4967 329 6 after after ADP fumecheng-4967 329 7 the the DET fumecheng-4967 329 8 arrival arrival NOUN fumecheng-4967 329 9 of of ADP fumecheng-4967 329 10 the the DET fumecheng-4967 329 11 front front NOUN fumecheng-4967 329 12 , , PUNCT fumecheng-4967 329 13 both both DET fumecheng-4967 329 14 densities density NOUN fumecheng-4967 329 15 ρ1,2 ρ1,2 ADJ fumecheng-4967 329 16 increase increase NOUN fumecheng-4967 329 17 essentially essentially ADV fumecheng-4967 329 18 simultaneously simultaneously ADV fumecheng-4967 329 19 and and CCONJ fumecheng-4967 329 20 very very ADV fumecheng-4967 329 21 fast fast ADV fumecheng-4967 329 22 , , PUNCT fumecheng-4967 329 23 to to PART fumecheng-4967 329 24 which which PRON fumecheng-4967 329 25 the the DET fumecheng-4967 329 26 first first ADJ fumecheng-4967 329 27 maximum maximum NOUN fumecheng-4967 329 28 in in ADP fumecheng-4967 329 29 the the DET fumecheng-4967 329 30 evolution evolution NOUN fumecheng-4967 329 31 rate rate NOUN fumecheng-4967 329 32 methods method NOUN fumecheng-4967 329 33 of of ADP fumecheng-4967 329 34 the the DET fumecheng-4967 329 35 pattern pattern NOUN fumecheng-4967 329 36 formation formation NOUN fumecheng-4967 329 37 in in ADP fumecheng-4967 329 38 numerical numerical ADJ fumecheng-4967 329 39 modeling modeling NOUN fumecheng-4967 329 40 of of ADP fumecheng-4967 329 41 biological biological ADJ fumecheng-4967 329 42 problems problem NOUN fumecheng-4967 329 43 231 231 NUM fumecheng-4967 329 44 2 2 NUM fumecheng-4967 329 45 2 2 NUM fumecheng-4967 329 46 2 2 NUM fumecheng-4967 329 47 1 1 NUM fumecheng-4967 329 48 2 2 NUM fumecheng-4967 329 49 ( ( PUNCT fumecheng-4967 329 50 ) ) PUNCT fumecheng-4967 330 1 [ [ X fumecheng-4967 330 2 ( ( PUNCT fumecheng-4967 330 3 / / SYM fumecheng-4967 330 4 ) ) PUNCT fumecheng-4967 330 5 ( ( PUNCT fumecheng-4967 330 6 / / SYM fumecheng-4967 330 7 ) ) PUNCT fumecheng-4967 330 8 ] ] X fumecheng-4967 330 9 w w X fumecheng-4967 330 10 t t PROPN fumecheng-4967 330 11 t t PROPN fumecheng-4967 330 12 t t PROPN fumecheng-4967 330 13   PROPN fumecheng-4967 330 14   PROPN fumecheng-4967 330 15   ADJ fumecheng-4967 330 16   ADJ fumecheng-4967 330 17   PROPN fumecheng-4967 330 18   NOUN fumecheng-4967 330 19 ( ( PUNCT fumecheng-4967 330 20 24 24 NUM fumecheng-4967 330 21 ) ) PUNCT fumecheng-4967 330 22 corresponds correspond NOUN fumecheng-4967 330 23 , , PUNCT fumecheng-4967 330 24 as as SCONJ fumecheng-4967 330 25 depicted depict VERB fumecheng-4967 330 26 in in ADP fumecheng-4967 330 27 fig fig NOUN fumecheng-4967 330 28 . . PUNCT fumecheng-4967 331 1 4 4 NUM fumecheng-4967 331 2 . . X fumecheng-4967 331 3 near near ADP fumecheng-4967 331 4 the the DET fumecheng-4967 331 5 saddle saddle NOUN fumecheng-4967 331 6 point point NOUN fumecheng-4967 331 7 , , PUNCT fumecheng-4967 331 8 there there PRON fumecheng-4967 331 9 can can AUX fumecheng-4967 331 10 be be AUX fumecheng-4967 331 11 no no DET fumecheng-4967 331 12 further further ADJ fumecheng-4967 331 13 increase increase NOUN fumecheng-4967 331 14 in in ADP fumecheng-4967 331 15 ρ1,2 ρ1,2 PROPN fumecheng-4967 331 16 . . PUNCT fumecheng-4967 332 1 the the DET fumecheng-4967 332 2 rate rate NOUN fumecheng-4967 332 3 w(t w(t PROPN fumecheng-4967 332 4 ) ) PUNCT fumecheng-4967 332 5 rapidly rapidly ADV fumecheng-4967 332 6 decreases decrease VERB fumecheng-4967 332 7 . . PUNCT fumecheng-4967 333 1 at at ADP fumecheng-4967 333 2 the the DET fumecheng-4967 333 3 same same ADJ fumecheng-4967 333 4 time time NOUN fumecheng-4967 333 5 , , PUNCT fumecheng-4967 333 6 there there PRON fumecheng-4967 333 7 is be VERB fumecheng-4967 333 8 phase phase NOUN fumecheng-4967 333 9 separation separation NOUN fumecheng-4967 333 10 in in ADP fumecheng-4967 333 11 the the DET fumecheng-4967 333 12 system system NOUN fumecheng-4967 333 13 , , PUNCT fumecheng-4967 333 14 with with ADP fumecheng-4967 333 15 one one NUM fumecheng-4967 333 16 of of ADP fumecheng-4967 333 17 the the DET fumecheng-4967 333 18 densities density NOUN fumecheng-4967 333 19 , , PUNCT fumecheng-4967 333 20 ρ1 ρ1 NOUN fumecheng-4967 333 21 or or CCONJ fumecheng-4967 333 22 ρ2 ρ2 NOUN fumecheng-4967 333 23 , , PUNCT fumecheng-4967 333 24 expelled expel VERB fumecheng-4967 333 25 from from ADP fumecheng-4967 333 26 the the DET fumecheng-4967 333 27 given give VERB fumecheng-4967 333 28 region region NOUN fumecheng-4967 333 29 in in ADP fumecheng-4967 333 30 space space NOUN fumecheng-4967 333 31 . . PUNCT fumecheng-4967 334 1 this this PRON fumecheng-4967 334 2 is be AUX fumecheng-4967 334 3 followed follow VERB fumecheng-4967 334 4 by by ADP fumecheng-4967 334 5 a a DET fumecheng-4967 334 6 sharp sharp ADJ fumecheng-4967 334 7 increase increase NOUN fumecheng-4967 334 8 in in ADP fumecheng-4967 334 9 w(t w(t PROPN fumecheng-4967 334 10 ) ) PUNCT fumecheng-4967 334 11 accompanied accompany VERB fumecheng-4967 334 12 by by ADP fumecheng-4967 334 13 a a DET fumecheng-4967 334 14 rapid rapid ADJ fumecheng-4967 334 15 buildup buildup NOUN fumecheng-4967 334 16 of of ADP fumecheng-4967 334 17 the the DET fumecheng-4967 334 18 remaining remain VERB fumecheng-4967 334 19 component component NOUN fumecheng-4967 334 20 , , PUNCT fumecheng-4967 334 21 a a DET fumecheng-4967 334 22 process process NOUN fumecheng-4967 334 23 that that PRON fumecheng-4967 334 24 is be AUX fumecheng-4967 334 25 slowed slow VERB fumecheng-4967 334 26 down down ADP fumecheng-4967 334 27 near near ADP fumecheng-4967 334 28 one one NUM fumecheng-4967 334 29 of of ADP fumecheng-4967 334 30 the the DET fumecheng-4967 334 31 stable stable ADJ fumecheng-4967 334 32 fixed fix VERB fumecheng-4967 334 33 states state NOUN fumecheng-4967 334 34 . . PUNCT fumecheng-4967 335 1 evolution evolution NOUN fumecheng-4967 335 2 rate rate NOUN fumecheng-4967 335 3 w(t w(t PROPN fumecheng-4967 335 4 ) ) PUNCT fumecheng-4967 336 1 as as SCONJ fumecheng-4967 336 2 a a DET fumecheng-4967 336 3 function function NOUN fumecheng-4967 336 4 of of ADP fumecheng-4967 336 5 time time NOUN fumecheng-4967 336 6 is be AUX fumecheng-4967 336 7 shown show VERB fumecheng-4967 336 8 in in ADP fumecheng-4967 336 9 fig fig NOUN fumecheng-4967 336 10 . . PUNCT fumecheng-4967 337 1 6 6 NUM fumecheng-4967 337 2 . . X fumecheng-4967 337 3 fig fig NOUN fumecheng-4967 337 4 . . PUNCT fumecheng-4967 338 1 6 6 NUM fumecheng-4967 338 2 evolution evolution NOUN fumecheng-4967 338 3 rate rate NOUN fumecheng-4967 338 4 w(t w(t PROPN fumecheng-4967 338 5 ) ) PUNCT fumecheng-4967 338 6 as as ADP fumecheng-4967 338 7 a a DET fumecheng-4967 338 8 function function NOUN fumecheng-4967 338 9 of of ADP fumecheng-4967 338 10 time time NOUN fumecheng-4967 338 11 . . PUNCT fumecheng-4967 339 1 good good ADJ fumecheng-4967 339 2 correlation correlation NOUN fumecheng-4967 339 3 with with ADP fumecheng-4967 339 4 the the DET fumecheng-4967 339 5 phase phase NOUN fumecheng-4967 339 6 portrait portrait NOUN fumecheng-4967 339 7 ( ( PUNCT fumecheng-4967 339 8 shown show VERB fumecheng-4967 339 9 in in ADP fumecheng-4967 339 10 the the DET fumecheng-4967 339 11 insert insert NOUN fumecheng-4967 339 12 ) ) PUNCT fumecheng-4967 339 13 is be AUX fumecheng-4967 339 14 clearly clearly ADV fumecheng-4967 339 15 seen see VERB fumecheng-4967 339 16 . . PUNCT fumecheng-4967 340 1 the the DET fumecheng-4967 340 2 particular particular ADJ fumecheng-4967 340 3 trajectory trajectory NOUN fumecheng-4967 340 4 for for ADP fumecheng-4967 340 5 which which PRON fumecheng-4967 340 6 w(t w(t PROPN fumecheng-4967 340 7 ) ) PUNCT fumecheng-4967 340 8 is be AUX fumecheng-4967 340 9 calculated calculate VERB fumecheng-4967 340 10 is be AUX fumecheng-4967 340 11 marked mark VERB fumecheng-4967 340 12 by by ADP fumecheng-4967 340 13 red red ADJ fumecheng-4967 340 14 color color NOUN fumecheng-4967 340 15 . . PUNCT fumecheng-4967 341 1 low low ADJ fumecheng-4967 341 2 evolution evolution NOUN fumecheng-4967 341 3 rate rate NOUN fumecheng-4967 341 4 corresponds correspond VERB fumecheng-4967 341 5 to to ADP fumecheng-4967 341 6 the the DET fumecheng-4967 341 7 vicinities vicinity NOUN fumecheng-4967 341 8 of of ADP fumecheng-4967 341 9 the the DET fumecheng-4967 341 10 fixed fix VERB fumecheng-4967 341 11 points point NOUN fumecheng-4967 341 12 and and CCONJ fumecheng-4967 341 13 “ " PUNCT fumecheng-4967 341 14 large large ADJ fumecheng-4967 341 15 river river NOUN fumecheng-4967 341 16 ” " PUNCT fumecheng-4967 341 17 leading lead VERB fumecheng-4967 341 18 to to ADP fumecheng-4967 341 19 final final ADJ fumecheng-4967 341 20 static static ADJ fumecheng-4967 341 21 configuration configuration NOUN fumecheng-4967 341 22 . . PUNCT fumecheng-4967 342 1 discrete discrete ADJ fumecheng-4967 342 2 set set NOUN fumecheng-4967 342 3 of of ADP fumecheng-4967 342 4 black black ADJ fumecheng-4967 342 5 points point NOUN fumecheng-4967 342 6 represent represent VERB fumecheng-4967 342 7 the the DET fumecheng-4967 342 8 mean mean ADJ fumecheng-4967 342 9 rate rate NOUN fumecheng-4967 342 10 numerically numerically ADV fumecheng-4967 342 11 found find VERB fumecheng-4967 342 12 for for ADP fumecheng-4967 342 13 the the DET fumecheng-4967 342 14 exact exact ADJ fumecheng-4967 342 15 nonlocal nonlocal ADJ fumecheng-4967 342 16 equations equation NOUN fumecheng-4967 342 17 . . PUNCT fumecheng-4967 343 1 the the DET fumecheng-4967 343 2 characteristic characteristic ADJ fumecheng-4967 343 3 double double ADJ fumecheng-4967 343 4 - - PUNCT fumecheng-4967 343 5 humped humped NOUN fumecheng-4967 343 6 curves curve NOUN fumecheng-4967 343 7 representing represent VERB fumecheng-4967 343 8 the the DET fumecheng-4967 343 9 evolution evolution NOUN fumecheng-4967 343 10 rate rate NOUN fumecheng-4967 343 11 are be AUX fumecheng-4967 343 12 indeed indeed ADV fumecheng-4967 343 13 observed observe VERB fumecheng-4967 343 14 , , PUNCT fumecheng-4967 343 15 when when SCONJ fumecheng-4967 343 16 the the DET fumecheng-4967 343 17 complete complete ADJ fumecheng-4967 343 18 system system NOUN fumecheng-4967 343 19 of of ADP fumecheng-4967 343 20 equations equation NOUN fumecheng-4967 343 21 is be AUX fumecheng-4967 343 22 solved solve VERB fumecheng-4967 343 23 numerically numerically ADV fumecheng-4967 343 24 . . PUNCT fumecheng-4967 344 1 in in ADP fumecheng-4967 344 2 accordance accordance NOUN fumecheng-4967 344 3 with with ADP fumecheng-4967 344 4 the the DET fumecheng-4967 344 5 physics physics NOUN fumecheng-4967 344 6 of of ADP fumecheng-4967 344 7 the the DET fumecheng-4967 344 8 problem problem NOUN fumecheng-4967 344 9 , , PUNCT fumecheng-4967 344 10 the the DET fumecheng-4967 344 11 initial initial ADJ fumecheng-4967 344 12 condition condition NOUN fumecheng-4967 344 13 is be AUX fumecheng-4967 344 14 selected select VERB fumecheng-4967 344 15 in in ADP fumecheng-4967 344 16 the the DET fumecheng-4967 344 17 form form NOUN fumecheng-4967 344 18 of of ADP fumecheng-4967 344 19 a a DET fumecheng-4967 344 20 narrow narrow ADJ fumecheng-4967 344 21 strip strip NOUN fumecheng-4967 344 22 of of ADP fumecheng-4967 344 23 density density NOUN fumecheng-4967 344 24 ρ1(r ρ1(r PROPN fumecheng-4967 344 25 , , PUNCT fumecheng-4967 344 26 t t PROPN fumecheng-4967 344 27 ) ) PUNCT fumecheng-4967 344 28 , , PUNCT fumecheng-4967 344 29 near near ADP fumecheng-4967 344 30 one one NUM fumecheng-4967 344 31 of of ADP fumecheng-4967 344 32 the the DET fumecheng-4967 344 33 boundaries boundary NOUN fumecheng-4967 344 34 of of ADP fumecheng-4967 344 35 the the DET fumecheng-4967 344 36 two two NUM fumecheng-4967 344 37 - - PUNCT fumecheng-4967 344 38 dimensional dimensional ADJ fumecheng-4967 344 39 system system NOUN fumecheng-4967 344 40 . . PUNCT fumecheng-4967 345 1 here here ADV fumecheng-4967 345 2 the the DET fumecheng-4967 345 3 process process NOUN fumecheng-4967 345 4 of of ADP fumecheng-4967 345 5 generation generation NOUN fumecheng-4967 345 6 and and CCONJ fumecheng-4967 345 7 separation separation NOUN fumecheng-4967 345 8 of of ADP fumecheng-4967 345 9 the the DET fumecheng-4967 345 10 densities density NOUN fumecheng-4967 345 11 ρ1,2(r ρ1,2(r PROPN fumecheng-4967 345 12 , , PUNCT fumecheng-4967 345 13 t t PROPN fumecheng-4967 345 14 ) ) PUNCT fumecheng-4967 345 15 is be AUX fumecheng-4967 345 16 accompanied accompany VERB fumecheng-4967 345 17 by by ADP fumecheng-4967 345 18 the the DET fumecheng-4967 345 19 formation formation NOUN fumecheng-4967 345 20 of of ADP fumecheng-4967 345 21 characteristic characteristic ADJ fumecheng-4967 345 22 dendritic dendritic ADJ fumecheng-4967 345 23 spatial spatial ADJ fumecheng-4967 345 24 distributions distribution NOUN fumecheng-4967 345 25 of of ADP fumecheng-4967 345 26 both both DET fumecheng-4967 345 27 densities density NOUN fumecheng-4967 345 28 . . PUNCT fumecheng-4967 346 1 the the DET fumecheng-4967 346 2 two two NUM fumecheng-4967 346 3 densities density NOUN fumecheng-4967 346 4 are be AUX fumecheng-4967 346 5 generated generate VERB fumecheng-4967 346 6 simultaneously simultaneously ADV fumecheng-4967 346 7 in in ADP fumecheng-4967 346 8 the the DET fumecheng-4967 346 9 vicinity vicinity NOUN fumecheng-4967 346 10 of of ADP fumecheng-4967 346 11 the the DET fumecheng-4967 346 12 front front NOUN fumecheng-4967 346 13 . . PUNCT fumecheng-4967 347 1 however however ADV fumecheng-4967 347 2 , , PUNCT fumecheng-4967 347 3 in in ADP fumecheng-4967 347 4 the the DET fumecheng-4967 347 5 absence absence NOUN fumecheng-4967 347 6 of of ADP fumecheng-4967 347 7 noise noise NOUN fumecheng-4967 347 8 , , PUNCT fumecheng-4967 347 9 the the DET fumecheng-4967 347 10 initial initial ADJ fumecheng-4967 347 11 density density NOUN fumecheng-4967 347 12 distribution distribution NOUN fumecheng-4967 347 13 leads lead VERB fumecheng-4967 347 14 to to ADP fumecheng-4967 347 15 the the DET fumecheng-4967 347 16 formation formation NOUN fumecheng-4967 347 17 behind behind ADP fumecheng-4967 347 18 the the DET fumecheng-4967 347 19 front front NOUN fumecheng-4967 347 20 of of ADP fumecheng-4967 347 21 a a DET fumecheng-4967 347 22 completely completely ADV fumecheng-4967 347 23 filled fill VERB fumecheng-4967 347 24 region region NOUN fumecheng-4967 347 25 . . PUNCT fumecheng-4967 348 1 numerical numerical ADJ fumecheng-4967 348 2 solution solution NOUN fumecheng-4967 348 3 shows show VERB fumecheng-4967 348 4 that that SCONJ fumecheng-4967 348 5 further far ADV fumecheng-4967 348 6 with with ADP fumecheng-4967 348 7 time time NOUN fumecheng-4967 348 8 the the DET fumecheng-4967 348 9 front front NOUN fumecheng-4967 348 10 becomes become VERB fumecheng-4967 348 11 discontinuous discontinuous ADJ fumecheng-4967 348 12 , , PUNCT fumecheng-4967 348 13 and and CCONJ fumecheng-4967 348 14 the the DET fumecheng-4967 348 15 expanding expand VERB fumecheng-4967 348 16 ordered order VERB fumecheng-4967 348 17 region region NOUN fumecheng-4967 348 18 is be AUX fumecheng-4967 348 19 transformed transform VERB fumecheng-4967 348 20 into into ADP fumecheng-4967 348 21 a a DET fumecheng-4967 348 22 fractal fractal NOUN fumecheng-4967 348 23 . . PUNCT fumecheng-4967 349 1 in in ADP fumecheng-4967 349 2 fig fig NOUN fumecheng-4967 349 3 . . PUNCT fumecheng-4967 350 1 5 5 NUM fumecheng-4967 350 2 , , PUNCT fumecheng-4967 350 3 we we PRON fumecheng-4967 350 4 use use VERB fumecheng-4967 350 5 a a DET fumecheng-4967 350 6 copper copper NOUN fumecheng-4967 350 7 scale scale NOUN fumecheng-4967 350 8 to to PART fumecheng-4967 350 9 show show VERB fumecheng-4967 350 10 a a DET fumecheng-4967 350 11 characteristic characteristic ADJ fumecheng-4967 350 12 fragment fragment NOUN fumecheng-4967 350 13 of of ADP fumecheng-4967 350 14 the the DET fumecheng-4967 350 15 system system NOUN fumecheng-4967 350 16 with with ADP fumecheng-4967 350 17 a a DET fumecheng-4967 350 18 distribution distribution NOUN fumecheng-4967 350 19 of of ADP fumecheng-4967 350 20 the the DET fumecheng-4967 350 21 total total ADJ fumecheng-4967 350 22 density density NOUN fumecheng-4967 350 23 that that PRON fumecheng-4967 350 24 emerges emerge VERB fumecheng-4967 350 25 at at ADP fumecheng-4967 350 26 the the DET fumecheng-4967 350 27 intermediate intermediate ADJ fumecheng-4967 350 28 stage stage NOUN fumecheng-4967 350 29 in in ADP fumecheng-4967 350 30 the the DET fumecheng-4967 350 31 transition transition NOUN fumecheng-4967 350 32 from from ADP fumecheng-4967 350 33 the the DET fumecheng-4967 350 34 homogeneous homogeneous ADJ fumecheng-4967 350 35 growth growth NOUN fumecheng-4967 350 36 to to ADP fumecheng-4967 350 37 the the DET fumecheng-4967 350 38 fractal fractal ADJ fumecheng-4967 350 39 growth growth NOUN fumecheng-4967 350 40 . . PUNCT fumecheng-4967 351 1 contaminated contaminate VERB fumecheng-4967 351 2 regions region NOUN fumecheng-4967 351 3 and and CCONJ fumecheng-4967 351 4 232 232 NUM fumecheng-4967 351 5 a.e a.e PROPN fumecheng-4967 351 6 . . PROPN fumecheng-4967 351 7 filippov filippov PROPN fumecheng-4967 351 8 , , PUNCT fumecheng-4967 351 9 s.n s.n PROPN fumecheng-4967 351 10 . . PROPN fumecheng-4967 351 11 gorb gorb PROPN fumecheng-4967 351 12 regions region NOUN fumecheng-4967 351 13 of of ADP fumecheng-4967 351 14 active active ADJ fumecheng-4967 351 15 growth growth NOUN fumecheng-4967 351 16 are be AUX fumecheng-4967 351 17 clearly clearly ADV fumecheng-4967 351 18 visible visible ADJ fumecheng-4967 351 19 . . PUNCT fumecheng-4967 352 1 these these PRON fumecheng-4967 352 2 are be AUX fumecheng-4967 352 3 characterized characterize VERB fumecheng-4967 352 4 by by ADP fumecheng-4967 352 5 intermediate intermediate ADJ fumecheng-4967 352 6 values value NOUN fumecheng-4967 352 7 of of ADP fumecheng-4967 352 8 the the DET fumecheng-4967 352 9 densities density NOUN fumecheng-4967 352 10 which which PRON fumecheng-4967 352 11 correspond correspond VERB fumecheng-4967 352 12 to to ADP fumecheng-4967 352 13 sections section NOUN fumecheng-4967 352 14 in in ADP fumecheng-4967 352 15 fig fig NOUN fumecheng-4967 352 16 . . PUNCT fumecheng-4967 353 1 5 5 NUM fumecheng-4967 353 2 with with ADP fumecheng-4967 353 3 intermediate intermediate ADJ fumecheng-4967 353 4 shades shade NOUN fumecheng-4967 353 5 of of ADP fumecheng-4967 353 6 copper copper NOUN fumecheng-4967 353 7 color color NOUN fumecheng-4967 353 8 . . PUNCT fumecheng-4967 354 1 fig fig NOUN fumecheng-4967 354 2 . . PUNCT fumecheng-4967 355 1 7 7 NUM fumecheng-4967 355 2 two two NUM fumecheng-4967 355 3 intermediate intermediate ADJ fumecheng-4967 355 4 stages stage NOUN fumecheng-4967 355 5 of of ADP fumecheng-4967 355 6 the the DET fumecheng-4967 355 7 porous porous ADJ fumecheng-4967 355 8 surface surface NOUN fumecheng-4967 355 9 layer layer NOUN fumecheng-4967 355 10 formation formation NOUN fumecheng-4967 355 11 ( ( PUNCT fumecheng-4967 355 12 from from ADP fumecheng-4967 355 13 subplot subplot NOUN fumecheng-4967 355 14 ( ( PUNCT fumecheng-4967 355 15 a a NOUN fumecheng-4967 355 16 ) ) PUNCT fumecheng-4967 355 17 to to ADP fumecheng-4967 355 18 ( ( PUNCT fumecheng-4967 355 19 b b NOUN fumecheng-4967 355 20 ) ) PUNCT fumecheng-4967 355 21 ) ) PUNCT fumecheng-4967 355 22 . . PUNCT fumecheng-4967 356 1 with with ADP fumecheng-4967 356 2 the the DET fumecheng-4967 356 3 time time NOUN fumecheng-4967 356 4 , , PUNCT fumecheng-4967 356 5 such such ADJ fumecheng-4967 356 6 system system NOUN fumecheng-4967 356 7 can can AUX fumecheng-4967 356 8 develop develop VERB fumecheng-4967 356 9 very very ADV fumecheng-4967 356 10 complex complex ADJ fumecheng-4967 356 11 structure structure NOUN fumecheng-4967 356 12 with with ADP fumecheng-4967 356 13 not not PART fumecheng-4967 356 14 simply simply ADV fumecheng-4967 356 15 fractal fractal ADJ fumecheng-4967 356 16 surface surface NOUN fumecheng-4967 356 17 , , PUNCT fumecheng-4967 356 18 but but CCONJ fumecheng-4967 356 19 also also ADV fumecheng-4967 356 20 with with ADP fumecheng-4967 356 21 lacunas lacuna NOUN fumecheng-4967 356 22 of of ADP fumecheng-4967 356 23 a a DET fumecheng-4967 356 24 negative negative ADJ fumecheng-4967 356 25 curvature curvature NOUN fumecheng-4967 356 26 , , PUNCT fumecheng-4967 356 27 which which PRON fumecheng-4967 356 28 effect effect NOUN fumecheng-4967 356 29 in in ADP fumecheng-4967 356 30 a a DET fumecheng-4967 356 31 strong strong ADJ fumecheng-4967 356 32 increase increase NOUN fumecheng-4967 356 33 of of ADP fumecheng-4967 356 34 adhesion adhesion NOUN fumecheng-4967 356 35 of of ADP fumecheng-4967 356 36 the the DET fumecheng-4967 356 37 soft soft ADJ fumecheng-4967 356 38 tissue tissue NOUN fumecheng-4967 356 39 contacting contact VERB fumecheng-4967 356 40 such such DET fumecheng-4967 356 41 a a DET fumecheng-4967 356 42 surface surface NOUN fumecheng-4967 356 43 . . PUNCT fumecheng-4967 357 1 in in ADP fumecheng-4967 357 2 comparison comparison NOUN fumecheng-4967 357 3 to to ADP fumecheng-4967 357 4 the the DET fumecheng-4967 357 5 study study NOUN fumecheng-4967 357 6 of of ADP fumecheng-4967 357 7 growth growth NOUN fumecheng-4967 357 8 processes process NOUN fumecheng-4967 357 9 with with ADP fumecheng-4967 357 10 models model NOUN fumecheng-4967 357 11 with with ADP fumecheng-4967 357 12 only only ADV fumecheng-4967 357 13 one one NUM fumecheng-4967 357 14 fluctuating fluctuate VERB fumecheng-4967 357 15 variable variable NOUN fumecheng-4967 357 16 , , PUNCT fumecheng-4967 357 17 the the DET fumecheng-4967 357 18 novel novel ADJ fumecheng-4967 357 19 property property NOUN fumecheng-4967 357 20 of of ADP fumecheng-4967 357 21 the the DET fumecheng-4967 357 22 system system NOUN fumecheng-4967 357 23 lies lie VERB fumecheng-4967 357 24 in in ADP fumecheng-4967 357 25 the the DET fumecheng-4967 357 26 possibility possibility NOUN fumecheng-4967 357 27 of of ADP fumecheng-4967 357 28 the the DET fumecheng-4967 357 29 emergence emergence NOUN fumecheng-4967 357 30 of of ADP fumecheng-4967 357 31 voids voids NOUN fumecheng-4967 357 32 behind behind ADP fumecheng-4967 357 33 the the DET fumecheng-4967 357 34 front front ADJ fumecheng-4967 357 35 , , PUNCT fumecheng-4967 357 36 i.e. i.e. X fumecheng-4967 357 37 regions region NOUN fumecheng-4967 357 38 filled fill VERB fumecheng-4967 357 39 with with ADP fumecheng-4967 357 40 neither neither PRON fumecheng-4967 357 41 of of ADP fumecheng-4967 357 42 the the DET fumecheng-4967 357 43 two two NUM fumecheng-4967 357 44 components component NOUN fumecheng-4967 357 45 . . PUNCT fumecheng-4967 358 1 when when SCONJ fumecheng-4967 358 2 there there PRON fumecheng-4967 358 3 is be VERB fumecheng-4967 358 4 only only ADV fumecheng-4967 358 5 one one NUM fumecheng-4967 358 6 field field NOUN fumecheng-4967 358 7 , , PUNCT fumecheng-4967 358 8 i.e. i.e. X fumecheng-4967 358 9 ρ1(r ρ1(r PROPN fumecheng-4967 358 10 , , PUNCT fumecheng-4967 358 11 t t PROPN fumecheng-4967 358 12 ) ) PUNCT fumecheng-4967 358 13 ( ( PUNCT fumecheng-4967 358 14 such such ADJ fumecheng-4967 358 15 lacunae lacunae NOUN fumecheng-4967 358 16 must must AUX fumecheng-4967 358 17 be be AUX fumecheng-4967 358 18 thought think VERB fumecheng-4967 358 19 of of ADP fumecheng-4967 358 20 as as ADP fumecheng-4967 358 21 being be AUX fumecheng-4967 358 22 filled fill VERB fumecheng-4967 358 23 with with ADP fumecheng-4967 358 24 the the DET fumecheng-4967 358 25 other other ADJ fumecheng-4967 358 26 , , PUNCT fumecheng-4967 358 27 „ „ PUNCT fumecheng-4967 358 28 „ „ PUNCT fumecheng-4967 358 29 contaminating‟‟ contaminating‟‟ PROPN fumecheng-4967 358 30 component component NOUN fumecheng-4967 358 31 of of ADP fumecheng-4967 358 32 density density NOUN fumecheng-4967 358 33 , , PUNCT fumecheng-4967 358 34 ρ2(r ρ2(r PROPN fumecheng-4967 358 35 , , PUNCT fumecheng-4967 358 36 t t PROPN fumecheng-4967 358 37 ) ) PUNCT fumecheng-4967 358 38 , , PUNCT fumecheng-4967 358 39 which which PRON fumecheng-4967 358 40 in in ADP fumecheng-4967 358 41 this this DET fumecheng-4967 358 42 case case NOUN fumecheng-4967 358 43 is be AUX fumecheng-4967 358 44 not not PART fumecheng-4967 358 45 explicitly explicitly ADV fumecheng-4967 358 46 present present ADJ fumecheng-4967 358 47 in in ADP fumecheng-4967 358 48 the the DET fumecheng-4967 358 49 equations equation NOUN fumecheng-4967 358 50 . . PUNCT fumecheng-4967 359 1 the the DET fumecheng-4967 359 2 model model NOUN fumecheng-4967 359 3 contains contain VERB fumecheng-4967 359 4 additional additional ADJ fumecheng-4967 359 5 information information NOUN fumecheng-4967 359 6 about about ADP fumecheng-4967 359 7 the the DET fumecheng-4967 359 8 second second ADJ fumecheng-4967 359 9 field field NOUN fumecheng-4967 359 10 ρ1(r ρ1(r PROPN fumecheng-4967 359 11 , , PUNCT fumecheng-4967 359 12 t t PROPN fumecheng-4967 359 13 ) ) PUNCT fumecheng-4967 359 14 , , PUNCT fumecheng-4967 359 15 which which PRON fumecheng-4967 359 16 makes make VERB fumecheng-4967 359 17 it it PRON fumecheng-4967 359 18 possible possible ADJ fumecheng-4967 359 19 to to PART fumecheng-4967 359 20 distinguish distinguish VERB fumecheng-4967 359 21 between between ADP fumecheng-4967 359 22 the the DET fumecheng-4967 359 23 regions region NOUN fumecheng-4967 359 24 occupied occupy VERB fumecheng-4967 359 25 by by ADP fumecheng-4967 359 26 ρ2(r ρ2(r PROPN fumecheng-4967 359 27 , , PUNCT fumecheng-4967 359 28 t t PROPN fumecheng-4967 359 29 ) ) PUNCT fumecheng-4967 359 30 and and CCONJ fumecheng-4967 359 31 the the DET fumecheng-4967 359 32 voids voids NOUN fumecheng-4967 359 33 . . PUNCT fumecheng-4967 360 1 the the DET fumecheng-4967 360 2 mechanism mechanism NOUN fumecheng-4967 360 3 of of ADP fumecheng-4967 360 4 void void ADJ fumecheng-4967 360 5 formation formation NOUN fumecheng-4967 360 6 is be AUX fumecheng-4967 360 7 clearly clearly ADV fumecheng-4967 360 8 seen see VERB fumecheng-4967 360 9 in in ADP fumecheng-4967 360 10 fig fig NOUN fumecheng-4967 360 11 . . PUNCT fumecheng-4967 361 1 7a 7a NUM fumecheng-4967 361 2 , , PUNCT fumecheng-4967 361 3 which which PRON fumecheng-4967 361 4 for for ADP fumecheng-4967 361 5 a a DET fumecheng-4967 361 6 small small ADJ fumecheng-4967 361 7 fragment fragment NOUN fumecheng-4967 361 8 of of ADP fumecheng-4967 361 9 the the DET fumecheng-4967 361 10 front front NOUN fumecheng-4967 361 11 depicts depict VERB fumecheng-4967 361 12 a a DET fumecheng-4967 361 13 typical typical ADJ fumecheng-4967 361 14 growth growth NOUN fumecheng-4967 361 15 sequence sequence NOUN fumecheng-4967 361 16 . . PUNCT fumecheng-4967 362 1 three three NUM fumecheng-4967 362 2 characteristic characteristic ADJ fumecheng-4967 362 3 moments moment NOUN fumecheng-4967 362 4 in in ADP fumecheng-4967 362 5 time time NOUN fumecheng-4967 362 6 are be AUX fumecheng-4967 362 7 singled single VERB fumecheng-4967 362 8 out out ADP fumecheng-4967 362 9 : : PUNCT fumecheng-4967 362 10 the the DET fumecheng-4967 362 11 emergence emergence NOUN fumecheng-4967 362 12 of of ADP fumecheng-4967 362 13 a a DET fumecheng-4967 362 14 dense dense ADJ fumecheng-4967 362 15 initial initial ADJ fumecheng-4967 362 16 layer layer NOUN fumecheng-4967 362 17 , , PUNCT fumecheng-4967 362 18 the the DET fumecheng-4967 362 19 emergence emergence NOUN fumecheng-4967 362 20 of of ADP fumecheng-4967 362 21 the the DET fumecheng-4967 362 22 first first ADJ fumecheng-4967 362 23 dendritic dendritic ADJ fumecheng-4967 362 24 protuberances protuberance NOUN fumecheng-4967 362 25 , , PUNCT fumecheng-4967 362 26 and and CCONJ fumecheng-4967 362 27 the the DET fumecheng-4967 362 28 collapse collapse NOUN fumecheng-4967 362 29 of of ADP fumecheng-4967 362 30 the the DET fumecheng-4967 362 31 first first ADJ fumecheng-4967 362 32 internal internal ADJ fumecheng-4967 362 33 pores pore NOUN fumecheng-4967 362 34 in in ADP fumecheng-4967 362 35 a a DET fumecheng-4967 362 36 structure structure NOUN fumecheng-4967 362 37 with with ADP fumecheng-4967 362 38 a a DET fumecheng-4967 362 39 total total ADJ fumecheng-4967 362 40 density density NOUN fumecheng-4967 362 41 ρ(r ρ(r PROPN fumecheng-4967 362 42 , , PUNCT fumecheng-4967 362 43 t)=ρ1(r t)=ρ1(r NUM fumecheng-4967 362 44 , , PUNCT fumecheng-4967 362 45 t)+ρ2(r t)+ρ2(r PROPN fumecheng-4967 362 46 , , PUNCT fumecheng-4967 362 47 t t PROPN fumecheng-4967 362 48 ) ) PUNCT fumecheng-4967 362 49 . . PUNCT fumecheng-4967 363 1 well well ADV fumecheng-4967 363 2 - - PUNCT fumecheng-4967 363 3 formed form VERB fumecheng-4967 363 4 voids voids NOUN fumecheng-4967 363 5 are be AUX fumecheng-4967 363 6 clearly clearly ADV fumecheng-4967 363 7 visible visible ADJ fumecheng-4967 363 8 in in ADP fumecheng-4967 363 9 fig fig NOUN fumecheng-4967 363 10 . . PUNCT fumecheng-4967 364 1 7b 7b NOUN fumecheng-4967 364 2 . . PUNCT fumecheng-4967 365 1 void void ADJ fumecheng-4967 365 2 formation formation NOUN fumecheng-4967 365 3 is be AUX fumecheng-4967 365 4 closely closely ADV fumecheng-4967 365 5 related relate VERB fumecheng-4967 365 6 to to ADP fumecheng-4967 365 7 the the DET fumecheng-4967 365 8 ability ability NOUN fumecheng-4967 365 9 of of ADP fumecheng-4967 365 10 the the DET fumecheng-4967 365 11 „ „ PUNCT fumecheng-4967 365 12 „ „ PUNCT fumecheng-4967 365 13 contaminant‟‟ contaminant‟‟ NOUN fumecheng-4967 365 14 ρ2(r ρ2(r PROPN fumecheng-4967 365 15 , , PUNCT fumecheng-4967 365 16 t t PROPN fumecheng-4967 365 17 ) ) PUNCT fumecheng-4967 365 18 to to PART fumecheng-4967 365 19 block block VERB fumecheng-4967 365 20 the the DET fumecheng-4967 365 21 active active ADJ fumecheng-4967 365 22 sections section NOUN fumecheng-4967 365 23 of of ADP fumecheng-4967 365 24 the the DET fumecheng-4967 365 25 front front ADJ fumecheng-4967 365 26 ρ1(r ρ1(r PROPN fumecheng-4967 365 27 , , PUNCT fumecheng-4967 365 28 t t PROPN fumecheng-4967 365 29 ) ) PUNCT fumecheng-4967 365 30 and and CCONJ fumecheng-4967 365 31 , , PUNCT fumecheng-4967 365 32 at at ADP fumecheng-4967 365 33 least least ADJ fumecheng-4967 365 34 in in ADP fumecheng-4967 365 35 principle principle NOUN fumecheng-4967 365 36 , , PUNCT fumecheng-4967 365 37 to to PART fumecheng-4967 365 38 terminate terminate VERB fumecheng-4967 365 39 the the DET fumecheng-4967 365 40 growth growth NOUN fumecheng-4967 365 41 process process NOUN fumecheng-4967 365 42 . . PUNCT fumecheng-4967 366 1 as as ADP fumecheng-4967 366 2 the the DET fumecheng-4967 366 3 pores pore NOUN fumecheng-4967 366 4 collapse collapse NOUN fumecheng-4967 366 5 , , PUNCT fumecheng-4967 366 6 the the DET fumecheng-4967 366 7 front front NOUN fumecheng-4967 366 8 usually usually ADV fumecheng-4967 366 9 continues continue VERB fumecheng-4967 366 10 to to PART fumecheng-4967 366 11 move move VERB fumecheng-4967 366 12 in in ADP fumecheng-4967 366 13 both both DET fumecheng-4967 366 14 directions direction NOUN fumecheng-4967 366 15 . . PUNCT fumecheng-4967 367 1 naturally naturally ADV fumecheng-4967 367 2 , , PUNCT fumecheng-4967 367 3 the the DET fumecheng-4967 367 4 outer outer ADJ fumecheng-4967 367 5 boundary boundary ADJ fumecheng-4967 367 6 ρ1(r ρ1(r PROPN fumecheng-4967 367 7 , , PUNCT fumecheng-4967 367 8 t t PROPN fumecheng-4967 367 9 ) ) PUNCT fumecheng-4967 367 10 is be AUX fumecheng-4967 367 11 almost almost ADV fumecheng-4967 367 12 insensitive insensitive ADJ fumecheng-4967 367 13 to to ADP fumecheng-4967 367 14 the the DET fumecheng-4967 367 15 presence presence NOUN fumecheng-4967 367 16 of of ADP fumecheng-4967 367 17 a a DET fumecheng-4967 367 18 pore pore NOUN fumecheng-4967 367 19 blocked block VERB fumecheng-4967 367 20 somewhere somewhere ADV fumecheng-4967 367 21 inside inside ADP fumecheng-4967 367 22 the the DET fumecheng-4967 367 23 system system NOUN fumecheng-4967 367 24 and and CCONJ fumecheng-4967 367 25 continues continue VERB fumecheng-4967 367 26 its its PRON fumecheng-4967 367 27 forward forward ADJ fumecheng-4967 367 28 motion motion NOUN fumecheng-4967 367 29 . . PUNCT fumecheng-4967 368 1 the the DET fumecheng-4967 368 2 inner inner ADJ fumecheng-4967 368 3 boundary boundary PROPN fumecheng-4967 368 4 ρ1(r ρ1(r PROPN fumecheng-4967 368 5 , , PUNCT fumecheng-4967 368 6 t t PROPN fumecheng-4967 368 7 ) ) PUNCT fumecheng-4967 368 8 surrounding surround VERB fumecheng-4967 368 9 a a DET fumecheng-4967 368 10 pore pore NOUN fumecheng-4967 368 11 is be AUX fumecheng-4967 368 12 qualitatively qualitatively ADV fumecheng-4967 368 13 similar similar ADJ fumecheng-4967 368 14 to to ADP fumecheng-4967 368 15 the the DET fumecheng-4967 368 16 outer outer ADJ fumecheng-4967 368 17 boundary boundary NOUN fumecheng-4967 368 18 and and CCONJ fumecheng-4967 368 19 can can AUX fumecheng-4967 368 20 move move VERB fumecheng-4967 368 21 „ „ PUNCT fumecheng-4967 368 22 „ „ PUNCT fumecheng-4967 368 23 back,‟‟ back,‟‟ NOUN fumecheng-4967 368 24 up up ADP fumecheng-4967 368 25 to to ADP fumecheng-4967 368 26 the the DET fumecheng-4967 368 27 point point NOUN fumecheng-4967 368 28 , , PUNCT fumecheng-4967 368 29 where where SCONJ fumecheng-4967 368 30 it it PRON fumecheng-4967 368 31 is be AUX fumecheng-4967 368 32 completely completely ADV fumecheng-4967 368 33 blocked block VERB fumecheng-4967 368 34 by by ADP fumecheng-4967 368 35 sections section NOUN fumecheng-4967 368 36 with with ADP fumecheng-4967 368 37 ρ2(r ρ2(r PROPN fumecheng-4967 368 38 , , PUNCT fumecheng-4967 368 39 t t PROPN fumecheng-4967 368 40 ) ) PUNCT fumecheng-4967 368 41 . . PUNCT fumecheng-4967 369 1 the the DET fumecheng-4967 369 2 scenario scenario NOUN fumecheng-4967 369 3 of of ADP fumecheng-4967 369 4 the the DET fumecheng-4967 369 5 evolution evolution NOUN fumecheng-4967 369 6 of of ADP fumecheng-4967 369 7 the the DET fumecheng-4967 369 8 system system NOUN fumecheng-4967 369 9 turns turn VERB fumecheng-4967 369 10 out out ADP fumecheng-4967 369 11 to to PART fumecheng-4967 369 12 be be AUX fumecheng-4967 369 13 exceptionally exceptionally ADV fumecheng-4967 369 14 multifaceted multifaceted ADJ fumecheng-4967 369 15 and and CCONJ fumecheng-4967 369 16 methods method NOUN fumecheng-4967 369 17 of of ADP fumecheng-4967 369 18 the the DET fumecheng-4967 369 19 pattern pattern NOUN fumecheng-4967 369 20 formation formation NOUN fumecheng-4967 369 21 in in ADP fumecheng-4967 369 22 numerical numerical ADJ fumecheng-4967 369 23 modeling modeling NOUN fumecheng-4967 369 24 of of ADP fumecheng-4967 369 25 biological biological ADJ fumecheng-4967 369 26 problems problem NOUN fumecheng-4967 369 27 233 233 NUM fumecheng-4967 369 28 under under ADP fumecheng-4967 369 29 a a DET fumecheng-4967 369 30 slight slight ADJ fumecheng-4967 369 31 variation variation NOUN fumecheng-4967 369 32 of of ADP fumecheng-4967 369 33 the the DET fumecheng-4967 369 34 coefficients coefficient NOUN fumecheng-4967 369 35 of of ADP fumecheng-4967 369 36 the the DET fumecheng-4967 369 37 model model NOUN fumecheng-4967 369 38 makes make VERB fumecheng-4967 369 39 possible possible ADJ fumecheng-4967 369 40 a a DET fumecheng-4967 369 41 reproduction reproduction NOUN fumecheng-4967 369 42 of of ADP fumecheng-4967 369 43 very very ADV fumecheng-4967 369 44 realistic realistic ADJ fumecheng-4967 369 45 configurations configuration NOUN fumecheng-4967 369 46 of of ADP fumecheng-4967 369 47 the the DET fumecheng-4967 369 48 densities density NOUN fumecheng-4967 369 49 ρ1(r ρ1(r PROPN fumecheng-4967 369 50 , , PUNCT fumecheng-4967 369 51 t t PROPN fumecheng-4967 369 52 ) ) PUNCT fumecheng-4967 369 53 and and CCONJ fumecheng-4967 369 54 ρ2(r ρ2(r PROPN fumecheng-4967 369 55 , , PUNCT fumecheng-4967 369 56 t t PROPN fumecheng-4967 369 57 ) ) PUNCT fumecheng-4967 369 58 . . PUNCT fumecheng-4967 370 1 6 6 X fumecheng-4967 370 2 . . X fumecheng-4967 370 3 formal formal ADJ fumecheng-4967 370 4 generation generation NOUN fumecheng-4967 370 5 of of ADP fumecheng-4967 370 6 fractal fractal ADJ fumecheng-4967 370 7 surfaces surface NOUN fumecheng-4967 370 8 it it PRON fumecheng-4967 370 9 was be AUX fumecheng-4967 370 10 an an DET fumecheng-4967 370 11 example example NOUN fumecheng-4967 370 12 of of ADP fumecheng-4967 370 13 creation creation NOUN fumecheng-4967 370 14 of of ADP fumecheng-4967 370 15 the the DET fumecheng-4967 370 16 fractal fractal ADJ fumecheng-4967 370 17 surface surface NOUN fumecheng-4967 370 18 by by ADP fumecheng-4967 370 19 growth growth NOUN fumecheng-4967 370 20 . . PUNCT fumecheng-4967 371 1 now now ADV fumecheng-4967 371 2 , , PUNCT fumecheng-4967 371 3 let let VERB fumecheng-4967 371 4 us we PRON fumecheng-4967 371 5 turn turn VERB fumecheng-4967 371 6 to to ADP fumecheng-4967 371 7 more more ADV fumecheng-4967 371 8 formal formal ADJ fumecheng-4967 371 9 methods method NOUN fumecheng-4967 371 10 of of ADP fumecheng-4967 371 11 numerical numerical ADJ fumecheng-4967 371 12 generation generation NOUN fumecheng-4967 371 13 of of ADP fumecheng-4967 371 14 surfaces surface NOUN fumecheng-4967 371 15 . . PUNCT fumecheng-4967 372 1 depending depend VERB fumecheng-4967 372 2 on on ADP fumecheng-4967 372 3 a a DET fumecheng-4967 372 4 particular particular ADJ fumecheng-4967 372 5 problem problem NOUN fumecheng-4967 372 6 , , PUNCT fumecheng-4967 372 7 we we PRON fumecheng-4967 372 8 use use VERB fumecheng-4967 372 9 at at ADV fumecheng-4967 372 10 least least ADV fumecheng-4967 372 11 two two NUM fumecheng-4967 372 12 ways way NOUN fumecheng-4967 372 13 to to PART fumecheng-4967 372 14 generate generate VERB fumecheng-4967 372 15 rough rough ADJ fumecheng-4967 372 16 surface surface NOUN fumecheng-4967 372 17 that that PRON fumecheng-4967 372 18 is be AUX fumecheng-4967 372 19 close close ADJ fumecheng-4967 372 20 to to ADP fumecheng-4967 372 21 the the DET fumecheng-4967 372 22 fractal fractal ADJ fumecheng-4967 372 23 one one NUM fumecheng-4967 372 24 . . PUNCT fumecheng-4967 373 1 one one NUM fumecheng-4967 373 2 is be AUX fumecheng-4967 373 3 to to PART fumecheng-4967 373 4 apply apply VERB fumecheng-4967 373 5 fourier fourier ADJ fumecheng-4967 373 6 expansion expansion NOUN fumecheng-4967 373 7 with with ADP fumecheng-4967 373 8 the the DET fumecheng-4967 373 9 harmonics harmonic NOUN fumecheng-4967 373 10 restricted restrict VERB fumecheng-4967 373 11 between between ADP fumecheng-4967 373 12 maximal maximal ADJ fumecheng-4967 373 13 and and CCONJ fumecheng-4967 373 14 minimal minimal ADJ fumecheng-4967 373 15 wavelengths wavelength NOUN fumecheng-4967 373 16 . . PUNCT fumecheng-4967 374 1 depending depend VERB fumecheng-4967 374 2 on on ADP fumecheng-4967 374 3 the the DET fumecheng-4967 374 4 number number NOUN fumecheng-4967 374 5 of of ADP fumecheng-4967 374 6 the the DET fumecheng-4967 374 7 waves wave NOUN fumecheng-4967 374 8 and and CCONJ fumecheng-4967 374 9 both both DET fumecheng-4967 374 10 limits limit NOUN fumecheng-4967 374 11 , , PUNCT fumecheng-4967 374 12 the the DET fumecheng-4967 374 13 surface surface NOUN fumecheng-4967 374 14 will will AUX fumecheng-4967 374 15 be be AUX fumecheng-4967 374 16 more more ADV fumecheng-4967 374 17 or or CCONJ fumecheng-4967 374 18 less less ADV fumecheng-4967 374 19 close close ADJ fumecheng-4967 374 20 to to ADP fumecheng-4967 374 21 the the DET fumecheng-4967 374 22 real real ADJ fumecheng-4967 374 23 fractal fractal NOUN fumecheng-4967 374 24 one one NOUN fumecheng-4967 374 25 and and CCONJ fumecheng-4967 374 26 include include VERB fumecheng-4967 374 27 or or CCONJ fumecheng-4967 374 28 not not PART fumecheng-4967 374 29 irregularities irregularity NOUN fumecheng-4967 374 30 with with ADP fumecheng-4967 374 31 small small ADJ fumecheng-4967 374 32 sizes size NOUN fumecheng-4967 374 33 [ [ X fumecheng-4967 374 34 10 10 NUM fumecheng-4967 374 35 ] ] PUNCT fumecheng-4967 374 36 . . PUNCT fumecheng-4967 375 1 another another DET fumecheng-4967 375 2 way way NOUN fumecheng-4967 375 3 is be AUX fumecheng-4967 375 4 to to PART fumecheng-4967 375 5 use use VERB fumecheng-4967 375 6 random random ADJ fumecheng-4967 375 7 deposition deposition NOUN fumecheng-4967 375 8 of of ADP fumecheng-4967 375 9 the the DET fumecheng-4967 375 10 gaussians gaussian NOUN fumecheng-4967 375 11 . . PUNCT fumecheng-4967 376 1 depending depend VERB fumecheng-4967 376 2 on on ADP fumecheng-4967 376 3 their their PRON fumecheng-4967 376 4 number number NOUN fumecheng-4967 376 5 , , PUNCT fumecheng-4967 376 6 height height NOUN fumecheng-4967 376 7 dispersion dispersion NOUN fumecheng-4967 376 8 , , PUNCT fumecheng-4967 376 9 minimal minimal ADJ fumecheng-4967 376 10 and and CCONJ fumecheng-4967 376 11 maximal maximal ADJ fumecheng-4967 376 12 widths width NOUN fumecheng-4967 376 13 , , PUNCT fumecheng-4967 376 14 the the DET fumecheng-4967 376 15 surface surface NOUN fumecheng-4967 376 16 will will AUX fumecheng-4967 376 17 be be AUX fumecheng-4967 376 18 closer close ADJ fumecheng-4967 376 19 to to ADP fumecheng-4967 376 20 fractal fractal ADJ fumecheng-4967 376 21 or or CCONJ fumecheng-4967 376 22 not not PART fumecheng-4967 376 23 . . PUNCT fumecheng-4967 377 1 many many ADJ fumecheng-4967 377 2 of of ADP fumecheng-4967 377 3 biological biological ADJ fumecheng-4967 377 4 surfaces surface NOUN fumecheng-4967 377 5 have have VERB fumecheng-4967 377 6 a a DET fumecheng-4967 377 7 structure structure NOUN fumecheng-4967 377 8 made make VERB fumecheng-4967 377 9 as as ADP fumecheng-4967 377 10 a a DET fumecheng-4967 377 11 pattern pattern NOUN fumecheng-4967 377 12 of of ADP fumecheng-4967 377 13 close close ADJ fumecheng-4967 377 14 objects object NOUN fumecheng-4967 377 15 with with ADP fumecheng-4967 377 16 some some DET fumecheng-4967 377 17 specific specific ADJ fumecheng-4967 377 18 scale scale NOUN fumecheng-4967 377 19 . . PUNCT fumecheng-4967 378 1 they they PRON fumecheng-4967 378 2 can can AUX fumecheng-4967 378 3 be be AUX fumecheng-4967 378 4 more more ADV fumecheng-4967 378 5 conveniently conveniently ADV fumecheng-4967 378 6 simulated simulate VERB fumecheng-4967 378 7 by by ADP fumecheng-4967 378 8 a a DET fumecheng-4967 378 9 set set NOUN fumecheng-4967 378 10 of of ADP fumecheng-4967 378 11 deposed depose VERB fumecheng-4967 378 12 objects object NOUN fumecheng-4967 378 13 . . PUNCT fumecheng-4967 379 1 that that PRON fumecheng-4967 379 2 is be AUX fumecheng-4967 379 3 why why SCONJ fumecheng-4967 379 4 , , PUNCT fumecheng-4967 379 5 for for ADP fumecheng-4967 379 6 our our PRON fumecheng-4967 379 7 studies study NOUN fumecheng-4967 379 8 we we PRON fumecheng-4967 379 9 usually usually ADV fumecheng-4967 379 10 choose choose VERB fumecheng-4967 379 11 the the DET fumecheng-4967 379 12 second second ADJ fumecheng-4967 379 13 method method NOUN fumecheng-4967 379 14 , , PUNCT fumecheng-4967 379 15 which which PRON fumecheng-4967 379 16 easily easily ADV fumecheng-4967 379 17 provides provide VERB fumecheng-4967 379 18 such such ADJ fumecheng-4967 379 19 possibility possibility NOUN fumecheng-4967 379 20 . . PUNCT fumecheng-4967 380 1 in in ADP fumecheng-4967 380 2 many many ADJ fumecheng-4967 380 3 cases case NOUN fumecheng-4967 380 4 , , PUNCT fumecheng-4967 380 5 such such ADJ fumecheng-4967 380 6 surface surface NOUN fumecheng-4967 380 7 appears appear VERB fumecheng-4967 380 8 as as ADP fumecheng-4967 380 9 a a DET fumecheng-4967 380 10 result result NOUN fumecheng-4967 380 11 of of ADP fumecheng-4967 380 12 random random ADJ fumecheng-4967 380 13 deposition deposition NOUN fumecheng-4967 380 14 of of ADP fumecheng-4967 380 15 some some DET fumecheng-4967 380 16 particles particle NOUN fumecheng-4967 380 17 , , PUNCT fumecheng-4967 380 18 balls ball NOUN fumecheng-4967 380 19 , , PUNCT fumecheng-4967 380 20 block block NOUN fumecheng-4967 380 21 of of ADP fumecheng-4967 380 22 some some DET fumecheng-4967 380 23 other other ADJ fumecheng-4967 380 24 objects object NOUN fumecheng-4967 380 25 . . PUNCT fumecheng-4967 381 1 we we PRON fumecheng-4967 381 2 definitely definitely ADV fumecheng-4967 381 3 admit admit VERB fumecheng-4967 381 4 that that SCONJ fumecheng-4967 381 5 the the DET fumecheng-4967 381 6 formal formal ADJ fumecheng-4967 381 7 model model NOUN fumecheng-4967 381 8 completely completely ADV fumecheng-4967 381 9 ignores ignore VERB fumecheng-4967 381 10 the the DET fumecheng-4967 381 11 fine fine ADJ fumecheng-4967 381 12 structure structure NOUN fumecheng-4967 381 13 of of ADP fumecheng-4967 381 14 adhesion adhesion NOUN fumecheng-4967 381 15 - - PUNCT fumecheng-4967 381 16 like like ADJ fumecheng-4967 381 17 weakening weaken VERB fumecheng-4967 381 18 at at ADP fumecheng-4967 381 19 motion motion NOUN fumecheng-4967 381 20 , , PUNCT fumecheng-4967 381 21 fracture fracture NOUN fumecheng-4967 381 22 and and CCONJ fumecheng-4967 381 23 restoration restoration NOUN fumecheng-4967 381 24 of of ADP fumecheng-4967 381 25 the the DET fumecheng-4967 381 26 bonds bond NOUN fumecheng-4967 381 27 , , PUNCT fumecheng-4967 381 28 so so ADV fumecheng-4967 381 29 on on ADV fumecheng-4967 381 30 . . PUNCT fumecheng-4967 382 1 often often ADV fumecheng-4967 382 2 just just ADV fumecheng-4967 382 3 only only ADV fumecheng-4967 382 4 two two NUM fumecheng-4967 382 5 basic basic ADJ fumecheng-4967 382 6 mechanisms mechanism NOUN fumecheng-4967 382 7 are be AUX fumecheng-4967 382 8 involved involve VERB fumecheng-4967 382 9 into into ADP fumecheng-4967 382 10 our our PRON fumecheng-4967 382 11 minimalistic minimalistic ADJ fumecheng-4967 382 12 models model NOUN fumecheng-4967 382 13 : : PUNCT fumecheng-4967 382 14 attraction attraction NOUN fumecheng-4967 382 15 to to ADP fumecheng-4967 382 16 the the DET fumecheng-4967 382 17 surface surface NOUN fumecheng-4967 382 18 and and CCONJ fumecheng-4967 382 19 energy energy NOUN fumecheng-4967 382 20 dissipation dissipation NOUN fumecheng-4967 382 21 . . PUNCT fumecheng-4967 383 1 the the DET fumecheng-4967 383 2 first first ADJ fumecheng-4967 383 3 one one NOUN fumecheng-4967 383 4 actually actually ADV fumecheng-4967 383 5 restricts restrict VERB fumecheng-4967 383 6 the the DET fumecheng-4967 383 7 scales scale NOUN fumecheng-4967 383 8 , , PUNCT fumecheng-4967 383 9 which which PRON fumecheng-4967 383 10 we we PRON fumecheng-4967 383 11 include include VERB fumecheng-4967 383 12 to to ADP fumecheng-4967 383 13 the the DET fumecheng-4967 383 14 surface surface NOUN fumecheng-4967 383 15 by by ADP fumecheng-4967 383 16 the the DET fumecheng-4967 383 17 irregularities irregularity NOUN fumecheng-4967 383 18 close close ADJ fumecheng-4967 383 19 to to ADP fumecheng-4967 383 20 the the DET fumecheng-4967 383 21 “ " PUNCT fumecheng-4967 383 22 size size NOUN fumecheng-4967 383 23 of of ADP fumecheng-4967 383 24 contact contact NOUN fumecheng-4967 383 25 points point NOUN fumecheng-4967 383 26 ” " PUNCT fumecheng-4967 383 27 ( ( PUNCT fumecheng-4967 383 28 radius radius NOUN fumecheng-4967 383 29 of of ADP fumecheng-4967 383 30 attraction attraction NOUN fumecheng-4967 383 31 in in ADP fumecheng-4967 383 32 the the DET fumecheng-4967 383 33 model model NOUN fumecheng-4967 383 34 ) ) PUNCT fumecheng-4967 383 35 . . PUNCT fumecheng-4967 384 1 in in ADP fumecheng-4967 384 2 particular particular ADJ fumecheng-4967 384 3 , , PUNCT fumecheng-4967 384 4 this this DET fumecheng-4967 384 5 limitation limitation NOUN fumecheng-4967 384 6 corresponds correspond VERB fumecheng-4967 384 7 to to ADP fumecheng-4967 384 8 a a DET fumecheng-4967 384 9 situation situation NOUN fumecheng-4967 384 10 with with ADP fumecheng-4967 384 11 adhesive adhesive ADJ fumecheng-4967 384 12 terminal terminal ADJ fumecheng-4967 384 13 elements element NOUN fumecheng-4967 384 14 ( ( PUNCT fumecheng-4967 384 15 spatulae spatulae NOUN fumecheng-4967 384 16 ) ) PUNCT fumecheng-4967 384 17 of of ADP fumecheng-4967 384 18 attachment attachment ADJ fumecheng-4967 384 19 organs organ NOUN fumecheng-4967 384 20 of of ADP fumecheng-4967 384 21 different different ADJ fumecheng-4967 384 22 animals animal NOUN fumecheng-4967 384 23 , , PUNCT fumecheng-4967 384 24 which which PRON fumecheng-4967 384 25 were be AUX fumecheng-4967 384 26 studied study VERB fumecheng-4967 384 27 elsewhere elsewhere ADV fumecheng-4967 384 28 [ [ X fumecheng-4967 384 29 11 11 NUM fumecheng-4967 384 30 ] ] PUNCT fumecheng-4967 384 31 . . PUNCT fumecheng-4967 385 1 the the DET fumecheng-4967 385 2 spatulae spatulae NOUN fumecheng-4967 385 3 practically practically ADV fumecheng-4967 385 4 ignore ignore VERB fumecheng-4967 385 5 irregularities irregularity NOUN fumecheng-4967 385 6 much much ADV fumecheng-4967 385 7 smaller small ADJ fumecheng-4967 385 8 or or CCONJ fumecheng-4967 385 9 larger large ADJ fumecheng-4967 385 10 than than ADP fumecheng-4967 385 11 their their PRON fumecheng-4967 385 12 size size NOUN fumecheng-4967 385 13 . . PUNCT fumecheng-4967 386 1 as as ADP fumecheng-4967 386 2 result result NOUN fumecheng-4967 386 3 , , PUNCT fumecheng-4967 386 4 such such ADJ fumecheng-4967 386 5 surfaces surface NOUN fumecheng-4967 386 6 can can AUX fumecheng-4967 386 7 be be AUX fumecheng-4967 386 8 treated treat VERB fumecheng-4967 386 9 as as ADP fumecheng-4967 386 10 almost almost ADV fumecheng-4967 386 11 flat flat ADJ fumecheng-4967 386 12 . . PUNCT fumecheng-4967 387 1 that that PRON fumecheng-4967 387 2 is be AUX fumecheng-4967 387 3 why why SCONJ fumecheng-4967 387 4 we we PRON fumecheng-4967 387 5 normally normally ADV fumecheng-4967 387 6 use use VERB fumecheng-4967 387 7 here here ADV fumecheng-4967 387 8 the the DET fumecheng-4967 387 9 surfaces surface NOUN fumecheng-4967 387 10 with with ADP fumecheng-4967 387 11 the the DET fumecheng-4967 387 12 irregularities irregularity NOUN fumecheng-4967 387 13 comparable comparable ADJ fumecheng-4967 387 14 to to ADP fumecheng-4967 387 15 the the DET fumecheng-4967 387 16 spatula spatula NOUN fumecheng-4967 387 17 . . PUNCT fumecheng-4967 388 1 such such ADJ fumecheng-4967 388 2 deposition deposition NOUN fumecheng-4967 388 3 with with ADP fumecheng-4967 388 4 fixed fix VERB fumecheng-4967 388 5 interval interval NOUN fumecheng-4967 388 6 of of ADP fumecheng-4967 388 7 scales scale NOUN fumecheng-4967 388 8 can can AUX fumecheng-4967 388 9 be be AUX fumecheng-4967 388 10 done do VERB fumecheng-4967 388 11 either either CCONJ fumecheng-4967 388 12 naturally naturally ADV fumecheng-4967 388 13 or or CCONJ fumecheng-4967 388 14 artificially artificially ADV fumecheng-4967 388 15 . . PUNCT fumecheng-4967 389 1 we we PRON fumecheng-4967 389 2 will will AUX fumecheng-4967 389 3 not not PART fumecheng-4967 389 4 concentrate concentrate VERB fumecheng-4967 389 5 on on ADP fumecheng-4967 389 6 any any DET fumecheng-4967 389 7 specific specific ADJ fumecheng-4967 389 8 case case NOUN fumecheng-4967 389 9 and and CCONJ fumecheng-4967 389 10 discuss discuss VERB fumecheng-4967 389 11 only only ADV fumecheng-4967 389 12 a a DET fumecheng-4967 389 13 couple couple NOUN fumecheng-4967 389 14 of of ADP fumecheng-4967 389 15 more more ADJ fumecheng-4967 389 16 or or CCONJ fumecheng-4967 389 17 less less ADJ fumecheng-4967 389 18 abstract abstract ADJ fumecheng-4967 389 19 examples example NOUN fumecheng-4967 389 20 . . PUNCT fumecheng-4967 390 1 despite despite SCONJ fumecheng-4967 390 2 of of ADP fumecheng-4967 390 3 formal formal ADJ fumecheng-4967 390 4 mathematical mathematical ADJ fumecheng-4967 390 5 generality generality NOUN fumecheng-4967 390 6 such such ADJ fumecheng-4967 390 7 approach approach NOUN fumecheng-4967 390 8 helps help VERB fumecheng-4967 390 9 in in ADP fumecheng-4967 390 10 developing develop VERB fumecheng-4967 390 11 a a DET fumecheng-4967 390 12 simple simple NOUN fumecheng-4967 390 13 , , PUNCT fumecheng-4967 390 14 but but CCONJ fumecheng-4967 390 15 realistic realistic ADJ fumecheng-4967 390 16 numerical numerical ADJ fumecheng-4967 390 17 model model NOUN fumecheng-4967 390 18 that that PRON fumecheng-4967 390 19 might might AUX fumecheng-4967 390 20 be be AUX fumecheng-4967 390 21 useful useful ADJ fumecheng-4967 390 22 , , PUNCT fumecheng-4967 390 23 for for ADP fumecheng-4967 390 24 example example NOUN fumecheng-4967 390 25 , , PUNCT fumecheng-4967 390 26 in in ADP fumecheng-4967 390 27 the the DET fumecheng-4967 390 28 study study NOUN fumecheng-4967 390 29 of of ADP fumecheng-4967 390 30 animal animal NOUN fumecheng-4967 390 31 spatula spatula NOUN fumecheng-4967 390 32 interaction interaction NOUN fumecheng-4967 390 33 with with ADP fumecheng-4967 390 34 various various ADJ fumecheng-4967 390 35 substrate substrate NOUN fumecheng-4967 390 36 profiles profile NOUN fumecheng-4967 390 37 . . PUNCT fumecheng-4967 391 1 formal formal ADJ fumecheng-4967 391 2 models model NOUN fumecheng-4967 391 3 can can AUX fumecheng-4967 391 4 well well ADV fumecheng-4967 391 5 explain explain VERB fumecheng-4967 391 6 results result NOUN fumecheng-4967 391 7 of of ADP fumecheng-4967 391 8 experimental experimental ADJ fumecheng-4967 391 9 studies study NOUN fumecheng-4967 391 10 , , PUNCT fumecheng-4967 391 11 and and CCONJ fumecheng-4967 391 12 also also ADV fumecheng-4967 391 13 predict predict VERB fumecheng-4967 391 14 adhesion adhesion NOUN fumecheng-4967 391 15 of of ADP fumecheng-4967 391 16 animals animal NOUN fumecheng-4967 391 17 to to ADP fumecheng-4967 391 18 the the DET fumecheng-4967 391 19 real real ADJ fumecheng-4967 391 20 surface surface NOUN fumecheng-4967 391 21 profiles profile NOUN fumecheng-4967 391 22 depending depend VERB fumecheng-4967 391 23 on on ADP fumecheng-4967 391 24 the the DET fumecheng-4967 391 25 dimension dimension NOUN fumecheng-4967 391 26 and and CCONJ fumecheng-4967 391 27 stiffness stiffness NOUN fumecheng-4967 391 28 of of ADP fumecheng-4967 391 29 the the DET fumecheng-4967 391 30 spatula spatula NOUN fumecheng-4967 391 31 . . PUNCT fumecheng-4967 392 1 previously previously ADV fumecheng-4967 392 2 , , PUNCT fumecheng-4967 392 3 we we PRON fumecheng-4967 392 4 studied study VERB fumecheng-4967 392 5 such such ADJ fumecheng-4967 392 6 biological biological ADJ fumecheng-4967 392 7 systems system NOUN fumecheng-4967 392 8 using use VERB fumecheng-4967 392 9 numerically numerically ADV fumecheng-4967 392 10 generated generate VERB fumecheng-4967 392 11 surfaces surface NOUN fumecheng-4967 392 12 and and CCONJ fumecheng-4967 392 13 compared compare VERB fumecheng-4967 392 14 the the DET fumecheng-4967 392 15 results result NOUN fumecheng-4967 392 16 obtained obtain VERB fumecheng-4967 392 17 with with ADP fumecheng-4967 392 18 the the DET fumecheng-4967 392 19 real real ADJ fumecheng-4967 392 20 3d 3d PROPN fumecheng-4967 392 21 surface surface NOUN fumecheng-4967 392 22 profiles profile NOUN fumecheng-4967 392 23 obtained obtain VERB fumecheng-4967 392 24 experimentally experimentally ADV fumecheng-4967 392 25 by by ADP fumecheng-4967 392 26 depositing deposit VERB fumecheng-4967 392 27 of of ADP fumecheng-4967 392 28 spheres sphere NOUN fumecheng-4967 392 29 . . PUNCT fumecheng-4967 393 1 in in ADP fumecheng-4967 393 2 the the DET fumecheng-4967 393 3 purely purely ADV fumecheng-4967 393 4 numerical numerical ADJ fumecheng-4967 393 5 approach approach NOUN fumecheng-4967 393 6 , , PUNCT fumecheng-4967 393 7 different different ADJ fumecheng-4967 393 8 roughness roughness NOUN fumecheng-4967 393 9 of of ADP fumecheng-4967 393 10 the the DET fumecheng-4967 393 11 surfaces surface NOUN fumecheng-4967 393 12 can can AUX fumecheng-4967 393 13 be be AUX fumecheng-4967 393 14 achieved achieve VERB fumecheng-4967 393 15 by by ADP fumecheng-4967 393 16 depositing deposit VERB fumecheng-4967 393 17 of of ADP fumecheng-4967 393 18 spheres sphere NOUN fumecheng-4967 393 19 with with ADP fumecheng-4967 393 20 defined define VERB fumecheng-4967 393 21 radius radius NOUN fumecheng-4967 393 22 on on ADP fumecheng-4967 393 23 originally originally ADV fumecheng-4967 393 24 flat flat ADJ fumecheng-4967 393 25 surface surface NOUN fumecheng-4967 393 26 . . PUNCT fumecheng-4967 394 1 to to PART fumecheng-4967 394 2 simulate simulate VERB fumecheng-4967 394 3 this this DET fumecheng-4967 394 4 process process NOUN fumecheng-4967 394 5 numerically numerically ADV fumecheng-4967 394 6 , , PUNCT fumecheng-4967 394 7 we we PRON fumecheng-4967 394 8 organized organize VERB fumecheng-4967 394 9 our our PRON fumecheng-4967 394 10 procedure procedure NOUN fumecheng-4967 394 11 as as SCONJ fumecheng-4967 394 12 follows follow VERB fumecheng-4967 394 13 . . PUNCT fumecheng-4967 395 1 at at ADP fumecheng-4967 395 2 every every DET fumecheng-4967 395 3 given give VERB fumecheng-4967 395 4 radius radius NOUN fumecheng-4967 395 5 r r NOUN fumecheng-4967 395 6 , , PUNCT fumecheng-4967 395 7 we we PRON fumecheng-4967 395 8 have have AUX fumecheng-4967 395 9 taken take VERB fumecheng-4967 395 10 an an DET fumecheng-4967 395 11 array array NOUN fumecheng-4967 395 12 of of ADP fumecheng-4967 395 13 equal equal ADJ fumecheng-4967 395 14 spheres sphere NOUN fumecheng-4967 395 15 , , PUNCT fumecheng-4967 395 16 or or CCONJ fumecheng-4967 395 17 circles circle NOUN fumecheng-4967 395 18 in in ADP fumecheng-4967 395 19 twodimensional twodimensional ADJ fumecheng-4967 395 20 ( ( PUNCT fumecheng-4967 395 21 d=1 d=1 NOUN fumecheng-4967 395 22 + + ADJ fumecheng-4967 395 23 1 1 NUM fumecheng-4967 395 24 ) ) PUNCT fumecheng-4967 395 25 case case NOUN fumecheng-4967 395 26 and and CCONJ fumecheng-4967 395 27 placed place VERB fumecheng-4967 395 28 them they PRON fumecheng-4967 395 29 successively successively ADV fumecheng-4967 395 30 into into ADP fumecheng-4967 395 31 the the DET fumecheng-4967 395 32 randomly randomly ADV fumecheng-4967 395 33 chosen choose VERB fumecheng-4967 395 34 positions position NOUN fumecheng-4967 395 35 xn xn PROPN fumecheng-4967 395 36 , , PUNCT fumecheng-4967 395 37 where where SCONJ fumecheng-4967 395 38 n=1,2, n=1,2, NOUN fumecheng-4967 395 39 … … SYM fumecheng-4967 395 40 ,n ,n NOUN fumecheng-4967 395 41 . . PUNCT fumecheng-4967 396 1 the the DET fumecheng-4967 396 2 number number NOUN fumecheng-4967 396 3 of of ADP fumecheng-4967 396 4 the the DET fumecheng-4967 396 5 spheres sphere NOUN fumecheng-4967 396 6 n=||l n=||l NOUN fumecheng-4967 396 7 / / SYM fumecheng-4967 396 8 r|| r|| PROPN fumecheng-4967 396 9 in in ADP fumecheng-4967 396 10 the the DET fumecheng-4967 396 11 array array NOUN fumecheng-4967 396 12 was be AUX fumecheng-4967 396 13 taken take VERB fumecheng-4967 396 14 to to PART fumecheng-4967 396 15 be be AUX fumecheng-4967 396 16 an an DET fumecheng-4967 396 17 integer integer NOUN fumecheng-4967 396 18 value value NOUN fumecheng-4967 396 19 corresponding correspond VERB fumecheng-4967 396 20 to to ADP fumecheng-4967 396 21 the the DET fumecheng-4967 396 22 total total ADJ fumecheng-4967 396 23 number number NOUN fumecheng-4967 396 24 of of ADP fumecheng-4967 396 25 the the DET fumecheng-4967 396 26 circles circle NOUN fumecheng-4967 396 27 of of ADP fumecheng-4967 396 28 radius radius NOUN fumecheng-4967 397 1 r r NOUN fumecheng-4967 397 2 234 234 NUM fumecheng-4967 397 3 a.e a.e PROPN fumecheng-4967 397 4 . . PROPN fumecheng-4967 397 5 filippov filippov PROPN fumecheng-4967 397 6 , , PUNCT fumecheng-4967 397 7 s.n s.n PROPN fumecheng-4967 397 8 . . PROPN fumecheng-4967 397 9 gorb gorb PROPN fumecheng-4967 397 10 which which PRON fumecheng-4967 397 11 are be AUX fumecheng-4967 397 12 necessary necessary ADJ fumecheng-4967 397 13 to to PART fumecheng-4967 397 14 cover cover VERB fumecheng-4967 397 15 the the DET fumecheng-4967 397 16 system system NOUN fumecheng-4967 397 17 of of ADP fumecheng-4967 397 18 the the DET fumecheng-4967 397 19 length length NOUN fumecheng-4967 397 20 l l NOUN fumecheng-4967 397 21 uniformly uniformly ADV fumecheng-4967 397 22 . . PUNCT fumecheng-4967 398 1 each each DET fumecheng-4967 398 2 sphere sphere NOUN fumecheng-4967 398 3 was be AUX fumecheng-4967 398 4 added add VERB fumecheng-4967 398 5 virtually virtually ADV fumecheng-4967 398 6 to to ADP fumecheng-4967 398 7 the the DET fumecheng-4967 398 8 corresponding corresponding ADJ fumecheng-4967 398 9 segment segment NOUN fumecheng-4967 398 10 of of ADP fumecheng-4967 398 11 the the DET fumecheng-4967 398 12 surface surface NOUN fumecheng-4967 398 13 : : PUNCT fumecheng-4967 398 14 2 2 NUM fumecheng-4967 398 15 2 2 NUM fumecheng-4967 398 16 ( ( PUNCT fumecheng-4967 398 17 ; ; PUNCT fumecheng-4967 398 18 ) ) PUNCT fumecheng-4967 398 19 ( ( PUNCT fumecheng-4967 398 20 ) ) PUNCT fumecheng-4967 398 21 n n CCONJ fumecheng-4967 398 22 n n NOUN fumecheng-4967 398 23 ny ny NOUN fumecheng-4967 398 24 x x PUNCT fumecheng-4967 399 1 x x SYM fumecheng-4967 399 2 r r NOUN fumecheng-4967 399 3 x x PROPN fumecheng-4967 399 4 x x PROPN fumecheng-4967 399 5   PROPN fumecheng-4967 399 6   PROPN fumecheng-4967 399 7 . . PUNCT fumecheng-4967 400 1 ( ( PUNCT fumecheng-4967 400 2 25 25 NUM fumecheng-4967 400 3 ) ) PUNCT fumecheng-4967 400 4 due due ADP fumecheng-4967 400 5 to to ADP fumecheng-4967 400 6 the the DET fumecheng-4967 400 7 random random ADJ fumecheng-4967 400 8 deposition deposition NOUN fumecheng-4967 400 9 , , PUNCT fumecheng-4967 400 10 the the DET fumecheng-4967 400 11 segments segment NOUN fumecheng-4967 400 12 can can AUX fumecheng-4967 400 13 fall fall VERB fumecheng-4967 400 14 either either CCONJ fumecheng-4967 400 15 on on ADP fumecheng-4967 400 16 the the DET fumecheng-4967 400 17 top top NOUN fumecheng-4967 400 18 of of ADP fumecheng-4967 400 19 already already ADV fumecheng-4967 400 20 existing exist VERB fumecheng-4967 400 21 coverage coverage NOUN fumecheng-4967 400 22 or or CCONJ fumecheng-4967 400 23 onto onto ADP fumecheng-4967 400 24 the the DET fumecheng-4967 400 25 empty empty ADJ fumecheng-4967 400 26 space space NOUN fumecheng-4967 400 27 . . PUNCT fumecheng-4967 401 1 as as ADP fumecheng-4967 401 2 a a DET fumecheng-4967 401 3 result result NOUN fumecheng-4967 401 4 of of ADP fumecheng-4967 401 5 such such DET fumecheng-4967 401 6 a a DET fumecheng-4967 401 7 deposition deposition NOUN fumecheng-4967 401 8 , , PUNCT fumecheng-4967 401 9 the the DET fumecheng-4967 401 10 total total ADJ fumecheng-4967 401 11 surface surface NOUN fumecheng-4967 401 12 gradually gradually ADV fumecheng-4967 401 13 accumulates accumulate VERB fumecheng-4967 401 14 all all DET fumecheng-4967 401 15 the the DET fumecheng-4967 401 16 segments segment NOUN fumecheng-4967 401 17 1 1 NUM fumecheng-4967 401 18 ( ( PUNCT fumecheng-4967 401 19 ) ) PUNCT fumecheng-4967 401 20 ( ( PUNCT fumecheng-4967 401 21 ; ; PUNCT fumecheng-4967 401 22 ) ) PUNCT fumecheng-4967 401 23 n n CCONJ fumecheng-4967 401 24 n n CCONJ fumecheng-4967 401 25 n n CCONJ fumecheng-4967 401 26 n n CCONJ fumecheng-4967 401 27 y y NOUN fumecheng-4967 401 28 x x SYM fumecheng-4967 401 29 y y NOUN fumecheng-4967 401 30 x x PUNCT fumecheng-4967 401 31 x x X fumecheng-4967 401 32   NUM fumecheng-4967 401 33   NOUN fumecheng-4967 401 34 , , PUNCT fumecheng-4967 401 35 which which PRON fumecheng-4967 401 36 are be AUX fumecheng-4967 401 37 generally generally ADV fumecheng-4967 401 38 speaking speak VERB fumecheng-4967 401 39 placed place VERB fumecheng-4967 401 40 one one NUM fumecheng-4967 401 41 on on ADP fumecheng-4967 401 42 top top NOUN fumecheng-4967 401 43 of of ADP fumecheng-4967 401 44 another another DET fumecheng-4967 401 45 one one NOUN fumecheng-4967 401 46 . . PUNCT fumecheng-4967 402 1 this this DET fumecheng-4967 402 2 procedure procedure NOUN fumecheng-4967 402 3 can can AUX fumecheng-4967 402 4 be be AUX fumecheng-4967 402 5 easily easily ADV fumecheng-4967 402 6 generalized generalize VERB fumecheng-4967 402 7 for for ADP fumecheng-4967 402 8 d=2 d=2 NOUN fumecheng-4967 402 9 + + ADJ fumecheng-4967 402 10 1 1 NUM fumecheng-4967 402 11 surfaces surface NOUN fumecheng-4967 402 12 . . PUNCT fumecheng-4967 403 1 typical typical ADJ fumecheng-4967 403 2 realizations realization NOUN fumecheng-4967 403 3 of of ADP fumecheng-4967 403 4 such such ADJ fumecheng-4967 403 5 surfaces surface NOUN fumecheng-4967 403 6 for for ADP fumecheng-4967 403 7 different different ADJ fumecheng-4967 403 8 radii radius NOUN fumecheng-4967 403 9 r r NOUN fumecheng-4967 403 10 are be AUX fumecheng-4967 403 11 presented present VERB fumecheng-4967 403 12 in in ADP fumecheng-4967 403 13 the the DET fumecheng-4967 403 14 fig fig NOUN fumecheng-4967 403 15 . . PUNCT fumecheng-4967 404 1 8 8 NUM fumecheng-4967 404 2 . . X fumecheng-4967 404 3 fig fig NOUN fumecheng-4967 404 4 . . PUNCT fumecheng-4967 405 1 8 8 NUM fumecheng-4967 405 2 consequent consequent ADJ fumecheng-4967 405 3 stages stage NOUN fumecheng-4967 405 4 of of ADP fumecheng-4967 405 5 the the DET fumecheng-4967 405 6 formation formation NOUN fumecheng-4967 405 7 of of ADP fumecheng-4967 405 8 rough rough ADJ fumecheng-4967 405 9 surface surface NOUN fumecheng-4967 405 10 by by ADP fumecheng-4967 405 11 the the DET fumecheng-4967 405 12 random random ADJ fumecheng-4967 405 13 deposition deposition NOUN fumecheng-4967 405 14 of of ADP fumecheng-4967 405 15 the the DET fumecheng-4967 405 16 hard hard ADJ fumecheng-4967 405 17 balls ball NOUN fumecheng-4967 405 18 with with ADP fumecheng-4967 405 19 fixed fix VERB fumecheng-4967 405 20 radius radius NOUN fumecheng-4967 405 21 on on ADP fumecheng-4967 405 22 the the DET fumecheng-4967 405 23 originally originally ADV fumecheng-4967 405 24 flat flat ADJ fumecheng-4967 405 25 surface surface NOUN fumecheng-4967 405 26 in in ADP fumecheng-4967 405 27 many many ADJ fumecheng-4967 405 28 cases case NOUN fumecheng-4967 405 29 specific specific ADJ fumecheng-4967 405 30 form form NOUN fumecheng-4967 405 31 of of ADP fumecheng-4967 405 32 the the DET fumecheng-4967 405 33 deposed depose VERB fumecheng-4967 405 34 particles particle NOUN fumecheng-4967 405 35 is be AUX fumecheng-4967 405 36 not not PART fumecheng-4967 405 37 very very ADV fumecheng-4967 405 38 important important ADJ fumecheng-4967 405 39 ( ( PUNCT fumecheng-4967 405 40 or or CCONJ fumecheng-4967 405 41 maybe maybe ADV fumecheng-4967 405 42 not not PART fumecheng-4967 405 43 important important ADJ fumecheng-4967 405 44 at at ADV fumecheng-4967 405 45 all all ADV fumecheng-4967 405 46 ) ) PUNCT fumecheng-4967 405 47 . . PUNCT fumecheng-4967 406 1 in in ADP fumecheng-4967 406 2 such such DET fumecheng-4967 406 3 a a DET fumecheng-4967 406 4 case case NOUN fumecheng-4967 406 5 , , PUNCT fumecheng-4967 406 6 one one PRON fumecheng-4967 406 7 can can AUX fumecheng-4967 406 8 treat treat VERB fumecheng-4967 406 9 random random ADJ fumecheng-4967 406 10 deposition deposition NOUN fumecheng-4967 406 11 procedure procedure NOUN fumecheng-4967 406 12 as as ADP fumecheng-4967 406 13 an an DET fumecheng-4967 406 14 absolutely absolutely ADV fumecheng-4967 406 15 abstract abstract ADJ fumecheng-4967 406 16 way way NOUN fumecheng-4967 406 17 of of ADP fumecheng-4967 406 18 constructing construct VERB fumecheng-4967 406 19 desirable desirable ADJ fumecheng-4967 406 20 surface surface NOUN fumecheng-4967 406 21 . . PUNCT fumecheng-4967 407 1 one one NUM fumecheng-4967 407 2 of of ADP fumecheng-4967 407 3 the the DET fumecheng-4967 407 4 simplest simple ADJ fumecheng-4967 407 5 ways way NOUN fumecheng-4967 407 6 to to PART fumecheng-4967 407 7 do do VERB fumecheng-4967 407 8 this this PRON fumecheng-4967 407 9 in in ADP fumecheng-4967 407 10 this this DET fumecheng-4967 407 11 case case NOUN fumecheng-4967 407 12 is be AUX fumecheng-4967 407 13 to to PART fumecheng-4967 407 14 model model VERB fumecheng-4967 407 15 rough rough ADJ fumecheng-4967 407 16 surface surface NOUN fumecheng-4967 407 17 z(x z(x PROPN fumecheng-4967 407 18 , , PUNCT fumecheng-4967 407 19 y y PROPN fumecheng-4967 407 20 ) ) PUNCT fumecheng-4967 407 21 by by ADP fumecheng-4967 407 22 a a DET fumecheng-4967 407 23 random random ADJ fumecheng-4967 407 24 deposition deposition NOUN fumecheng-4967 407 25 of of ADP fumecheng-4967 407 26 the the DET fumecheng-4967 407 27 gaussians gaussian NOUN fumecheng-4967 407 28 : : PUNCT fumecheng-4967 407 29 2 2 NUM fumecheng-4967 407 30 2 2 NUM fumecheng-4967 407 31 2 2 NUM fumecheng-4967 407 32 ( ( PUNCT fumecheng-4967 407 33 , , PUNCT fumecheng-4967 407 34 ) ) PUNCT fumecheng-4967 407 35 ( ( PUNCT fumecheng-4967 407 36 , , PUNCT fumecheng-4967 407 37 , , PUNCT fumecheng-4967 407 38 { { PUNCT fumecheng-4967 407 39 , , PUNCT fumecheng-4967 407 40 } } PUNCT fumecheng-4967 407 41 ) ) PUNCT fumecheng-4967 407 42 exp exp NOUN fumecheng-4967 407 43 [ [ PUNCT fumecheng-4967 407 44 ( ( PUNCT fumecheng-4967 407 45 ( ( PUNCT fumecheng-4967 407 46 ) ) PUNCT fumecheng-4967 407 47 ( ( PUNCT fumecheng-4967 407 48 ) ) PUNCT fumecheng-4967 407 49 ) ) PUNCT fumecheng-4967 407 50 / / PUNCT fumecheng-4967 408 1 ] ] X fumecheng-4967 408 2 n n CCONJ fumecheng-4967 408 3 n n CCONJ fumecheng-4967 408 4 n n CCONJ fumecheng-4967 408 5 n n CCONJ fumecheng-4967 408 6 n n CCONJ fumecheng-4967 408 7 n n CCONJ fumecheng-4967 408 8 n n CCONJ fumecheng-4967 408 9 n n CCONJ fumecheng-4967 408 10 n n NOUN fumecheng-4967 408 11 z z NOUN fumecheng-4967 408 12 x x SYM fumecheng-4967 408 13 y y NOUN fumecheng-4967 408 14 g g NOUN fumecheng-4967 408 15 x x X fumecheng-4967 408 16 y y NOUN fumecheng-4967 408 17 x x X fumecheng-4967 408 18 y y PROPN fumecheng-4967 408 19 a a X fumecheng-4967 408 20 x x X fumecheng-4967 408 21 x x SYM fumecheng-4967 408 22 y y PROPN fumecheng-4967 408 23 y y PROPN fumecheng-4967 408 24 w w VERB fumecheng-4967 408 25   PROPN fumecheng-4967 408 26   PROPN fumecheng-4967 408 27   PROPN fumecheng-4967 408 28   CCONJ fumecheng-4967 408 29   X fumecheng-4967 408 30   X fumecheng-4967 408 31 . . PUNCT fumecheng-4967 409 1 ( ( PUNCT fumecheng-4967 409 2 26 26 NUM fumecheng-4967 409 3 ) ) PUNCT fumecheng-4967 409 4 the the DET fumecheng-4967 409 5 advantage advantage NOUN fumecheng-4967 409 6 of of ADP fumecheng-4967 409 7 this this DET fumecheng-4967 409 8 approach approach NOUN fumecheng-4967 409 9 is be AUX fumecheng-4967 409 10 its its PRON fumecheng-4967 409 11 mathematical mathematical ADJ fumecheng-4967 409 12 transparency transparency NOUN fumecheng-4967 409 13 . . PUNCT fumecheng-4967 410 1 one one PRON fumecheng-4967 410 2 can can AUX fumecheng-4967 410 3 regulate regulate VERB fumecheng-4967 410 4 everything everything PRON fumecheng-4967 410 5 by by ADP fumecheng-4967 410 6 simple simple ADJ fumecheng-4967 410 7 manipulation manipulation NOUN fumecheng-4967 410 8 with with ADP fumecheng-4967 410 9 varied varied ADJ fumecheng-4967 410 10 positions position NOUN fumecheng-4967 410 11 , , PUNCT fumecheng-4967 410 12 amplitudes amplitude NOUN fumecheng-4967 410 13 and and CCONJ fumecheng-4967 410 14 widths width NOUN fumecheng-4967 410 15 of of ADP fumecheng-4967 410 16 the the DET fumecheng-4967 410 17 gaussian gaussian ADJ fumecheng-4967 410 18 functions function NOUN fumecheng-4967 410 19 . . PUNCT fumecheng-4967 411 1 the the DET fumecheng-4967 411 2 only only ADJ fumecheng-4967 411 3 limitation limitation NOUN fumecheng-4967 411 4 is be AUX fumecheng-4967 411 5 generally generally ADV fumecheng-4967 411 6 that that SCONJ fumecheng-4967 411 7 the the DET fumecheng-4967 411 8 characteristic characteristic ADJ fumecheng-4967 411 9 scale scale NOUN fumecheng-4967 411 10 of of ADP fumecheng-4967 411 11 the the DET fumecheng-4967 411 12 artificial artificial ADJ fumecheng-4967 411 13 surface surface NOUN fumecheng-4967 411 14 irregularities irregularity NOUN fumecheng-4967 411 15 should should AUX fumecheng-4967 411 16 be be AUX fumecheng-4967 411 17 adjusted adjust VERB fumecheng-4967 411 18 to to PART fumecheng-4967 411 19 be be AUX fumecheng-4967 411 20 smaller small ADJ fumecheng-4967 411 21 or or CCONJ fumecheng-4967 411 22 comparable comparable ADJ fumecheng-4967 411 23 with with ADP fumecheng-4967 411 24 the the DET fumecheng-4967 411 25 scale scale NOUN fumecheng-4967 411 26 of of ADP fumecheng-4967 411 27 the the DET fumecheng-4967 411 28 elements element NOUN fumecheng-4967 411 29 interacting interact VERB fumecheng-4967 411 30 with with ADP fumecheng-4967 411 31 the the DET fumecheng-4967 411 32 surface surface NOUN fumecheng-4967 411 33 ( ( PUNCT fumecheng-4967 411 34 spatulae spatulae NOUN fumecheng-4967 411 35 of of ADP fumecheng-4967 411 36 animals animal NOUN fumecheng-4967 411 37 , , PUNCT fumecheng-4967 411 38 for for ADP fumecheng-4967 411 39 example example NOUN fumecheng-4967 411 40 ) ) PUNCT fumecheng-4967 411 41 . . PUNCT fumecheng-4967 412 1 in in ADP fumecheng-4967 412 2 particular particular ADJ fumecheng-4967 412 3 , , PUNCT fumecheng-4967 412 4 the the DET fumecheng-4967 412 5 typical typical ADJ fumecheng-4967 412 6 distance distance NOUN fumecheng-4967 412 7 between between ADP fumecheng-4967 412 8 the the DET fumecheng-4967 412 9 hills hill NOUN fumecheng-4967 412 10 and and CCONJ fumecheng-4967 412 11 valleys valley NOUN fumecheng-4967 412 12 of of ADP fumecheng-4967 412 13 the the DET fumecheng-4967 412 14 randomly randomly ADV fumecheng-4967 412 15 accumulated accumulate VERB fumecheng-4967 412 16 surface surface NOUN fumecheng-4967 412 17 z(x z(x NOUN fumecheng-4967 412 18 , , PUNCT fumecheng-4967 412 19 y)=gn y)=gn NOUN fumecheng-4967 412 20 can can AUX fumecheng-4967 412 21 be be AUX fumecheng-4967 412 22 regulated regulate VERB fumecheng-4967 412 23 by by ADP fumecheng-4967 412 24 the the DET fumecheng-4967 412 25 number number NOUN fumecheng-4967 412 26 of of ADP fumecheng-4967 412 27 gaussians gaussian NOUN fumecheng-4967 412 28 . . PUNCT fumecheng-4967 413 1 an an DET fumecheng-4967 413 2 additional additional ADJ fumecheng-4967 413 3 convenience convenience NOUN fumecheng-4967 413 4 of of ADP fumecheng-4967 413 5 the the DET fumecheng-4967 413 6 method method NOUN fumecheng-4967 413 7 is be AUX fumecheng-4967 413 8 in in ADP fumecheng-4967 413 9 the the DET fumecheng-4967 413 10 fact fact NOUN fumecheng-4967 413 11 that that SCONJ fumecheng-4967 413 12 one one PRON fumecheng-4967 413 13 can can AUX fumecheng-4967 413 14 even even ADV fumecheng-4967 413 15 not not PART fumecheng-4967 413 16 control control VERB fumecheng-4967 413 17 the the DET fumecheng-4967 413 18 amplitude amplitude NOUN fumecheng-4967 413 19 of of ADP fumecheng-4967 413 20 the the DET fumecheng-4967 413 21 asperities asperity NOUN fumecheng-4967 413 22 during during ADP fumecheng-4967 413 23 accumulation accumulation NOUN fumecheng-4967 413 24 of of ADP fumecheng-4967 413 25 the the DET fumecheng-4967 413 26 sum sum NOUN fumecheng-4967 413 27 gn gn PROPN fumecheng-4967 413 28 . . PUNCT fumecheng-4967 414 1 the the DET fumecheng-4967 414 2 amplitude amplitude NOUN fumecheng-4967 414 3 of of ADP fumecheng-4967 414 4 roughness roughness NOUN fumecheng-4967 414 5 after after ADP fumecheng-4967 414 6 accumulation accumulation NOUN fumecheng-4967 414 7 is be AUX fumecheng-4967 414 8 finally finally ADV fumecheng-4967 414 9 regulated regulate VERB fumecheng-4967 414 10 by by ADP fumecheng-4967 414 11 the the DET fumecheng-4967 414 12 normalization normalization NOUN fumecheng-4967 414 13 z(x z(x PROPN fumecheng-4967 414 14 , , PUNCT fumecheng-4967 414 15 y y NOUN fumecheng-4967 414 16 ) ) PUNCT fumecheng-4967 414 17 → → SYM fumecheng-4967 414 18 a(z(x a(z(x PROPN fumecheng-4967 414 19 , , PUNCT fumecheng-4967 414 20 y)−min(z))/(max(z)−min(z y)−min(z))/(max(z)−min(z PROPN fumecheng-4967 414 21 ) ) PUNCT fumecheng-4967 414 22 ) ) PUNCT fumecheng-4967 414 23 , , PUNCT fumecheng-4967 414 24 where where SCONJ fumecheng-4967 414 25 desirable desirable ADJ fumecheng-4967 414 26 amplitude amplitude NOUN fumecheng-4967 414 27 a a PRON fumecheng-4967 414 28 can can AUX fumecheng-4967 414 29 be be AUX fumecheng-4967 414 30 chosen choose VERB fumecheng-4967 414 31 from from ADP fumecheng-4967 414 32 the the DET fumecheng-4967 414 33 limit limit NOUN fumecheng-4967 414 34 of of ADP fumecheng-4967 414 35 the the DET fumecheng-4967 414 36 flat flat ADJ fumecheng-4967 414 37 surface surface NOUN fumecheng-4967 415 1 a=0 a=0 X fumecheng-4967 415 2 to to ADP fumecheng-4967 415 3 the the DET fumecheng-4967 415 4 values value NOUN fumecheng-4967 415 5 comparable comparable ADJ fumecheng-4967 415 6 with with ADP fumecheng-4967 415 7 the the DET fumecheng-4967 415 8 characteristic characteristic ADJ fumecheng-4967 415 9 lengths length NOUN fumecheng-4967 415 10 of of ADP fumecheng-4967 415 11 the the DET fumecheng-4967 415 12 system system NOUN fumecheng-4967 415 13 under under ADP fumecheng-4967 415 14 consideration consideration NOUN fumecheng-4967 415 15 . . PUNCT fumecheng-4967 416 1 different different ADJ fumecheng-4967 416 2 variants variant NOUN fumecheng-4967 416 3 of of ADP fumecheng-4967 416 4 the the DET fumecheng-4967 416 5 rough rough ADJ fumecheng-4967 416 6 surface surface NOUN fumecheng-4967 416 7 generated generate VERB fumecheng-4967 416 8 by by ADP fumecheng-4967 416 9 the the DET fumecheng-4967 416 10 random random ADJ fumecheng-4967 416 11 deposition deposition NOUN fumecheng-4967 416 12 of of ADP fumecheng-4967 416 13 gaussians gaussian NOUN fumecheng-4967 416 14 are be AUX fumecheng-4967 416 15 shown show VERB fumecheng-4967 416 16 in in ADP fumecheng-4967 416 17 fig fig NOUN fumecheng-4967 416 18 . . PUNCT fumecheng-4967 417 1 9 9 X fumecheng-4967 417 2 . . X fumecheng-4967 417 3 methods method NOUN fumecheng-4967 417 4 of of ADP fumecheng-4967 417 5 the the DET fumecheng-4967 417 6 pattern pattern NOUN fumecheng-4967 417 7 formation formation NOUN fumecheng-4967 417 8 in in ADP fumecheng-4967 417 9 numerical numerical ADJ fumecheng-4967 417 10 modeling modeling NOUN fumecheng-4967 417 11 of of ADP fumecheng-4967 417 12 biological biological ADJ fumecheng-4967 417 13 problems problem NOUN fumecheng-4967 417 14 235 235 NUM fumecheng-4967 417 15 fig fig NOUN fumecheng-4967 417 16 . . PUNCT fumecheng-4967 418 1 9 9 NUM fumecheng-4967 418 2 different different ADJ fumecheng-4967 418 3 variants variant NOUN fumecheng-4967 418 4 of of ADP fumecheng-4967 418 5 the the DET fumecheng-4967 418 6 rough rough ADJ fumecheng-4967 418 7 surface surface NOUN fumecheng-4967 418 8 generated generate VERB fumecheng-4967 418 9 by by ADP fumecheng-4967 418 10 the the DET fumecheng-4967 418 11 random random ADJ fumecheng-4967 418 12 deposition deposition NOUN fumecheng-4967 418 13 of of ADP fumecheng-4967 418 14 gaussians gaussian NOUN fumecheng-4967 418 15 . . PUNCT fumecheng-4967 419 1 the the DET fumecheng-4967 419 2 number number NOUN fumecheng-4967 419 3 of of ADP fumecheng-4967 419 4 gaussians gaussian NOUN fumecheng-4967 419 5 used use VERB fumecheng-4967 419 6 to to PART fumecheng-4967 419 7 generate generate VERB fumecheng-4967 419 8 the the DET fumecheng-4967 419 9 surface surface NOUN fumecheng-4967 419 10 grows grow VERB fumecheng-4967 419 11 from from ADP fumecheng-4967 419 12 left left ADJ fumecheng-4967 419 13 to to ADP fumecheng-4967 419 14 right right NOUN fumecheng-4967 419 15 . . PUNCT fumecheng-4967 420 1 one one NUM fumecheng-4967 420 2 of of ADP fumecheng-4967 420 3 the the DET fumecheng-4967 420 4 widely widely ADV fumecheng-4967 420 5 known know VERB fumecheng-4967 420 6 reasons reason NOUN fumecheng-4967 420 7 to to PART fumecheng-4967 420 8 generate generate VERB fumecheng-4967 420 9 numerical numerical ADJ fumecheng-4967 420 10 surface surface NOUN fumecheng-4967 420 11 or or CCONJ fumecheng-4967 420 12 potential potential ADJ fumecheng-4967 420 13 u u NOUN fumecheng-4967 420 14 is be AUX fumecheng-4967 420 15 its its PRON fumecheng-4967 420 16 application application NOUN fumecheng-4967 420 17 to to ADP fumecheng-4967 420 18 tribology tribology NOUN fumecheng-4967 420 19 . . PUNCT fumecheng-4967 421 1 let let VERB fumecheng-4967 421 2 us we PRON fumecheng-4967 421 3 mention mention VERB fumecheng-4967 421 4 , , PUNCT fumecheng-4967 421 5 in in ADP fumecheng-4967 421 6 this this DET fumecheng-4967 421 7 context context NOUN fumecheng-4967 421 8 , , PUNCT fumecheng-4967 421 9 a a DET fumecheng-4967 421 10 commonly commonly ADV fumecheng-4967 421 11 used use VERB fumecheng-4967 421 12 prandtltomlinson prandtltomlinson NOUN fumecheng-4967 421 13 model model NOUN fumecheng-4967 421 14 that that PRON fumecheng-4967 421 15 has have AUX fumecheng-4967 421 16 proven prove VERB fumecheng-4967 421 17 to to PART fumecheng-4967 421 18 be be AUX fumecheng-4967 421 19 successful successful ADJ fumecheng-4967 421 20 in in ADP fumecheng-4967 421 21 describing describe VERB fumecheng-4967 421 22 shear shear NOUN fumecheng-4967 421 23 response response NOUN fumecheng-4967 421 24 in in ADP fumecheng-4967 421 25 surface surface NOUN fumecheng-4967 421 26 force force NOUN fumecheng-4967 421 27 apparatus apparatus NOUN fumecheng-4967 421 28 configuration configuration NOUN fumecheng-4967 421 29 . . PUNCT fumecheng-4967 422 1 this this DET fumecheng-4967 422 2 model model NOUN fumecheng-4967 422 3 describes describe VERB fumecheng-4967 422 4 the the DET fumecheng-4967 422 5 lateral lateral ADJ fumecheng-4967 422 6 motion motion NOUN fumecheng-4967 422 7 of of ADP fumecheng-4967 422 8 a a DET fumecheng-4967 422 9 driven drive VERB fumecheng-4967 422 10 plate plate NOUN fumecheng-4967 422 11 and and CCONJ fumecheng-4967 422 12 has have VERB fumecheng-4967 422 13 the the DET fumecheng-4967 422 14 following follow VERB fumecheng-4967 422 15 form form NOUN fumecheng-4967 422 16 : : PUNCT fumecheng-4967 422 17 2 2 NUM fumecheng-4967 422 18 2/ 2/ NUM fumecheng-4967 422 19 / / SYM fumecheng-4967 422 20 ( ( PUNCT fumecheng-4967 422 21 ) ) PUNCT fumecheng-4967 422 22 / / SYM fumecheng-4967 422 23 ( ( PUNCT fumecheng-4967 422 24 ) ) PUNCT fumecheng-4967 422 25 0x 0x NOUN fumecheng-4967 422 26 t t NOUN fumecheng-4967 422 27 x x SYM fumecheng-4967 422 28 t t NOUN fumecheng-4967 422 29 u u X fumecheng-4967 422 30 x x X fumecheng-4967 422 31 x x X fumecheng-4967 422 32 k k NOUN fumecheng-4967 422 33 x x X fumecheng-4967 422 34 vt vt PROPN fumecheng-4967 422 35   PROPN fumecheng-4967 422 36   VERB fumecheng-4967 422 37   PROPN fumecheng-4967 422 38   PROPN fumecheng-4967 422 39   PROPN fumecheng-4967 422 40   PROPN fumecheng-4967 422 41   PUNCT fumecheng-4967 422 42   PROPN fumecheng-4967 422 43   PROPN fumecheng-4967 422 44 ( ( PUNCT fumecheng-4967 422 45 27 27 NUM fumecheng-4967 422 46 ) ) PUNCT fumecheng-4967 422 47 here here ADV fumecheng-4967 422 48 a a DET fumecheng-4967 422 49 driven drive VERB fumecheng-4967 422 50 plate plate NOUN fumecheng-4967 422 51 of of ADP fumecheng-4967 422 52 mass mass NOUN fumecheng-4967 422 53 m m PROPN fumecheng-4967 422 54 and and CCONJ fumecheng-4967 422 55 the the DET fumecheng-4967 422 56 center center NOUN fumecheng-4967 422 57 - - PUNCT fumecheng-4967 422 58 of of ADP fumecheng-4967 422 59 - - PUNCT fumecheng-4967 422 60 mass mass NOUN fumecheng-4967 422 61 coordinate coordinate NOUN fumecheng-4967 422 62 x x VERB fumecheng-4967 422 63 is be AUX fumecheng-4967 422 64 pulled pull VERB fumecheng-4967 422 65 by by ADP fumecheng-4967 422 66 a a DET fumecheng-4967 422 67 spring spring NOUN fumecheng-4967 422 68 of of ADP fumecheng-4967 422 69 a a DET fumecheng-4967 422 70 spring spring NOUN fumecheng-4967 422 71 constant constant ADJ fumecheng-4967 422 72 k. k. PROPN fumecheng-4967 422 73 in in ADP fumecheng-4967 422 74 standard standard PROPN fumecheng-4967 422 75 tomlinson tomlinson PROPN fumecheng-4967 422 76 equation equation NOUN fumecheng-4967 422 77 that that PRON fumecheng-4967 422 78 is be AUX fumecheng-4967 422 79 normally normally ADV fumecheng-4967 422 80 applied apply VERB fumecheng-4967 422 81 to to PART fumecheng-4967 422 82 study study VERB fumecheng-4967 422 83 atomically atomically ADV fumecheng-4967 422 84 flat flat ADJ fumecheng-4967 422 85 surfaces surface NOUN fumecheng-4967 422 86 , , PUNCT fumecheng-4967 422 87 u(x u(x NOUN fumecheng-4967 422 88 ) ) PUNCT fumecheng-4967 422 89 is be AUX fumecheng-4967 422 90 the the DET fumecheng-4967 422 91 effective effective ADJ fumecheng-4967 422 92 periodic periodic ADJ fumecheng-4967 422 93 potential potential ADJ fumecheng-4967 422 94 u(x)=u0cos(2x u(x)=u0cos(2x NOUN fumecheng-4967 422 95 / / SYM fumecheng-4967 422 96 b b NOUN fumecheng-4967 422 97 ) ) PUNCT fumecheng-4967 422 98 experienced experience VERB fumecheng-4967 422 99 by by ADP fumecheng-4967 422 100 the the DET fumecheng-4967 422 101 plate plate NOUN fumecheng-4967 422 102 due due ADP fumecheng-4967 422 103 to to ADP fumecheng-4967 422 104 the the DET fumecheng-4967 422 105 presence presence NOUN fumecheng-4967 422 106 of of ADP fumecheng-4967 422 107 an an DET fumecheng-4967 422 108 embedded embed VERB fumecheng-4967 422 109 system system NOUN fumecheng-4967 422 110 . . PUNCT fumecheng-4967 423 1 in in ADP fumecheng-4967 423 2 some some DET fumecheng-4967 423 3 sense sense NOUN fumecheng-4967 423 4 , , PUNCT fumecheng-4967 423 5 such such ADJ fumecheng-4967 423 6 simple simple ADJ fumecheng-4967 423 7 potential potential NOUN fumecheng-4967 423 8 is be AUX fumecheng-4967 423 9 also also ADV fumecheng-4967 423 10 particular particular ADJ fumecheng-4967 423 11 realization realization NOUN fumecheng-4967 423 12 of of ADP fumecheng-4967 423 13 the the DET fumecheng-4967 423 14 surface surface NOUN fumecheng-4967 423 15 pattern pattern NOUN fumecheng-4967 423 16 appearing appear VERB fumecheng-4967 423 17 on on ADP fumecheng-4967 423 18 microscopic microscopic ADJ fumecheng-4967 423 19 level level NOUN fumecheng-4967 423 20 , , PUNCT fumecheng-4967 423 21 where where SCONJ fumecheng-4967 423 22 its its PRON fumecheng-4967 423 23 creation creation NOUN fumecheng-4967 423 24 is be AUX fumecheng-4967 423 25 regulated regulate VERB fumecheng-4967 423 26 by by ADP fumecheng-4967 423 27 the the DET fumecheng-4967 423 28 process process NOUN fumecheng-4967 423 29 of of ADP fumecheng-4967 423 30 crystallization crystallization NOUN fumecheng-4967 423 31 , , PUNCT fumecheng-4967 423 32 which which PRON fumecheng-4967 423 33 normally normally ADV fumecheng-4967 423 34 leads lead VERB fumecheng-4967 423 35 to to ADP fumecheng-4967 423 36 an an DET fumecheng-4967 423 37 ideally ideally ADV fumecheng-4967 423 38 periodic periodic ADJ fumecheng-4967 423 39 crystal crystal NOUN fumecheng-4967 423 40 lattice lattice NOUN fumecheng-4967 423 41 . . PUNCT fumecheng-4967 424 1 below below ADP fumecheng-4967 424 2 for for ADP fumecheng-4967 424 3 general general ADJ fumecheng-4967 424 4 theoretical theoretical ADJ fumecheng-4967 424 5 study study NOUN fumecheng-4967 424 6 , , PUNCT fumecheng-4967 424 7 we we PRON fumecheng-4967 424 8 use use VERB fumecheng-4967 424 9 dimensionless dimensionless NOUN fumecheng-4967 424 10 units unit NOUN fumecheng-4967 424 11 normalized normalize VERB fumecheng-4967 424 12 to to ADP fumecheng-4967 424 13 characteristic characteristic ADJ fumecheng-4967 424 14 microscopic microscopic ADJ fumecheng-4967 424 15 scales scale NOUN fumecheng-4967 424 16 and and CCONJ fumecheng-4967 424 17 energies energy NOUN fumecheng-4967 424 18 of of ADP fumecheng-4967 424 19 the the DET fumecheng-4967 424 20 particular particular ADJ fumecheng-4967 424 21 system system NOUN fumecheng-4967 424 22 under under ADP fumecheng-4967 424 23 consideration consideration NOUN fumecheng-4967 424 24 . . PUNCT fumecheng-4967 425 1 parameter parameter NOUN fumecheng-4967 425 2   PROPN fumecheng-4967 425 3 , , PUNCT fumecheng-4967 425 4 as as ADP fumecheng-4967 425 5 usually usually ADV fumecheng-4967 425 6 , , PUNCT fumecheng-4967 425 7 is be AUX fumecheng-4967 425 8 responsible responsible ADJ fumecheng-4967 425 9 for for ADP fumecheng-4967 425 10 the the DET fumecheng-4967 425 11 dissipation dissipation NOUN fumecheng-4967 425 12 . . PUNCT fumecheng-4967 426 1 the the DET fumecheng-4967 426 2 spring spring NOUN fumecheng-4967 426 3 is be AUX fumecheng-4967 426 4 connected connect VERB fumecheng-4967 426 5 to to ADP fumecheng-4967 426 6 a a DET fumecheng-4967 426 7 stage stage NOUN fumecheng-4967 426 8 which which PRON fumecheng-4967 426 9 moves move VERB fumecheng-4967 426 10 with with ADP fumecheng-4967 426 11 a a DET fumecheng-4967 426 12 velocity velocity NOUN fumecheng-4967 426 13 v. v. ADP fumecheng-4967 426 14 tomlinson tomlinson PROPN fumecheng-4967 426 15 equation equation NOUN fumecheng-4967 426 16 was be AUX fumecheng-4967 426 17 well well ADV fumecheng-4967 426 18 supported support VERB fumecheng-4967 426 19 microscopically microscopically ADV fumecheng-4967 426 20 , , PUNCT fumecheng-4967 426 21 but but CCONJ fumecheng-4967 426 22 usually usually ADV fumecheng-4967 426 23 people people NOUN fumecheng-4967 426 24 do do AUX fumecheng-4967 426 25 not not PART fumecheng-4967 426 26 extend extend VERB fumecheng-4967 426 27 its its PRON fumecheng-4967 426 28 application application NOUN fumecheng-4967 426 29 even even ADV fumecheng-4967 426 30 to to ADP fumecheng-4967 426 31 the the DET fumecheng-4967 426 32 mesoscopic mesoscopic NOUN fumecheng-4967 426 33 scales scale NOUN fumecheng-4967 426 34 . . PUNCT fumecheng-4967 427 1 however however ADV fumecheng-4967 427 2 , , PUNCT fumecheng-4967 427 3 as as SCONJ fumecheng-4967 427 4 we we PRON fumecheng-4967 427 5 saw see VERB fumecheng-4967 427 6 in in ADP fumecheng-4967 427 7 many many ADJ fumecheng-4967 427 8 examples example NOUN fumecheng-4967 427 9 of of ADP fumecheng-4967 427 10 the the DET fumecheng-4967 427 11 formation formation NOUN fumecheng-4967 427 12 of of ADP fumecheng-4967 427 13 many many ADJ fumecheng-4967 427 14 surfaces surface NOUN fumecheng-4967 427 15 ( ( PUNCT fumecheng-4967 427 16 may may AUX fumecheng-4967 427 17 be be AUX fumecheng-4967 427 18 better well ADJ fumecheng-4967 427 19 to to PART fumecheng-4967 427 20 say say VERB fumecheng-4967 427 21 all all DET fumecheng-4967 427 22 the the DET fumecheng-4967 427 23 surfaces surface NOUN fumecheng-4967 427 24 which which PRON fumecheng-4967 427 25 we we PRON fumecheng-4967 427 26 meet meet VERB fumecheng-4967 427 27 in in ADP fumecheng-4967 427 28 normal normal ADJ fumecheng-4967 427 29 life life NOUN fumecheng-4967 427 30 ) ) PUNCT fumecheng-4967 427 31 , , PUNCT fumecheng-4967 427 32 the the DET fumecheng-4967 427 33 surface surface NOUN fumecheng-4967 427 34 is be AUX fumecheng-4967 427 35 dictated dictate VERB fumecheng-4967 427 36 by by ADP fumecheng-4967 427 37 frozen frozen ADJ fumecheng-4967 427 38 kinetics kinetic NOUN fumecheng-4967 427 39 , , PUNCT fumecheng-4967 427 40 which which PRON fumecheng-4967 427 41 leads lead VERB fumecheng-4967 427 42 to to ADP fumecheng-4967 427 43 the the DET fumecheng-4967 427 44 relief relief NOUN fumecheng-4967 427 45 , , PUNCT fumecheng-4967 427 46 which which PRON fumecheng-4967 427 47 is be AUX fumecheng-4967 427 48 quite quite ADV fumecheng-4967 427 49 far far ADV fumecheng-4967 427 50 from from ADP fumecheng-4967 427 51 an an DET fumecheng-4967 427 52 ideal ideal ADJ fumecheng-4967 427 53 periodic periodic ADJ fumecheng-4967 427 54 structure structure NOUN fumecheng-4967 427 55 . . PUNCT fumecheng-4967 428 1 as as ADP fumecheng-4967 428 2 a a DET fumecheng-4967 428 3 result result NOUN fumecheng-4967 428 4 , , PUNCT fumecheng-4967 428 5 one one PRON fumecheng-4967 428 6 partially partially ADV fumecheng-4967 428 7 knows know VERB fumecheng-4967 428 8 how how SCONJ fumecheng-4967 428 9 to to PART fumecheng-4967 428 10 relate relate VERB fumecheng-4967 428 11 the the DET fumecheng-4967 428 12 parameters parameter NOUN fumecheng-4967 428 13 that that PRON fumecheng-4967 428 14 appear appear VERB fumecheng-4967 428 15 in in ADP fumecheng-4967 428 16 eq eq ADP fumecheng-4967 428 17 . . PUNCT fumecheng-4967 429 1 ( ( PUNCT fumecheng-4967 429 2 27 27 NUM fumecheng-4967 429 3 ) ) PUNCT fumecheng-4967 429 4 to to ADP fumecheng-4967 429 5 the the DET fumecheng-4967 429 6 microscopic microscopic ADJ fumecheng-4967 429 7 characteristics characteristic NOUN fumecheng-4967 429 8 of of ADP fumecheng-4967 429 9 the the DET fumecheng-4967 429 10 system system NOUN fumecheng-4967 429 11 , , PUNCT fumecheng-4967 429 12 but but CCONJ fumecheng-4967 429 13 can can AUX fumecheng-4967 429 14 not not PART fumecheng-4967 429 15 correlate correlate VERB fumecheng-4967 429 16 them they PRON fumecheng-4967 429 17 with with ADP fumecheng-4967 429 18 the the DET fumecheng-4967 429 19 macroscopic macroscopic ADJ fumecheng-4967 429 20 friction friction NOUN fumecheng-4967 429 21 . . PUNCT fumecheng-4967 430 1 this this DET fumecheng-4967 430 2 problem problem NOUN fumecheng-4967 430 3 is be AUX fumecheng-4967 430 4 not not PART fumecheng-4967 430 5 solely solely ADV fumecheng-4967 430 6 limited limit VERB fumecheng-4967 430 7 to to ADP fumecheng-4967 430 8 the the DET fumecheng-4967 430 9 friction friction NOUN fumecheng-4967 430 10 studies study NOUN fumecheng-4967 430 11 , , PUNCT fumecheng-4967 430 12 but but CCONJ fumecheng-4967 430 13 appears appear VERB fumecheng-4967 430 14 also also ADV fumecheng-4967 430 15 when when SCONJ fumecheng-4967 430 16 dealing deal VERB fumecheng-4967 430 17 with with ADP fumecheng-4967 430 18 adhesion adhesion NOUN fumecheng-4967 430 19 . . PUNCT fumecheng-4967 431 1 in in ADP fumecheng-4967 431 2 the the DET fumecheng-4967 431 3 previous previous ADJ fumecheng-4967 431 4 papers paper NOUN fumecheng-4967 431 5 , , PUNCT fumecheng-4967 431 6 we we PRON fumecheng-4967 431 7 have have AUX fumecheng-4967 431 8 seen see VERB fumecheng-4967 431 9 how how SCONJ fumecheng-4967 431 10 important important ADJ fumecheng-4967 431 11 it it PRON fumecheng-4967 431 12 is be AUX fumecheng-4967 431 13 for for ADP fumecheng-4967 431 14 the the DET fumecheng-4967 431 15 study study NOUN fumecheng-4967 431 16 of of ADP fumecheng-4967 431 17 attachment attachment NOUN fumecheng-4967 431 18 devices device NOUN fumecheng-4967 431 19 of of ADP fumecheng-4967 431 20 animals animal NOUN fumecheng-4967 431 21 , , PUNCT fumecheng-4967 431 22 which which PRON fumecheng-4967 431 23 have have VERB fumecheng-4967 431 24 to to PART fumecheng-4967 431 25 adapt adapt VERB fumecheng-4967 431 26 to to ADP fumecheng-4967 431 27 real real ADJ fumecheng-4967 431 28 surfaces surface NOUN fumecheng-4967 431 29 also also ADV fumecheng-4967 431 30 on on ADP fumecheng-4967 431 31 intermediate intermediate ADJ fumecheng-4967 431 32 mesoscopic mesoscopic NOUN fumecheng-4967 431 33 scales scale NOUN fumecheng-4967 431 34 , , PUNCT fumecheng-4967 431 35 but but CCONJ fumecheng-4967 431 36 not not PART fumecheng-4967 431 37 only only ADV fumecheng-4967 431 38 at at ADP fumecheng-4967 431 39 the the DET fumecheng-4967 431 40 microscopic microscopic ADJ fumecheng-4967 431 41 one one NOUN fumecheng-4967 431 42 , , PUNCT fumecheng-4967 431 43 where where SCONJ fumecheng-4967 431 44 pattern pattern NOUN fumecheng-4967 431 45 either either CCONJ fumecheng-4967 431 46 can can AUX fumecheng-4967 431 47 be be AUX fumecheng-4967 431 48 approximately approximately ADV fumecheng-4967 431 49 treated treat VERB fumecheng-4967 431 50 as as ADP fumecheng-4967 431 51 a a DET fumecheng-4967 431 52 flat flat ADJ fumecheng-4967 431 53 or or CCONJ fumecheng-4967 431 54 even even ADV fumecheng-4967 431 55 simply simply ADV fumecheng-4967 431 56 periodic periodic ADJ fumecheng-4967 431 57 [ [ X fumecheng-4967 431 58 12 12 NUM fumecheng-4967 431 59 ] ] PUNCT fumecheng-4967 431 60 . . PUNCT fumecheng-4967 432 1 so so ADV fumecheng-4967 432 2 , , PUNCT fumecheng-4967 432 3 what what PRON fumecheng-4967 432 4 becomes become VERB fumecheng-4967 432 5 a a DET fumecheng-4967 432 6 major major ADJ fumecheng-4967 432 7 problem problem NOUN fumecheng-4967 432 8 here here ADV fumecheng-4967 432 9 is be AUX fumecheng-4967 432 10 that that SCONJ fumecheng-4967 432 11 the the DET fumecheng-4967 432 12 mesoscopic mesoscopic NOUN fumecheng-4967 432 13 structure structure NOUN fumecheng-4967 432 14 of of ADP fumecheng-4967 432 15 frictional frictional ADJ fumecheng-4967 432 16 surfaces surface NOUN fumecheng-4967 432 17 is be AUX fumecheng-4967 432 18 of of ADP fumecheng-4967 432 19 a a DET fumecheng-4967 432 20 fractal fractal ADJ fumecheng-4967 432 21 character character NOUN fumecheng-4967 432 22 and and CCONJ fumecheng-4967 432 23 thereby thereby ADV fumecheng-4967 432 24 can can AUX fumecheng-4967 432 25 not not PART fumecheng-4967 432 26 be be AUX fumecheng-4967 432 27 characterized characterize VERB fumecheng-4967 432 28 by by ADP fumecheng-4967 432 29 a a DET fumecheng-4967 432 30 certain certain ADJ fumecheng-4967 432 31 wave wave NOUN fumecheng-4967 432 32 vector vector NOUN fumecheng-4967 432 33 ( ( PUNCT fumecheng-4967 432 34 or or CCONJ fumecheng-4967 432 35 even even ADV fumecheng-4967 432 36 few few ADJ fumecheng-4967 432 37 ones one NOUN fumecheng-4967 432 38 ) ) PUNCT fumecheng-4967 432 39 , , PUNCT fumecheng-4967 432 40 like like SCONJ fumecheng-4967 432 41 it it PRON fumecheng-4967 432 42 is be AUX fumecheng-4967 432 43 normally normally ADV fumecheng-4967 432 44 used use VERB fumecheng-4967 432 45 in in ADP fumecheng-4967 432 46 applications application NOUN fumecheng-4967 432 47 of of ADP fumecheng-4967 432 48 the the DET fumecheng-4967 432 49 tomlinson tomlinson PROPN fumecheng-4967 432 50 model model NOUN fumecheng-4967 432 51 . . PUNCT fumecheng-4967 433 1 on on ADP fumecheng-4967 433 2 the the DET fumecheng-4967 433 3 other other ADJ fumecheng-4967 433 4 hand hand NOUN fumecheng-4967 433 5 , , PUNCT fumecheng-4967 433 6 it it PRON fumecheng-4967 433 7 could could AUX fumecheng-4967 433 8 be be AUX fumecheng-4967 433 9 inconvenient inconvenient ADJ fumecheng-4967 433 10 or or CCONJ fumecheng-4967 433 11 simply simply ADV fumecheng-4967 433 12 senseless senseless ADJ fumecheng-4967 433 13 to to PART fumecheng-4967 433 14 reproduce reproduce VERB fumecheng-4967 433 15 each each DET fumecheng-4967 433 16 time time NOUN fumecheng-4967 433 17 one one NUM fumecheng-4967 433 18 of of ADP fumecheng-4967 433 19 the the DET fumecheng-4967 433 20 physical physical ADJ fumecheng-4967 433 21 or or CCONJ fumecheng-4967 433 22 chemical chemical NOUN fumecheng-4967 433 23 processes process NOUN fumecheng-4967 433 24 described describe VERB fumecheng-4967 433 25 here here ADV fumecheng-4967 433 26 . . PUNCT fumecheng-4967 434 1 it it PRON fumecheng-4967 434 2 is be AUX fumecheng-4967 434 3 important important ADJ fumecheng-4967 434 4 to to PART fumecheng-4967 434 5 know know VERB fumecheng-4967 434 6 , , PUNCT fumecheng-4967 434 7 236 236 NUM fumecheng-4967 434 8 a.e a.e PROPN fumecheng-4967 434 9 . . PROPN fumecheng-4967 434 10 filippov filippov PROPN fumecheng-4967 434 11 , , PUNCT fumecheng-4967 434 12 s.n s.n PROPN fumecheng-4967 434 13 . . PROPN fumecheng-4967 434 14 gorb gorb PROPN fumecheng-4967 434 15 how how SCONJ fumecheng-4967 434 16 such such ADJ fumecheng-4967 434 17 surfaces surface NOUN fumecheng-4967 434 18 appear appear VERB fumecheng-4967 434 19 , , PUNCT fumecheng-4967 434 20 or or CCONJ fumecheng-4967 434 21 maybe maybe ADV fumecheng-4967 434 22 it it PRON fumecheng-4967 434 23 becomes become VERB fumecheng-4967 434 24 important important ADJ fumecheng-4967 434 25 , , PUNCT fumecheng-4967 434 26 if if SCONJ fumecheng-4967 434 27 the the DET fumecheng-4967 434 28 studied studied ADJ fumecheng-4967 434 29 surface surface NOUN fumecheng-4967 434 30 really really ADV fumecheng-4967 434 31 has have VERB fumecheng-4967 434 32 specific specific ADJ fumecheng-4967 434 33 substructure substructure NOUN fumecheng-4967 434 34 with with ADP fumecheng-4967 434 35 the the DET fumecheng-4967 434 36 periodicity periodicity NOUN fumecheng-4967 434 37 important important ADJ fumecheng-4967 434 38 for for ADP fumecheng-4967 434 39 the the DET fumecheng-4967 434 40 modeling modeling NOUN fumecheng-4967 434 41 . . PUNCT fumecheng-4967 435 1 however however ADV fumecheng-4967 435 2 , , PUNCT fumecheng-4967 435 3 if if SCONJ fumecheng-4967 435 4 we we PRON fumecheng-4967 435 5 can can AUX fumecheng-4967 435 6 forget forget VERB fumecheng-4967 435 7 about about ADP fumecheng-4967 435 8 underlining underline VERB fumecheng-4967 435 9 process process NOUN fumecheng-4967 435 10 and and CCONJ fumecheng-4967 435 11 accept accept VERB fumecheng-4967 435 12 a a DET fumecheng-4967 435 13 naive naive ADJ fumecheng-4967 435 14 hypothesis hypothesis NOUN fumecheng-4967 435 15 that that PRON fumecheng-4967 435 16 the the DET fumecheng-4967 435 17 majority majority NOUN fumecheng-4967 435 18 of of ADP fumecheng-4967 435 19 the the DET fumecheng-4967 435 20 surfaces surface NOUN fumecheng-4967 435 21 are be AUX fumecheng-4967 435 22 simply simply ADV fumecheng-4967 435 23 fractal fractal ADJ fumecheng-4967 435 24 , , PUNCT fumecheng-4967 435 25 it it PRON fumecheng-4967 435 26 is be AUX fumecheng-4967 435 27 natural natural ADJ fumecheng-4967 435 28 to to PART fumecheng-4967 435 29 extend extend VERB fumecheng-4967 435 30 the the DET fumecheng-4967 435 31 model model NOUN fumecheng-4967 435 32 into into ADP fumecheng-4967 435 33 a a DET fumecheng-4967 435 34 directly directly ADV fumecheng-4967 435 35 generated generate VERB fumecheng-4967 435 36 pattern pattern NOUN fumecheng-4967 435 37 according accord VERB fumecheng-4967 435 38 to to ADP fumecheng-4967 435 39 very very ADV fumecheng-4967 435 40 formal formal ADJ fumecheng-4967 435 41 mathematical mathematical ADJ fumecheng-4967 435 42 definition definition NOUN fumecheng-4967 435 43 of of ADP fumecheng-4967 435 44 the the DET fumecheng-4967 435 45 fractal fractal NOUN fumecheng-4967 435 46 . . PUNCT fumecheng-4967 436 1 let let VERB fumecheng-4967 436 2 us we PRON fumecheng-4967 436 3 consider consider VERB fumecheng-4967 436 4 a a DET fumecheng-4967 436 5 fractal fractal ADJ fumecheng-4967 436 6 potential potential NOUN fumecheng-4967 436 7 of of ADP fumecheng-4967 436 8 the the DET fumecheng-4967 436 9 form form NOUN fumecheng-4967 436 10 : : PUNCT fumecheng-4967 436 11 2 2 NUM fumecheng-4967 436 12 1 1 NUM fumecheng-4967 436 13 0 0 NUM fumecheng-4967 436 14 ( ( PUNCT fumecheng-4967 436 15 ) ) PUNCT fumecheng-4967 436 16 ( ( PUNCT fumecheng-4967 436 17 ) ) PUNCT fumecheng-4967 436 18 cos cos PROPN fumecheng-4967 436 19 ( ( PUNCT fumecheng-4967 436 20 ) ) PUNCT fumecheng-4967 436 21 q q NOUN fumecheng-4967 436 22 q q PUNCT fumecheng-4967 436 23 u u NOUN fumecheng-4967 436 24 x x X fumecheng-4967 436 25 u u NOUN fumecheng-4967 436 26 dqc dqc VERB fumecheng-4967 436 27 q q PROPN fumecheng-4967 436 28 qx qx ADJ fumecheng-4967 436 29   NUM fumecheng-4967 436 30   NOUN fumecheng-4967 436 31 , , PUNCT fumecheng-4967 436 32 ( ( PUNCT fumecheng-4967 436 33 ) ) PUNCT fumecheng-4967 436 34 c c NOUN fumecheng-4967 437 1 q q PROPN fumecheng-4967 437 2 q q INTJ fumecheng-4967 437 3   PROPN fumecheng-4967 437 4 ( ( PUNCT fumecheng-4967 437 5 28 28 NUM fumecheng-4967 437 6 ) ) PUNCT fumecheng-4967 437 7 here here ADV fumecheng-4967 437 8 q1 q1 PROPN fumecheng-4967 437 9 and and CCONJ fumecheng-4967 437 10 q2 q2 NOUN fumecheng-4967 437 11 are be AUX fumecheng-4967 437 12 characteristic characteristic ADJ fumecheng-4967 437 13 cut cut VERB fumecheng-4967 437 14 off off ADP fumecheng-4967 437 15 wave wave NOUN fumecheng-4967 437 16 vectors vector NOUN fumecheng-4967 437 17 and and CCONJ fumecheng-4967 437 18 δ(x δ(x NOUN fumecheng-4967 437 19 ) ) PUNCT fumecheng-4967 438 1 is be AUX fumecheng-4967 438 2 the the DET fumecheng-4967 438 3 random random ADJ fumecheng-4967 438 4 phase phase NOUN fumecheng-4967 438 5 that that PRON fumecheng-4967 438 6 we we PRON fumecheng-4967 438 7 assume assume VERB fumecheng-4967 438 8 δ δ X fumecheng-4967 438 9 - - PUNCT fumecheng-4967 438 10 correlated correlate VERB fumecheng-4967 438 11 < < X fumecheng-4967 438 12 δ(q)δ(q‟)>=2πδ(q δ(q)δ(q‟)>=2πδ(q ADJ fumecheng-4967 438 13 - - NOUN fumecheng-4967 438 14 q‟ q‟ NUM fumecheng-4967 438 15 ) ) PUNCT fumecheng-4967 438 16 . . PUNCT fumecheng-4967 439 1 for for ADP fumecheng-4967 439 2 the the DET fumecheng-4967 439 3 majority majority NOUN fumecheng-4967 439 4 of of ADP fumecheng-4967 439 5 physically physically ADV fumecheng-4967 439 6 interesting interesting ADJ fumecheng-4967 439 7 systems system NOUN fumecheng-4967 439 8 , , PUNCT fumecheng-4967 439 9 index index NOUN fumecheng-4967 439 10 β β NOUN fumecheng-4967 439 11 is be AUX fumecheng-4967 439 12 close close ADJ fumecheng-4967 439 13 to to ADP fumecheng-4967 439 14 β≈0.9 β≈0.9 VERB fumecheng-4967 439 15 . . PUNCT fumecheng-4967 440 1 below below ADP fumecheng-4967 440 2 we we PRON fumecheng-4967 440 3 will will AUX fumecheng-4967 440 4 keep keep VERB fumecheng-4967 440 5 this this DET fumecheng-4967 440 6 value value NOUN fumecheng-4967 440 7 for for ADP fumecheng-4967 440 8 definiteness definiteness NOUN fumecheng-4967 440 9 . . PUNCT fumecheng-4967 441 1 for for ADP fumecheng-4967 441 2 further further ADJ fumecheng-4967 441 3 study study NOUN fumecheng-4967 441 4 , , PUNCT fumecheng-4967 441 5 it it PRON fumecheng-4967 441 6 is be AUX fumecheng-4967 441 7 convenient convenient ADJ fumecheng-4967 441 8 to to PART fumecheng-4967 441 9 go go VERB fumecheng-4967 441 10 over over ADP fumecheng-4967 441 11 to to ADP fumecheng-4967 441 12 a a DET fumecheng-4967 441 13 discrete discrete ADJ fumecheng-4967 441 14 representation representation NOUN fumecheng-4967 441 15 of of ADP fumecheng-4967 441 16 the the DET fumecheng-4967 441 17 integral integral NOUN fumecheng-4967 441 18 in in ADP fumecheng-4967 441 19 eq eq ADP fumecheng-4967 441 20 . . PUNCT fumecheng-4967 442 1 ( ( PUNCT fumecheng-4967 442 2 2 2 NUM fumecheng-4967 442 3 ) ) PUNCT fumecheng-4967 442 4 ∫dqc(q)→σ ∫dqc(q)→σ NOUN fumecheng-4967 442 5 with with ADP fumecheng-4967 442 6 a a DET fumecheng-4967 442 7 discrete discrete ADJ fumecheng-4967 442 8 step step NOUN fumecheng-4967 442 9 between between ADP fumecheng-4967 442 10 the the DET fumecheng-4967 442 11 wave wave NOUN fumecheng-4967 442 12 vectors vector NOUN fumecheng-4967 442 13 δq δq PRON fumecheng-4967 442 14 determined determine VERB fumecheng-4967 442 15 by by ADP fumecheng-4967 442 16 the the DET fumecheng-4967 442 17 smallest small ADJ fumecheng-4967 442 18 vector vector NOUN fumecheng-4967 442 19 q1 q1 NOUN fumecheng-4967 442 20 corresponding correspond VERB fumecheng-4967 442 21 to to ADP fumecheng-4967 442 22 an an DET fumecheng-4967 442 23 inverse inverse NOUN fumecheng-4967 442 24 maximal maximal ADJ fumecheng-4967 442 25 length length NOUN fumecheng-4967 442 26 lmax lmax NOUN fumecheng-4967 442 27 of of ADP fumecheng-4967 442 28 the the DET fumecheng-4967 442 29 system system NOUN fumecheng-4967 442 30 , , PUNCT fumecheng-4967 442 31 which which PRON fumecheng-4967 442 32 equals equal VERB fumecheng-4967 442 33 normally normally ADV fumecheng-4967 442 34 to to ADP fumecheng-4967 442 35 its its PRON fumecheng-4967 442 36 size size NOUN fumecheng-4967 442 37 lmax lmax NOUN fumecheng-4967 442 38 = = SYM fumecheng-4967 442 39 l l NOUN fumecheng-4967 442 40 . . PUNCT fumecheng-4967 443 1 total total ADJ fumecheng-4967 443 2 number number NOUN fumecheng-4967 443 3 ntot ntot NOUN fumecheng-4967 443 4 of of ADP fumecheng-4967 443 5 the the DET fumecheng-4967 443 6 terms term NOUN fumecheng-4967 443 7 in in ADP fumecheng-4967 443 8 the the DET fumecheng-4967 443 9 sum sum NOUN fumecheng-4967 443 10 is be AUX fumecheng-4967 443 11 given give VERB fumecheng-4967 443 12 by by ADP fumecheng-4967 443 13 ntot ntot NOUN fumecheng-4967 443 14 = = SYM fumecheng-4967 443 15 q2 q2 X fumecheng-4967 443 16 / / SYM fumecheng-4967 443 17 q1≡q2 q1≡q2 PROPN fumecheng-4967 443 18 / / SYM fumecheng-4967 443 19 δq δq PROPN fumecheng-4967 443 20 . . PUNCT fumecheng-4967 444 1 the the DET fumecheng-4967 444 2 discrete discrete ADJ fumecheng-4967 444 3 approach approach NOUN fumecheng-4967 444 4 is be AUX fumecheng-4967 444 5 natural natural ADJ fumecheng-4967 444 6 for for ADP fumecheng-4967 444 7 our our PRON fumecheng-4967 444 8 further further ADJ fumecheng-4967 444 9 numerical numerical ADJ fumecheng-4967 444 10 studies study NOUN fumecheng-4967 444 11 . . PUNCT fumecheng-4967 445 1 it it PRON fumecheng-4967 445 2 allows allow VERB fumecheng-4967 445 3 us we PRON fumecheng-4967 445 4 to to PART fumecheng-4967 445 5 adjust adjust VERB fumecheng-4967 445 6 the the DET fumecheng-4967 445 7 potential potential NOUN fumecheng-4967 445 8 to to ADP fumecheng-4967 445 9 different different ADJ fumecheng-4967 445 10 scales scale NOUN fumecheng-4967 445 11 by by ADP fumecheng-4967 445 12 a a DET fumecheng-4967 445 13 number number NOUN fumecheng-4967 445 14 of of ADP fumecheng-4967 445 15 the the DET fumecheng-4967 445 16 modes mode NOUN fumecheng-4967 445 17 included include VERB fumecheng-4967 445 18 into into ADP fumecheng-4967 445 19 summation summation NOUN fumecheng-4967 445 20 nmodes nmode NOUN fumecheng-4967 445 21 < < X fumecheng-4967 445 22 ntot ntot NOUN fumecheng-4967 445 23 . . PUNCT fumecheng-4967 446 1 the the DET fumecheng-4967 446 2 tomlinson tomlinson PROPN fumecheng-4967 446 3 model model NOUN fumecheng-4967 446 4 based base VERB fumecheng-4967 446 5 on on ADP fumecheng-4967 446 6 analytical analytical ADJ fumecheng-4967 446 7 definition definition NOUN fumecheng-4967 446 8 of of ADP fumecheng-4967 446 9 the the DET fumecheng-4967 446 10 potential potential NOUN fumecheng-4967 446 11 is be AUX fumecheng-4967 446 12 much much ADV fumecheng-4967 446 13 simpler simple ADJ fumecheng-4967 446 14 for for ADP fumecheng-4967 446 15 computer computer NOUN fumecheng-4967 446 16 implementation implementation NOUN fumecheng-4967 446 17 . . PUNCT fumecheng-4967 447 1 the the DET fumecheng-4967 447 2 force force NOUN fumecheng-4967 447 3 is be AUX fumecheng-4967 447 4 calculated calculate VERB fumecheng-4967 447 5 using use VERB fumecheng-4967 447 6 analytical analytical ADJ fumecheng-4967 447 7 formula formula NOUN fumecheng-4967 447 8 at at ADP fumecheng-4967 447 9 each each DET fumecheng-4967 447 10 time time NOUN fumecheng-4967 447 11 - - PUNCT fumecheng-4967 447 12 step step NOUN fumecheng-4967 447 13 and and CCONJ fumecheng-4967 447 14 procedure procedure NOUN fumecheng-4967 447 15 can can AUX fumecheng-4967 447 16 be be AUX fumecheng-4967 447 17 formally formally ADV fumecheng-4967 447 18 extended extend VERB fumecheng-4967 447 19 to to PART fumecheng-4967 447 20 infinite infinite VERB fumecheng-4967 447 21 time time NOUN fumecheng-4967 447 22 - - PUNCT fumecheng-4967 447 23 space space NOUN fumecheng-4967 447 24 runs run NOUN fumecheng-4967 447 25 . . PUNCT fumecheng-4967 448 1 the the DET fumecheng-4967 448 2 modified modify VERB fumecheng-4967 448 3 fractal fractal ADJ fumecheng-4967 448 4 model model NOUN fumecheng-4967 448 5 operates operate VERB fumecheng-4967 448 6 with with ADP fumecheng-4967 448 7 the the DET fumecheng-4967 448 8 data datum NOUN fumecheng-4967 448 9 array array NOUN fumecheng-4967 448 10 ufractal(x)=u{xj ufractal(x)=u{xj NOUN fumecheng-4967 448 11 } } PUNCT fumecheng-4967 448 12 , , PUNCT fumecheng-4967 448 13 where where SCONJ fumecheng-4967 448 14 j=1,2, j=1,2, NOUN fumecheng-4967 448 15 … … SYM fumecheng-4967 448 16 nmodes nmode VERB fumecheng-4967 448 17 . . PUNCT fumecheng-4967 449 1 it it PRON fumecheng-4967 449 2 means mean VERB fumecheng-4967 449 3 that that SCONJ fumecheng-4967 449 4 its its PRON fumecheng-4967 449 5 numerical numerical ADJ fumecheng-4967 449 6 generation generation NOUN fumecheng-4967 449 7 has have VERB fumecheng-4967 449 8 to to PART fumecheng-4967 449 9 be be AUX fumecheng-4967 449 10 extended extend VERB fumecheng-4967 449 11 to to ADP fumecheng-4967 449 12 an an DET fumecheng-4967 449 13 infinite infinite ADJ fumecheng-4967 449 14 run run NOUN fumecheng-4967 449 15 too too ADV fumecheng-4967 449 16 . . PUNCT fumecheng-4967 450 1 for for ADP fumecheng-4967 450 2 this this DET fumecheng-4967 450 3 sake sake NOUN fumecheng-4967 450 4 , , PUNCT fumecheng-4967 450 5 instead instead ADV fumecheng-4967 450 6 of of ADP fumecheng-4967 450 7 eg eg NOUN fumecheng-4967 450 8 . . PUNCT fumecheng-4967 451 1 ( ( PUNCT fumecheng-4967 451 2 2 2 NUM fumecheng-4967 451 3 ) ) PUNCT fumecheng-4967 451 4 , , PUNCT fumecheng-4967 451 5 we we PRON fumecheng-4967 451 6 use use VERB fumecheng-4967 451 7 the the DET fumecheng-4967 451 8 following follow VERB fumecheng-4967 451 9 differential differential ADJ fumecheng-4967 451 10 definition definition NOUN fumecheng-4967 451 11 of of ADP fumecheng-4967 451 12 the the DET fumecheng-4967 451 13 force force NOUN fumecheng-4967 451 14 caused cause VERB fumecheng-4967 451 15 by by ADP fumecheng-4967 451 16 the the DET fumecheng-4967 451 17 fractal fractal ADJ fumecheng-4967 451 18 potential potential NOUN fumecheng-4967 451 19 : : PUNCT fumecheng-4967 451 20 0 0 NUM fumecheng-4967 451 21 ( ( PUNCT fumecheng-4967 451 22 ) ) PUNCT fumecheng-4967 451 23 / / SYM fumecheng-4967 451 24 ( ( PUNCT fumecheng-4967 451 25 ) ) PUNCT fumecheng-4967 451 26 sin sin NOUN fumecheng-4967 451 27 ( ( PUNCT fumecheng-4967 451 28 ) ) PUNCT fumecheng-4967 451 29 ; ; PUNCT fumecheng-4967 451 30 fractal fractal PROPN fumecheng-4967 451 31 j j PROPN fumecheng-4967 451 32 j j PROPN fumecheng-4967 451 33 j j PROPN fumecheng-4967 451 34 j j PROPN fumecheng-4967 451 35 u u PROPN fumecheng-4967 451 36 x x X fumecheng-4967 451 37 x x PUNCT fumecheng-4967 451 38 u u NOUN fumecheng-4967 451 39 x x X fumecheng-4967 451 40 q q X fumecheng-4967 451 41 c c X fumecheng-4967 451 42 q q NOUN fumecheng-4967 451 43 q q PUNCT fumecheng-4967 452 1 x x PROPN fumecheng-4967 452 2   PROPN fumecheng-4967 452 3   NUM fumecheng-4967 452 4   NOUN fumecheng-4967 452 5   NOUN fumecheng-4967 452 6   NOUN fumecheng-4967 452 7 . . PUNCT fumecheng-4967 453 1 it it PRON fumecheng-4967 453 2 allows allow VERB fumecheng-4967 453 3 us we PRON fumecheng-4967 453 4 to to PART fumecheng-4967 453 5 extend extend VERB fumecheng-4967 453 6 ufractal(x ufractal(x NOUN fumecheng-4967 453 7 ) ) PUNCT fumecheng-4967 453 8 infinitely infinitely ADV fumecheng-4967 453 9 each each DET fumecheng-4967 453 10 time time NOUN fumecheng-4967 453 11 , , PUNCT fumecheng-4967 453 12 when when SCONJ fumecheng-4967 453 13 x x X fumecheng-4967 453 14 - - NOUN fumecheng-4967 453 15 coordinate coordinate NOUN fumecheng-4967 453 16 runs run VERB fumecheng-4967 453 17 out out ADP fumecheng-4967 453 18 of of ADP fumecheng-4967 453 19 the the DET fumecheng-4967 453 20 array array NOUN fumecheng-4967 453 21 bonds bond NOUN fumecheng-4967 453 22 . . PUNCT fumecheng-4967 454 1 for for ADP fumecheng-4967 454 2 the the DET fumecheng-4967 454 3 numerical numerical ADJ fumecheng-4967 454 4 procedure procedure NOUN fumecheng-4967 454 5 , , PUNCT fumecheng-4967 454 6 it it PRON fumecheng-4967 454 7 means mean VERB fumecheng-4967 454 8 that that SCONJ fumecheng-4967 454 9 the the DET fumecheng-4967 454 10 modified modify VERB fumecheng-4967 454 11 tomlinson tomlinson PROPN fumecheng-4967 454 12 equation equation NOUN fumecheng-4967 454 13 2 2 NUM fumecheng-4967 454 14 2/ 2/ NUM fumecheng-4967 454 15 / / SYM fumecheng-4967 454 16 ( ( PUNCT fumecheng-4967 454 17 ) ) PUNCT fumecheng-4967 454 18 / / SYM fumecheng-4967 454 19 ( ( PUNCT fumecheng-4967 454 20 ) ) PUNCT fumecheng-4967 454 21 0fractalx 0fractalx NUM fumecheng-4967 454 22 t t NOUN fumecheng-4967 454 23 x x SYM fumecheng-4967 454 24 t t NOUN fumecheng-4967 454 25 u u X fumecheng-4967 454 26 x x X fumecheng-4967 454 27 x x X fumecheng-4967 454 28 k k NOUN fumecheng-4967 454 29 x x X fumecheng-4967 454 30 vt vt PROPN fumecheng-4967 454 31   PROPN fumecheng-4967 454 32   VERB fumecheng-4967 454 33   PROPN fumecheng-4967 454 34   PROPN fumecheng-4967 454 35   PROPN fumecheng-4967 454 36   PROPN fumecheng-4967 454 37   PUNCT fumecheng-4967 454 38   PROPN fumecheng-4967 454 39   PROPN fumecheng-4967 454 40 ( ( PUNCT fumecheng-4967 454 41 29 29 NUM fumecheng-4967 454 42 ) ) PUNCT fumecheng-4967 454 43 is be AUX fumecheng-4967 454 44 actually actually ADV fumecheng-4967 454 45 extended extend VERB fumecheng-4967 454 46 by by ADP fumecheng-4967 454 47 an an DET fumecheng-4967 454 48 additional additional ADJ fumecheng-4967 454 49 differential differential ADJ fumecheng-4967 454 50 equation equation NOUN fumecheng-4967 454 51 defining define VERB fumecheng-4967 454 52 ufractal(x)/∂x ufractal(x)/∂x NOUN fumecheng-4967 454 53 , , PUNCT fumecheng-4967 454 54 which which PRON fumecheng-4967 454 55 is be AUX fumecheng-4967 454 56 solved solve VERB fumecheng-4967 454 57 in in ADP fumecheng-4967 454 58 parallel parallel NOUN fumecheng-4967 454 59 . . PUNCT fumecheng-4967 455 1 to to PART fumecheng-4967 455 2 study study VERB fumecheng-4967 455 3 the the DET fumecheng-4967 455 4 scale scale NOUN fumecheng-4967 455 5 dependence dependence NOUN fumecheng-4967 455 6 of of ADP fumecheng-4967 455 7 friction friction NOUN fumecheng-4967 455 8 force force NOUN fumecheng-4967 455 9 , , PUNCT fumecheng-4967 455 10 one one PRON fumecheng-4967 455 11 can can AUX fumecheng-4967 455 12 generate generate VERB fumecheng-4967 455 13 a a DET fumecheng-4967 455 14 set set NOUN fumecheng-4967 455 15 of of ADP fumecheng-4967 455 16 fractal fractal ADJ fumecheng-4967 455 17 potentials potential NOUN fumecheng-4967 455 18 for for ADP fumecheng-4967 455 19 different different ADJ fumecheng-4967 455 20 number number NOUN fumecheng-4967 455 21 of of ADP fumecheng-4967 455 22 modes mode NOUN fumecheng-4967 455 23 included include VERB fumecheng-4967 455 24 ( ( PUNCT fumecheng-4967 455 25 nmodes nmode NOUN fumecheng-4967 455 26 < < X fumecheng-4967 455 27 ntot ntot NOUN fumecheng-4967 455 28 ) ) PUNCT fumecheng-4967 455 29 . . PUNCT fumecheng-4967 456 1 this this DET fumecheng-4967 456 2 number number NOUN fumecheng-4967 456 3 defines define VERB fumecheng-4967 456 4 a a DET fumecheng-4967 456 5 cutoff cutoff NOUN fumecheng-4967 456 6 wave wave NOUN fumecheng-4967 456 7 vector vector NOUN fumecheng-4967 456 8 qcutoff qcutoff NOUN fumecheng-4967 456 9 = = NOUN fumecheng-4967 456 10 δqnmodes δqnmode NOUN fumecheng-4967 456 11 and and CCONJ fumecheng-4967 456 12 the the DET fumecheng-4967 456 13 corresponding correspond VERB fumecheng-4967 456 14 cutoff cutoff NOUN fumecheng-4967 456 15 wave wave NOUN fumecheng-4967 456 16 length length NOUN fumecheng-4967 456 17 λcutoff=2π λcutoff=2π NOUN fumecheng-4967 456 18 / / SYM fumecheng-4967 456 19 qcutoff qcutoff NOUN fumecheng-4967 456 20 of of ADP fumecheng-4967 456 21 the the DET fumecheng-4967 456 22 potential potential NOUN fumecheng-4967 456 23 . . PUNCT fumecheng-4967 457 1 the the DET fumecheng-4967 457 2 potentials potential NOUN fumecheng-4967 457 3 with with ADP fumecheng-4967 457 4 different different ADJ fumecheng-4967 457 5 nmodes nmode NOUN fumecheng-4967 457 6 can can AUX fumecheng-4967 457 7 be be AUX fumecheng-4967 457 8 treated treat VERB fumecheng-4967 457 9 as as ADP fumecheng-4967 457 10 to to ADP fumecheng-4967 457 11 the the DET fumecheng-4967 457 12 same same ADJ fumecheng-4967 457 13 potential potential NOUN fumecheng-4967 457 14 " " PUNCT fumecheng-4967 457 15 measured measure VERB fumecheng-4967 457 16 " " PUNCT fumecheng-4967 457 17 with with ADP fumecheng-4967 457 18 different different ADJ fumecheng-4967 457 19 spatial spatial ADJ fumecheng-4967 457 20 resolution resolution NOUN fumecheng-4967 457 21 . . PUNCT fumecheng-4967 458 1 all all DET fumecheng-4967 458 2 space space NOUN fumecheng-4967 458 3 scales scale NOUN fumecheng-4967 458 4 larger large ADJ fumecheng-4967 458 5 then then ADV fumecheng-4967 458 6 the the DET fumecheng-4967 458 7 cutoff cutoff NOUN fumecheng-4967 458 8 wave wave NOUN fumecheng-4967 458 9 length length NOUN fumecheng-4967 458 10 are be AUX fumecheng-4967 458 11 included include VERB fumecheng-4967 458 12 in in ADP fumecheng-4967 458 13 the the DET fumecheng-4967 458 14 potential potential ADJ fumecheng-4967 458 15 ufractal(x ufractal(x NOUN fumecheng-4967 458 16 ) ) PUNCT fumecheng-4967 458 17 and and CCONJ fumecheng-4967 458 18 should should AUX fumecheng-4967 458 19 be be AUX fumecheng-4967 458 20 treated treat VERB fumecheng-4967 458 21 explicitly explicitly ADV fumecheng-4967 458 22 in in ADP fumecheng-4967 458 23 the the DET fumecheng-4967 458 24 frame frame NOUN fumecheng-4967 458 25 of of ADP fumecheng-4967 458 26 the the DET fumecheng-4967 458 27 dynamic dynamic ADJ fumecheng-4967 458 28 model model NOUN fumecheng-4967 458 29 like like ADP fumecheng-4967 458 30 eq eq PROPN fumecheng-4967 458 31 . . PUNCT fumecheng-4967 459 1 ( ( PUNCT fumecheng-4967 459 2 29 29 NUM fumecheng-4967 459 3 ) ) PUNCT fumecheng-4967 459 4 . . PUNCT fumecheng-4967 460 1 analogous analogous ADJ fumecheng-4967 460 2 procedure procedure NOUN fumecheng-4967 460 3 based base VERB fumecheng-4967 460 4 on on ADP fumecheng-4967 460 5 fourier fourier ADJ fumecheng-4967 460 6 transformation transformation NOUN fumecheng-4967 460 7 can can AUX fumecheng-4967 460 8 be be AUX fumecheng-4967 460 9 extended extend VERB fumecheng-4967 460 10 to to PART fumecheng-4967 460 11 generate generate VERB fumecheng-4967 460 12 realistic realistic ADJ fumecheng-4967 460 13 3d 3d PROPN fumecheng-4967 460 14 surface surface NOUN fumecheng-4967 460 15 covering cover VERB fumecheng-4967 460 16 2d 2d NUM fumecheng-4967 460 17 plane plane NOUN fumecheng-4967 460 18 . . PUNCT fumecheng-4967 461 1 typical typical ADJ fumecheng-4967 461 2 fractal fractal ADJ fumecheng-4967 461 3 surface surface NOUN fumecheng-4967 461 4 generated generate VERB fumecheng-4967 461 5 by by ADP fumecheng-4967 461 6 the the DET fumecheng-4967 461 7 formal formal ADJ fumecheng-4967 461 8 application application NOUN fumecheng-4967 461 9 of of ADP fumecheng-4967 461 10 fourier fourier ADJ fumecheng-4967 461 11 transformation transformation NOUN fumecheng-4967 461 12 shown show VERB fumecheng-4967 461 13 in in ADP fumecheng-4967 461 14 fig fig NOUN fumecheng-4967 461 15 . . PUNCT fumecheng-4967 462 1 10 10 NUM fumecheng-4967 462 2 by by ADP fumecheng-4967 462 3 the the DET fumecheng-4967 462 4 colormap colormap NOUN fumecheng-4967 462 5 . . PUNCT fumecheng-4967 463 1 the the DET fumecheng-4967 463 2 red red ADJ fumecheng-4967 463 3 color color NOUN fumecheng-4967 463 4 corresponds correspond VERB fumecheng-4967 463 5 to to ADP fumecheng-4967 463 6 the the DET fumecheng-4967 463 7 higher high ADJ fumecheng-4967 463 8 vertical vertical ADJ fumecheng-4967 463 9 coordinate coordinate NOUN fumecheng-4967 463 10 . . PUNCT fumecheng-4967 464 1 the the DET fumecheng-4967 464 2 second second ADJ fumecheng-4967 464 3 subplot subplot NOUN fumecheng-4967 464 4 in in ADP fumecheng-4967 464 5 the the DET fumecheng-4967 464 6 same same ADJ fumecheng-4967 464 7 figure figure NOUN fumecheng-4967 464 8 methods method NOUN fumecheng-4967 464 9 of of ADP fumecheng-4967 464 10 the the DET fumecheng-4967 464 11 pattern pattern NOUN fumecheng-4967 464 12 formation formation NOUN fumecheng-4967 464 13 in in ADP fumecheng-4967 464 14 numerical numerical ADJ fumecheng-4967 464 15 modeling modeling NOUN fumecheng-4967 464 16 of of ADP fumecheng-4967 464 17 biological biological ADJ fumecheng-4967 464 18 problems problem NOUN fumecheng-4967 464 19 237 237 NUM fumecheng-4967 464 20 presents present VERB fumecheng-4967 464 21 2d 2d NUM fumecheng-4967 464 22 cross cross NOUN fumecheng-4967 464 23 - - NOUN fumecheng-4967 464 24 section section NOUN fumecheng-4967 464 25 of of ADP fumecheng-4967 464 26 the the DET fumecheng-4967 464 27 same same ADJ fumecheng-4967 464 28 surface surface NOUN fumecheng-4967 464 29 along along ADP fumecheng-4967 464 30 one one NUM fumecheng-4967 464 31 of of ADP fumecheng-4967 464 32 the the DET fumecheng-4967 464 33 horizontal horizontal ADJ fumecheng-4967 464 34 lines line NOUN fumecheng-4967 464 35 . . PUNCT fumecheng-4967 465 1 in in ADP fumecheng-4967 465 2 some some DET fumecheng-4967 465 3 numerical numerical ADJ fumecheng-4967 465 4 experiments experiment NOUN fumecheng-4967 465 5 each each DET fumecheng-4967 465 6 such such DET fumecheng-4967 465 7 a a DET fumecheng-4967 465 8 crossection crossection NOUN fumecheng-4967 465 9 can can AUX fumecheng-4967 465 10 be be AUX fumecheng-4967 465 11 used use VERB fumecheng-4967 465 12 as as ADP fumecheng-4967 465 13 a a DET fumecheng-4967 465 14 particular particular ADJ fumecheng-4967 465 15 realization realization NOUN fumecheng-4967 465 16 to to PART fumecheng-4967 465 17 accumulate accumulate VERB fumecheng-4967 465 18 statistics statistic NOUN fumecheng-4967 465 19 . . PUNCT fumecheng-4967 466 1 fig fig NOUN fumecheng-4967 466 2 . . PUNCT fumecheng-4967 467 1 10 10 NUM fumecheng-4967 467 2 fractal fractal ADJ fumecheng-4967 467 3 3d 3d PROPN fumecheng-4967 467 4 surface surface NOUN fumecheng-4967 467 5 generated generate VERB fumecheng-4967 467 6 by by ADP fumecheng-4967 467 7 the the DET fumecheng-4967 467 8 formal formal ADJ fumecheng-4967 467 9 application application NOUN fumecheng-4967 467 10 of of ADP fumecheng-4967 467 11 fourier fourier ADJ fumecheng-4967 467 12 transformation transformation NOUN fumecheng-4967 467 13 shown show VERB fumecheng-4967 467 14 by by ADP fumecheng-4967 467 15 the the DET fumecheng-4967 467 16 colormap colormap NOUN fumecheng-4967 467 17 . . PUNCT fumecheng-4967 468 1 the the DET fumecheng-4967 468 2 red red ADJ fumecheng-4967 468 3 color color NOUN fumecheng-4967 468 4 corresponds correspond VERB fumecheng-4967 468 5 to to ADP fumecheng-4967 468 6 the the DET fumecheng-4967 468 7 higher high ADJ fumecheng-4967 468 8 vertical vertical ADJ fumecheng-4967 468 9 coordinate coordinate NOUN fumecheng-4967 468 10 . . PUNCT fumecheng-4967 469 1 the the DET fumecheng-4967 469 2 lower low ADJ fumecheng-4967 469 3 subplot subplot NOUN fumecheng-4967 469 4 presents present VERB fumecheng-4967 469 5 2d 2d NUM fumecheng-4967 469 6 cross cross NOUN fumecheng-4967 469 7 - - NOUN fumecheng-4967 469 8 section section NOUN fumecheng-4967 469 9 of of ADP fumecheng-4967 469 10 the the DET fumecheng-4967 469 11 same same ADJ fumecheng-4967 469 12 surface surface NOUN fumecheng-4967 469 13 along along ADP fumecheng-4967 469 14 one one NUM fumecheng-4967 469 15 horizontal horizontal ADJ fumecheng-4967 469 16 line line NOUN fumecheng-4967 469 17 ( ( PUNCT fumecheng-4967 469 18 the the DET fumecheng-4967 469 19 central central ADJ fumecheng-4967 469 20 line line NOUN fumecheng-4967 469 21 in in ADP fumecheng-4967 469 22 this this DET fumecheng-4967 469 23 particular particular ADJ fumecheng-4967 469 24 case case NOUN fumecheng-4967 469 25 ) ) PUNCT fumecheng-4967 469 26 . . PUNCT fumecheng-4967 470 1 both both DET fumecheng-4967 470 2 representations representation NOUN fumecheng-4967 470 3 of of ADP fumecheng-4967 470 4 the the DET fumecheng-4967 470 5 surface surface NOUN fumecheng-4967 470 6 can can AUX fumecheng-4967 470 7 be be AUX fumecheng-4967 470 8 used use VERB fumecheng-4967 470 9 in in ADP fumecheng-4967 470 10 numerical numerical ADJ fumecheng-4967 470 11 experiments experiment NOUN fumecheng-4967 470 12 depending depend VERB fumecheng-4967 470 13 on on ADP fumecheng-4967 470 14 the the DET fumecheng-4967 470 15 particular particular ADJ fumecheng-4967 470 16 problem problem NOUN fumecheng-4967 470 17 . . PUNCT fumecheng-4967 471 1 the the DET fumecheng-4967 471 2 generation generation NOUN fumecheng-4967 471 3 of of ADP fumecheng-4967 471 4 the the DET fumecheng-4967 471 5 structured structured ADJ fumecheng-4967 471 6 surfaces surface NOUN fumecheng-4967 471 7 is be AUX fumecheng-4967 471 8 not not PART fumecheng-4967 471 9 limited limit VERB fumecheng-4967 471 10 only only ADV fumecheng-4967 471 11 by by ADP fumecheng-4967 471 12 the the DET fumecheng-4967 471 13 friction friction NOUN fumecheng-4967 471 14 or or CCONJ fumecheng-4967 471 15 adhesion adhesion NOUN fumecheng-4967 471 16 problems problem NOUN fumecheng-4967 471 17 . . PUNCT fumecheng-4967 472 1 in in ADP fumecheng-4967 472 2 principle principle NOUN fumecheng-4967 472 3 , , PUNCT fumecheng-4967 472 4 surface surface NOUN fumecheng-4967 472 5 modification modification NOUN fumecheng-4967 472 6 and and CCONJ fumecheng-4967 472 7 functionalization functionalization NOUN fumecheng-4967 472 8 through through ADP fumecheng-4967 472 9 nanostructures nanostructure NOUN fumecheng-4967 472 10 is be AUX fumecheng-4967 472 11 a a DET fumecheng-4967 472 12 well well ADV fumecheng-4967 472 13 known know VERB fumecheng-4967 472 14 way way NOUN fumecheng-4967 472 15 of of ADP fumecheng-4967 472 16 producing produce VERB fumecheng-4967 472 17 desirable desirable ADJ fumecheng-4967 472 18 properties property NOUN fumecheng-4967 472 19 of of ADP fumecheng-4967 472 20 various various ADJ fumecheng-4967 472 21 materials material NOUN fumecheng-4967 472 22 . . PUNCT fumecheng-4967 473 1 however however ADV fumecheng-4967 473 2 , , PUNCT fumecheng-4967 473 3 it it PRON fumecheng-4967 473 4 is be AUX fumecheng-4967 473 5 not not PART fumecheng-4967 473 6 an an DET fumecheng-4967 473 7 innovation innovation NOUN fumecheng-4967 473 8 since since SCONJ fumecheng-4967 473 9 it it PRON fumecheng-4967 473 10 was be AUX fumecheng-4967 473 11 employed employ VERB fumecheng-4967 473 12 by by ADP fumecheng-4967 473 13 nature nature NOUN fumecheng-4967 473 14 a a DET fumecheng-4967 473 15 long long ADJ fumecheng-4967 473 16 time time NOUN fumecheng-4967 473 17 before before ADV fumecheng-4967 473 18 . . PUNCT fumecheng-4967 474 1 7 7 X fumecheng-4967 474 2 . . X fumecheng-4967 474 3 combination combination NOUN fumecheng-4967 474 4 of of ADP fumecheng-4967 474 5 discrete discrete ADJ fumecheng-4967 474 6 and and CCONJ fumecheng-4967 474 7 continuous continuous ADJ fumecheng-4967 474 8 techniques technique NOUN fumecheng-4967 474 9 the the DET fumecheng-4967 474 10 main main ADJ fumecheng-4967 474 11 idea idea NOUN fumecheng-4967 474 12 of of ADP fumecheng-4967 474 13 the the DET fumecheng-4967 474 14 simplification simplification NOUN fumecheng-4967 474 15 using use VERB fumecheng-4967 474 16 a a DET fumecheng-4967 474 17 combination combination NOUN fumecheng-4967 474 18 of of ADP fumecheng-4967 474 19 two two NUM fumecheng-4967 474 20 techniques technique NOUN fumecheng-4967 474 21 is be AUX fumecheng-4967 474 22 to to PART fumecheng-4967 474 23 substitute substitute VERB fumecheng-4967 474 24 an an DET fumecheng-4967 474 25 original original ADJ fumecheng-4967 474 26 continuous continuous ADJ fumecheng-4967 474 27 problem problem NOUN fumecheng-4967 474 28 by by ADP fumecheng-4967 474 29 its its PRON fumecheng-4967 474 30 combination combination NOUN fumecheng-4967 474 31 with with ADP fumecheng-4967 474 32 some some DET fumecheng-4967 474 33 preliminary preliminary ADJ fumecheng-4967 474 34 applied apply VERB fumecheng-4967 474 35 discrete discrete ADJ fumecheng-4967 474 36 approach approach NOUN fumecheng-4967 474 37 ( ( PUNCT fumecheng-4967 474 38 which which PRON fumecheng-4967 474 39 is be AUX fumecheng-4967 474 40 used use VERB fumecheng-4967 474 41 to to PART fumecheng-4967 474 42 get get VERB fumecheng-4967 474 43 more more ADV fumecheng-4967 474 44 or or CCONJ fumecheng-4967 474 45 less less ADV fumecheng-4967 474 46 final final ADJ fumecheng-4967 474 47 or or CCONJ fumecheng-4967 474 48 , , PUNCT fumecheng-4967 474 49 at at ADP fumecheng-4967 474 50 least least ADJ fumecheng-4967 474 51 , , PUNCT fumecheng-4967 474 52 almost almost ADV fumecheng-4967 474 53 stationary stationary ADJ fumecheng-4967 474 54 ) ) PUNCT fumecheng-4967 474 55 configuration configuration NOUN fumecheng-4967 474 56 and and CCONJ fumecheng-4967 474 57 further further ADJ fumecheng-4967 474 58 continuous continuous ADJ fumecheng-4967 474 59 density density NOUN fumecheng-4967 474 60 calculation calculation NOUN fumecheng-4967 474 61 . . PUNCT fumecheng-4967 475 1 combination combination NOUN fumecheng-4967 475 2 of of ADP fumecheng-4967 475 3 the the DET fumecheng-4967 475 4 discrete discrete ADJ fumecheng-4967 475 5 and and CCONJ fumecheng-4967 475 6 continuous continuous ADJ fumecheng-4967 475 7 approaches approach NOUN fumecheng-4967 475 8 was be AUX fumecheng-4967 475 9 applied apply VERB fumecheng-4967 475 10 to to ADP fumecheng-4967 475 11 many many ADJ fumecheng-4967 475 12 different different ADJ fumecheng-4967 475 13 chemical chemical NOUN fumecheng-4967 475 14 and and CCONJ fumecheng-4967 475 15 physical physical ADJ fumecheng-4967 475 16 systems system NOUN fumecheng-4967 475 17 ( ( PUNCT fumecheng-4967 475 18 including include VERB fumecheng-4967 475 19 such such ADJ fumecheng-4967 475 20 underlying underlie VERB fumecheng-4967 475 21 processes process NOUN fumecheng-4967 475 22 in in ADP fumecheng-4967 475 23 biological biological ADJ fumecheng-4967 475 24 systems system NOUN fumecheng-4967 475 25 ) ) PUNCT fumecheng-4967 476 1 [ [ X fumecheng-4967 476 2 13 13 NUM fumecheng-4967 476 3 ] ] PUNCT fumecheng-4967 476 4 . . PUNCT fumecheng-4967 477 1 for for ADP fumecheng-4967 477 2 example example NOUN fumecheng-4967 477 3 , , PUNCT fumecheng-4967 477 4 it it PRON fumecheng-4967 477 5 can can AUX fumecheng-4967 477 6 be be AUX fumecheng-4967 477 7 applied apply VERB fumecheng-4967 477 8 to to PART fumecheng-4967 477 9 study study VERB fumecheng-4967 477 10 of of ADP fumecheng-4967 477 11 superconducting superconducte VERB fumecheng-4967 477 12 or or CCONJ fumecheng-4967 477 13 magnetic magnetic ADJ fumecheng-4967 477 14 ordering ordering NOUN fumecheng-4967 477 15 in in ADP fumecheng-4967 477 16 quasi quasi ADJ fumecheng-4967 477 17 2 2 NUM fumecheng-4967 477 18 - - PUNCT fumecheng-4967 477 19 dimensional dimensional ADJ fumecheng-4967 477 20 systems system NOUN fumecheng-4967 477 21 , , PUNCT fumecheng-4967 477 22 or or CCONJ fumecheng-4967 477 23 to to PART fumecheng-4967 477 24 study study VERB fumecheng-4967 477 25 growth growth NOUN fumecheng-4967 477 26 of of ADP fumecheng-4967 477 27 surface surface NOUN fumecheng-4967 477 28 structures structure NOUN fumecheng-4967 477 29 , , PUNCT fumecheng-4967 477 30 and and CCONJ fumecheng-4967 477 31 so so ADV fumecheng-4967 477 32 on on ADV fumecheng-4967 477 33 . . PUNCT fumecheng-4967 478 1 in in ADP fumecheng-4967 478 2 all all DET fumecheng-4967 478 3 such such ADJ fumecheng-4967 478 4 cases case NOUN fumecheng-4967 478 5 , , PUNCT fumecheng-4967 478 6 the the DET fumecheng-4967 478 7 real real ADJ fumecheng-4967 478 8 process process NOUN fumecheng-4967 478 9 involves involve VERB fumecheng-4967 478 10 an an DET fumecheng-4967 478 11 interaction interaction NOUN fumecheng-4967 478 12 of of ADP fumecheng-4967 478 13 many many ADJ fumecheng-4967 478 14 spatially spatially ADV fumecheng-4967 478 15 distributed distribute VERB fumecheng-4967 478 16 densities density NOUN fumecheng-4967 478 17 and and CCONJ fumecheng-4967 478 18 its its PRON fumecheng-4967 478 19 direct direct ADJ fumecheng-4967 478 20 simulation simulation NOUN fumecheng-4967 478 21 can can AUX fumecheng-4967 478 22 cause cause VERB fumecheng-4967 478 23 extremely extremely ADV fumecheng-4967 478 24 time time NOUN fumecheng-4967 478 25 consuming consume VERB fumecheng-4967 478 26 calculations calculation NOUN fumecheng-4967 478 27 . . PUNCT fumecheng-4967 479 1 a a DET fumecheng-4967 479 2 famous famous ADJ fumecheng-4967 479 3 example example NOUN fumecheng-4967 479 4 of of ADP fumecheng-4967 479 5 such such DET fumecheng-4967 479 6 an an DET fumecheng-4967 479 7 approach approach NOUN fumecheng-4967 479 8 is be AUX fumecheng-4967 479 9 the the DET fumecheng-4967 479 10 study study NOUN fumecheng-4967 479 11 of of ADP fumecheng-4967 479 12 topological topological ADJ fumecheng-4967 479 13 phase phase NOUN fumecheng-4967 479 14 transition transition NOUN fumecheng-4967 479 15 in in ADP fumecheng-4967 479 16 quasi quasi ADJ fumecheng-4967 479 17 2 2 NUM fumecheng-4967 479 18 - - ADJ fumecheng-4967 479 19 dimensional dimensional ADJ fumecheng-4967 479 20 superconducting superconducting ADJ fumecheng-4967 479 21 systems system NOUN fumecheng-4967 479 22 , , PUNCT fumecheng-4967 479 23 mentioned mention VERB fumecheng-4967 479 24 above above ADV fumecheng-4967 479 25 , , PUNCT fumecheng-4967 479 26 where where SCONJ fumecheng-4967 479 27 extremely extremely ADV fumecheng-4967 479 28 complex complex ADJ fumecheng-4967 479 29 238 238 NUM fumecheng-4967 479 30 a.e a.e PROPN fumecheng-4967 479 31 . . PROPN fumecheng-4967 479 32 filippov filippov PROPN fumecheng-4967 479 33 , , PUNCT fumecheng-4967 479 34 s.n s.n PROPN fumecheng-4967 479 35 . . PROPN fumecheng-4967 479 36 gorb gorb PROPN fumecheng-4967 479 37 evolution evolution NOUN fumecheng-4967 479 38 of of ADP fumecheng-4967 479 39 the the DET fumecheng-4967 479 40 superconducting superconducte VERB fumecheng-4967 479 41 vortices vortex NOUN fumecheng-4967 479 42 was be AUX fumecheng-4967 479 43 substituted substitute VERB fumecheng-4967 479 44 to to ADP fumecheng-4967 479 45 some some DET fumecheng-4967 479 46 extend extend NOUN fumecheng-4967 479 47 by by ADP fumecheng-4967 479 48 a a DET fumecheng-4967 479 49 motion motion NOUN fumecheng-4967 479 50 of of ADP fumecheng-4967 479 51 “ " PUNCT fumecheng-4967 479 52 charged charge VERB fumecheng-4967 479 53 particles particle NOUN fumecheng-4967 479 54 ” " PUNCT fumecheng-4967 479 55 [ [ X fumecheng-4967 479 56 14 14 NUM fumecheng-4967 479 57 ] ] PUNCT fumecheng-4967 479 58 . . PUNCT fumecheng-4967 480 1 this this DET fumecheng-4967 480 2 approach approach NOUN fumecheng-4967 480 3 was be AUX fumecheng-4967 480 4 found find VERB fumecheng-4967 480 5 to to PART fumecheng-4967 480 6 be be AUX fumecheng-4967 480 7 extremely extremely ADV fumecheng-4967 480 8 fruitful fruitful ADJ fumecheng-4967 480 9 and and CCONJ fumecheng-4967 480 10 was be AUX fumecheng-4967 480 11 even even ADV fumecheng-4967 480 12 awarded award VERB fumecheng-4967 480 13 by by ADP fumecheng-4967 480 14 the the DET fumecheng-4967 480 15 nobel nobel PROPN fumecheng-4967 480 16 prize prize PROPN fumecheng-4967 480 17 in in ADP fumecheng-4967 480 18 2016 2016 NUM fumecheng-4967 480 19 . . PUNCT fumecheng-4967 481 1 one one NUM fumecheng-4967 481 2 important important ADJ fumecheng-4967 481 3 example example NOUN fumecheng-4967 481 4 is be AUX fumecheng-4967 481 5 the the DET fumecheng-4967 481 6 surface surface NOUN fumecheng-4967 481 7 nanostructure nanostructure NOUN fumecheng-4967 481 8 in in ADP fumecheng-4967 481 9 the the DET fumecheng-4967 481 10 snakeskin snakeskin NOUN fumecheng-4967 481 11 that that PRON fumecheng-4967 481 12 is be AUX fumecheng-4967 481 13 supposed suppose VERB fumecheng-4967 481 14 to to PART fumecheng-4967 481 15 reduce reduce VERB fumecheng-4967 481 16 both both PRON fumecheng-4967 481 17 abrasion abrasion NOUN fumecheng-4967 481 18 and and CCONJ fumecheng-4967 481 19 friction friction NOUN fumecheng-4967 481 20 , , PUNCT fumecheng-4967 481 21 as as SCONJ fumecheng-4967 481 22 it it PRON fumecheng-4967 481 23 has have AUX fumecheng-4967 481 24 been be AUX fumecheng-4967 481 25 previously previously ADV fumecheng-4967 481 26 shown show VERB fumecheng-4967 481 27 for for ADP fumecheng-4967 481 28 similar similar ADJ fumecheng-4967 481 29 artificial artificial ADJ fumecheng-4967 481 30 nanostructures nanostructure NOUN fumecheng-4967 481 31 [ [ X fumecheng-4967 481 32 15 15 NUM fumecheng-4967 481 33 ] ] PUNCT fumecheng-4967 481 34 . . PUNCT fumecheng-4967 482 1 on on ADP fumecheng-4967 482 2 the the DET fumecheng-4967 482 3 ventral ventral ADJ fumecheng-4967 482 4 surface surface NOUN fumecheng-4967 482 5 of of ADP fumecheng-4967 482 6 snakes snake NOUN fumecheng-4967 482 7 , , PUNCT fumecheng-4967 482 8 this this DET fumecheng-4967 482 9 nanostructure nanostructure NOUN fumecheng-4967 482 10 is be AUX fumecheng-4967 482 11 typically typically ADV fumecheng-4967 482 12 constituted constitute VERB fumecheng-4967 482 13 by by ADP fumecheng-4967 482 14 arrays array NOUN fumecheng-4967 482 15 of of ADP fumecheng-4967 482 16 the the DET fumecheng-4967 482 17 nano nano NOUN fumecheng-4967 482 18 - - PUNCT fumecheng-4967 482 19 dimples dimple NOUN fumecheng-4967 482 20 . . PUNCT fumecheng-4967 483 1 one one NUM fumecheng-4967 483 2 of of ADP fumecheng-4967 483 3 the the DET fumecheng-4967 483 4 most most ADV fumecheng-4967 483 5 widely widely ADV fumecheng-4967 483 6 spread spread VERB fumecheng-4967 483 7 structural structural ADJ fumecheng-4967 483 8 arrangement arrangement NOUN fumecheng-4967 483 9 type type NOUN fumecheng-4967 483 10 in in ADP fumecheng-4967 483 11 biological biological ADJ fumecheng-4967 483 12 systems system NOUN fumecheng-4967 483 13 is be AUX fumecheng-4967 483 14 the the DET fumecheng-4967 483 15 hexagonal hexagonal ADJ fumecheng-4967 483 16 arrangement arrangement NOUN fumecheng-4967 483 17 , , PUNCT fumecheng-4967 483 18 which which PRON fumecheng-4967 483 19 provides provide VERB fumecheng-4967 483 20 the the DET fumecheng-4967 483 21 highest high ADJ fumecheng-4967 483 22 packaging packaging NOUN fumecheng-4967 483 23 of of ADP fumecheng-4967 483 24 the the DET fumecheng-4967 483 25 structure structure NOUN fumecheng-4967 483 26 and and CCONJ fumecheng-4967 483 27 the the DET fumecheng-4967 483 28 highest high ADJ fumecheng-4967 483 29 structure structure NOUN fumecheng-4967 483 30 density density NOUN fumecheng-4967 483 31 . . PUNCT fumecheng-4967 484 1 visually visually ADV fumecheng-4967 484 2 arrays array VERB fumecheng-4967 484 3 of of ADP fumecheng-4967 484 4 nano nano NOUN fumecheng-4967 484 5 - - PUNCT fumecheng-4967 484 6 dimples dimple NOUN fumecheng-4967 484 7 remind remind VERB fumecheng-4967 484 8 such such ADJ fumecheng-4967 484 9 structure structure NOUN fumecheng-4967 484 10 . . PUNCT fumecheng-4967 485 1 fig fig NOUN fumecheng-4967 485 2 . . PUNCT fumecheng-4967 486 1 11 11 NUM fumecheng-4967 486 2 scanning scan VERB fumecheng-4967 486 3 electron electron NOUN fumecheng-4967 486 4 microscopy microscopy NOUN fumecheng-4967 486 5 image image NOUN fumecheng-4967 486 6 of of ADP fumecheng-4967 486 7 the the DET fumecheng-4967 486 8 tail tail NOUN fumecheng-4967 486 9 ventral ventral ADJ fumecheng-4967 486 10 scale scale NOUN fumecheng-4967 486 11 in in ADP fumecheng-4967 486 12 the the DET fumecheng-4967 486 13 snake snake NOUN fumecheng-4967 486 14 morelia morelia PROPN fumecheng-4967 486 15 viridis viridis PROPN fumecheng-4967 486 16 . . PUNCT fumecheng-4967 487 1 the the DET fumecheng-4967 487 2 black black ADJ fumecheng-4967 487 3 shadowed shadow VERB fumecheng-4967 487 4 gray gray ADJ fumecheng-4967 487 5 circle circle NOUN fumecheng-4967 487 6 marks mark VERB fumecheng-4967 487 7 a a DET fumecheng-4967 487 8 typical typical ADJ fumecheng-4967 487 9 hexagonal hexagonal ADJ fumecheng-4967 487 10 arrangement arrangement NOUN fumecheng-4967 487 11 of of ADP fumecheng-4967 487 12 dimples dimple NOUN fumecheng-4967 487 13 , , PUNCT fumecheng-4967 487 14 whereas whereas SCONJ fumecheng-4967 487 15 both both CCONJ fumecheng-4967 487 16 white white ADJ fumecheng-4967 487 17 and and CCONJ fumecheng-4967 487 18 black black ADJ fumecheng-4967 487 19 circles circle NOUN fumecheng-4967 487 20 mark mark VERB fumecheng-4967 487 21 fiveand fiveand PROPN fumecheng-4967 487 22 sevenfold sevenfold ADJ fumecheng-4967 487 23 symmetrical symmetrical ADJ fumecheng-4967 487 24 arrangement arrangement NOUN fumecheng-4967 487 25 of of ADP fumecheng-4967 487 26 dimples dimple NOUN fumecheng-4967 487 27 , , PUNCT fumecheng-4967 487 28 respectively respectively ADV fumecheng-4967 487 29 . . PUNCT fumecheng-4967 488 1 however however ADV fumecheng-4967 488 2 , , PUNCT fumecheng-4967 488 3 it it PRON fumecheng-4967 488 4 is be AUX fumecheng-4967 488 5 well well ADV fumecheng-4967 488 6 known know VERB fumecheng-4967 488 7 that that SCONJ fumecheng-4967 488 8 there there PRON fumecheng-4967 488 9 is be VERB fumecheng-4967 488 10 no no DET fumecheng-4967 488 11 ideal ideal ADJ fumecheng-4967 488 12 arrangement arrangement NOUN fumecheng-4967 488 13 in in ADP fumecheng-4967 488 14 biological biological ADJ fumecheng-4967 488 15 systems system NOUN fumecheng-4967 488 16 . . PUNCT fumecheng-4967 489 1 previously previously ADV fumecheng-4967 489 2 , , PUNCT fumecheng-4967 489 3 we we PRON fumecheng-4967 489 4 performed perform VERB fumecheng-4967 489 5 the the DET fumecheng-4967 489 6 analysis analysis NOUN fumecheng-4967 489 7 of of ADP fumecheng-4967 489 8 the the DET fumecheng-4967 489 9 arrangement arrangement NOUN fumecheng-4967 489 10 imperfections imperfection NOUN fumecheng-4967 489 11 ( ( PUNCT fumecheng-4967 489 12 disorder disorder NOUN fumecheng-4967 489 13 ) ) PUNCT fumecheng-4967 489 14 using use VERB fumecheng-4967 489 15 correlation correlation NOUN fumecheng-4967 489 16 analysis analysis NOUN fumecheng-4967 489 17 in in ADP fumecheng-4967 489 18 a a DET fumecheng-4967 489 19 way way NOUN fumecheng-4967 489 20 similar similar ADJ fumecheng-4967 489 21 to to ADP fumecheng-4967 489 22 the the PRON fumecheng-4967 489 23 previously previously ADV fumecheng-4967 489 24 used use VERB fumecheng-4967 489 25 for for ADP fumecheng-4967 489 26 other other ADJ fumecheng-4967 489 27 systems system NOUN fumecheng-4967 489 28 appearing appear VERB fumecheng-4967 489 29 as as ADP fumecheng-4967 489 30 frozen frozen ADJ fumecheng-4967 489 31 kinetics kinetic NOUN fumecheng-4967 489 32 [ [ X fumecheng-4967 489 33 6 6 NUM fumecheng-4967 489 34 ] ] PUNCT fumecheng-4967 489 35 . . PUNCT fumecheng-4967 490 1 correlation correlation NOUN fumecheng-4967 490 2 analysis analysis NOUN fumecheng-4967 490 3 is be AUX fumecheng-4967 490 4 expected expect VERB fumecheng-4967 490 5 to to PART fumecheng-4967 490 6 quantitatively quantitatively ADV fumecheng-4967 490 7 reveal reveal VERB fumecheng-4967 490 8 the the DET fumecheng-4967 490 9 difference difference NOUN fumecheng-4967 490 10 in in ADP fumecheng-4967 490 11 hexagonal hexagonal ADJ fumecheng-4967 490 12 nanostructure nanostructure NOUN fumecheng-4967 490 13 arrangements arrangement NOUN fumecheng-4967 490 14 , , PUNCT fumecheng-4967 490 15 and and CCONJ fumecheng-4967 490 16 in in ADP fumecheng-4967 490 17 the the DET fumecheng-4967 490 18 snakeskin snakeskin NOUN fumecheng-4967 490 19 . . PUNCT fumecheng-4967 491 1 we we PRON fumecheng-4967 491 2 will will AUX fumecheng-4967 491 3 also also ADV fumecheng-4967 491 4 suggest suggest VERB fumecheng-4967 491 5 here here ADV fumecheng-4967 491 6 a a DET fumecheng-4967 491 7 simple simple ADJ fumecheng-4967 491 8 mathematical mathematical ADJ fumecheng-4967 491 9 model model NOUN fumecheng-4967 491 10 that that PRON fumecheng-4967 491 11 helped help VERB fumecheng-4967 491 12 to to PART fumecheng-4967 491 13 explain explain VERB fumecheng-4967 491 14 the the DET fumecheng-4967 491 15 difference difference NOUN fumecheng-4967 491 16 in in ADP fumecheng-4967 491 17 these these DET fumecheng-4967 491 18 correlation correlation NOUN fumecheng-4967 491 19 functions function NOUN fumecheng-4967 491 20 and and CCONJ fumecheng-4967 491 21 obtain obtain VERB fumecheng-4967 491 22 some some DET fumecheng-4967 491 23 hints hint NOUN fumecheng-4967 491 24 related relate VERB fumecheng-4967 491 25 to to ADP fumecheng-4967 491 26 the the DET fumecheng-4967 491 27 mechanisms mechanism NOUN fumecheng-4967 491 28 of of ADP fumecheng-4967 491 29 formation formation NOUN fumecheng-4967 491 30 of of ADP fumecheng-4967 491 31 nanostructural nanostructural ADJ fumecheng-4967 491 32 patterns pattern NOUN fumecheng-4967 491 33 in in ADP fumecheng-4967 491 34 biological biological ADJ fumecheng-4967 491 35 systems system NOUN fumecheng-4967 491 36 additional additional ADJ fumecheng-4967 491 37 to to ADP fumecheng-4967 491 38 the the DET fumecheng-4967 491 39 previously previously ADV fumecheng-4967 491 40 discussed discuss VERB fumecheng-4967 491 41 ones one NOUN fumecheng-4967 491 42 . . PUNCT fumecheng-4967 492 1 in in ADP fumecheng-4967 492 2 this this DET fumecheng-4967 492 3 model model NOUN fumecheng-4967 492 4 , , PUNCT fumecheng-4967 492 5 the the DET fumecheng-4967 492 6 structure structure NOUN fumecheng-4967 492 7 with with ADP fumecheng-4967 492 8 the the DET fumecheng-4967 492 9 structure structure NOUN fumecheng-4967 492 10 arrangement arrangement NOUN fumecheng-4967 492 11 similar similar ADJ fumecheng-4967 492 12 to to ADP fumecheng-4967 492 13 that that PRON fumecheng-4967 492 14 found find VERB fumecheng-4967 492 15 in in ADP fumecheng-4967 492 16 snakeskin snakeskin NOUN fumecheng-4967 492 17 appears appear VERB fumecheng-4967 492 18 due due ADJ fumecheng-4967 492 19 to to ADP fumecheng-4967 492 20 the the DET fumecheng-4967 492 21 " " PUNCT fumecheng-4967 492 22 freezing freezing NOUN fumecheng-4967 492 23 " " PUNCT fumecheng-4967 492 24 of of ADP fumecheng-4967 492 25 an an DET fumecheng-4967 492 26 overdamped overdampe VERB fumecheng-4967 492 27 relaxation relaxation NOUN fumecheng-4967 492 28 . . PUNCT fumecheng-4967 493 1 it it PRON fumecheng-4967 493 2 is be AUX fumecheng-4967 493 3 caused cause VERB fumecheng-4967 493 4 by by ADP fumecheng-4967 493 5 a a DET fumecheng-4967 493 6 weak weak ADJ fumecheng-4967 493 7 repulsion repulsion NOUN fumecheng-4967 493 8 between between ADP fumecheng-4967 493 9 the the DET fumecheng-4967 493 10 structures structure NOUN fumecheng-4967 493 11 from from ADP fumecheng-4967 493 12 an an DET fumecheng-4967 493 13 initially initially ADV fumecheng-4967 493 14 random random ADJ fumecheng-4967 493 15 distribution distribution NOUN fumecheng-4967 493 16 . . PUNCT fumecheng-4967 494 1 further far ADV fumecheng-4967 494 2 , , PUNCT fumecheng-4967 494 3 analogous analogous ADJ fumecheng-4967 494 4 methods method NOUN fumecheng-4967 494 5 of of ADP fumecheng-4967 494 6 the the DET fumecheng-4967 494 7 pattern pattern NOUN fumecheng-4967 494 8 formation formation NOUN fumecheng-4967 494 9 in in ADP fumecheng-4967 494 10 numerical numerical ADJ fumecheng-4967 494 11 modeling modeling NOUN fumecheng-4967 494 12 of of ADP fumecheng-4967 494 13 biological biological ADJ fumecheng-4967 494 14 problems problem NOUN fumecheng-4967 494 15 239 239 NUM fumecheng-4967 494 16 correlation correlation NOUN fumecheng-4967 494 17 analysis analysis NOUN fumecheng-4967 494 18 is be AUX fumecheng-4967 494 19 applied apply VERB fumecheng-4967 494 20 to to ADP fumecheng-4967 494 21 this this DET fumecheng-4967 494 22 model model NOUN fumecheng-4967 494 23 and and CCONJ fumecheng-4967 494 24 its‟ its‟ ADJ fumecheng-4967 494 25 results result NOUN fumecheng-4967 494 26 are be AUX fumecheng-4967 494 27 compared compare VERB fumecheng-4967 494 28 with with ADP fumecheng-4967 494 29 the the DET fumecheng-4967 494 30 results result NOUN fumecheng-4967 494 31 of of ADP fumecheng-4967 494 32 the the DET fumecheng-4967 494 33 correlation correlation NOUN fumecheng-4967 494 34 analysis analysis NOUN fumecheng-4967 494 35 of of ADP fumecheng-4967 494 36 the the DET fumecheng-4967 494 37 real real ADJ fumecheng-4967 494 38 nanostructure nanostructure NOUN fumecheng-4967 494 39 arrangement arrangement NOUN fumecheng-4967 494 40 in in ADP fumecheng-4967 494 41 the the DET fumecheng-4967 494 42 snakeskin snakeskin NOUN fumecheng-4967 494 43 . . PUNCT fumecheng-4967 495 1 power power NOUN fumecheng-4967 495 2 spectrum spectrum NOUN fumecheng-4967 495 3 and and CCONJ fumecheng-4967 495 4 distribution distribution NOUN fumecheng-4967 495 5 of of ADP fumecheng-4967 495 6 distances distance NOUN fumecheng-4967 495 7 between between ADP fumecheng-4967 495 8 the the DET fumecheng-4967 495 9 nearest near ADJ fumecheng-4967 495 10 neighbors neighbor NOUN fumecheng-4967 495 11 can can AUX fumecheng-4967 495 12 be be AUX fumecheng-4967 495 13 calculated calculate VERB fumecheng-4967 495 14 for for ADP fumecheng-4967 495 15 the the DET fumecheng-4967 495 16 snakeskin snakeskin NOUN fumecheng-4967 495 17 in in ADP fumecheng-4967 495 18 the the DET fumecheng-4967 495 19 same same ADJ fumecheng-4967 495 20 manner manner NOUN fumecheng-4967 495 21 as as ADP fumecheng-4967 495 22 for for ADP fumecheng-4967 495 23 any any DET fumecheng-4967 495 24 crystal crystal NOUN fumecheng-4967 495 25 microscopic microscopic ADJ fumecheng-4967 495 26 structure structure NOUN fumecheng-4967 495 27 . . PUNCT fumecheng-4967 496 1 it it PRON fumecheng-4967 496 2 was be AUX fumecheng-4967 496 3 done do VERB fumecheng-4967 496 4 and and CCONJ fumecheng-4967 496 5 found find VERB fumecheng-4967 496 6 that that SCONJ fumecheng-4967 496 7 , , PUNCT fumecheng-4967 496 8 despite despite SCONJ fumecheng-4967 496 9 of of ADP fumecheng-4967 496 10 the the DET fumecheng-4967 496 11 structure structure NOUN fumecheng-4967 496 12 in in ADP fumecheng-4967 496 13 the the DET fumecheng-4967 496 14 snakeskin snakeskin NOUN fumecheng-4967 496 15 looks look VERB fumecheng-4967 496 16 like like SCONJ fumecheng-4967 496 17 hexagonally hexagonally ADV fumecheng-4967 496 18 ordered order VERB fumecheng-4967 496 19 : : PUNCT fumecheng-4967 496 20 the the DET fumecheng-4967 496 21 power power NOUN fumecheng-4967 496 22 spectrum spectrum NOUN fumecheng-4967 496 23 here here ADV fumecheng-4967 496 24 does do AUX fumecheng-4967 496 25 not not PART fumecheng-4967 496 26 demonstrate demonstrate VERB fumecheng-4967 496 27 pronounced pronounced ADJ fumecheng-4967 496 28 peaks peak NOUN fumecheng-4967 496 29 , , PUNCT fumecheng-4967 496 30 even even ADV fumecheng-4967 496 31 in in ADP fumecheng-4967 496 32 the the DET fumecheng-4967 496 33 first first ADJ fumecheng-4967 496 34 ring ring NOUN fumecheng-4967 496 35 . . PUNCT fumecheng-4967 497 1 it it PRON fumecheng-4967 497 2 is be AUX fumecheng-4967 497 3 because because SCONJ fumecheng-4967 497 4 of of ADP fumecheng-4967 497 5 the the DET fumecheng-4967 497 6 absence absence NOUN fumecheng-4967 497 7 of of ADP fumecheng-4967 497 8 highly highly ADV fumecheng-4967 497 9 - - PUNCT fumecheng-4967 497 10 oriented orient VERB fumecheng-4967 497 11 domains domain NOUN fumecheng-4967 497 12 with with ADP fumecheng-4967 497 13 a a DET fumecheng-4967 497 14 prominent prominent ADJ fumecheng-4967 497 15 arrangement arrangement NOUN fumecheng-4967 497 16 . . PUNCT fumecheng-4967 498 1 at at ADP fumecheng-4967 498 2 the the DET fumecheng-4967 498 3 same same ADJ fumecheng-4967 498 4 time time NOUN fumecheng-4967 498 5 , , PUNCT fumecheng-4967 498 6 there there PRON fumecheng-4967 498 7 is be VERB fumecheng-4967 498 8 characteristic characteristic ADJ fumecheng-4967 498 9 distance distance NOUN fumecheng-4967 498 10 between between ADP fumecheng-4967 498 11 the the DET fumecheng-4967 498 12 nearest near ADJ fumecheng-4967 498 13 neighbors neighbor NOUN fumecheng-4967 498 14 , , PUNCT fumecheng-4967 498 15 around around ADV fumecheng-4967 498 16 0.4 0.4 NUM fumecheng-4967 498 17 µm µm NOUN fumecheng-4967 498 18 . . PUNCT fumecheng-4967 499 1 because because SCONJ fumecheng-4967 499 2 the the DET fumecheng-4967 499 3 first first ADJ fumecheng-4967 499 4 ring ring NOUN fumecheng-4967 499 5 in in ADP fumecheng-4967 499 6 the the DET fumecheng-4967 499 7 correlation correlation NOUN fumecheng-4967 499 8 function function NOUN fumecheng-4967 499 9 , , PUNCT fumecheng-4967 499 10 matching match VERB fumecheng-4967 499 11 the the DET fumecheng-4967 499 12 maximum maximum ADJ fumecheng-4967 499 13 probability probability NOUN fumecheng-4967 499 14 of of ADP fumecheng-4967 499 15 the the DET fumecheng-4967 499 16 distances distance NOUN fumecheng-4967 499 17 , , PUNCT fumecheng-4967 499 18 is be AUX fumecheng-4967 499 19 well well ADV fumecheng-4967 499 20 pronounced pronounce VERB fumecheng-4967 499 21 . . PUNCT fumecheng-4967 500 1 it it PRON fumecheng-4967 500 2 can can AUX fumecheng-4967 500 3 be be AUX fumecheng-4967 500 4 assumed assume VERB fumecheng-4967 500 5 that that SCONJ fumecheng-4967 500 6 isotropy isotropy VERB fumecheng-4967 500 7 of of ADP fumecheng-4967 500 8 the the DET fumecheng-4967 500 9 correlation correlation NOUN fumecheng-4967 500 10 function function NOUN fumecheng-4967 500 11 , , PUNCT fumecheng-4967 500 12 which which PRON fumecheng-4967 500 13 does do AUX fumecheng-4967 500 14 not not PART fumecheng-4967 500 15 show show VERB fumecheng-4967 500 16 specific specific ADJ fumecheng-4967 500 17 directions direction NOUN fumecheng-4967 500 18 in in ADP fumecheng-4967 500 19 dimple dimple ADJ fumecheng-4967 500 20 arrangement arrangement NOUN fumecheng-4967 500 21 in in ADP fumecheng-4967 500 22 the the DET fumecheng-4967 500 23 snakeskin snakeskin NOUN fumecheng-4967 500 24 , , PUNCT fumecheng-4967 500 25 is be AUX fumecheng-4967 500 26 important important ADJ fumecheng-4967 500 27 for for ADP fumecheng-4967 500 28 e.g. e.g. ADV fumecheng-4967 500 29 maintaining maintain VERB fumecheng-4967 500 30 isotropic isotropic ADJ fumecheng-4967 500 31 tribological tribological ADJ fumecheng-4967 500 32 properties property NOUN fumecheng-4967 500 33 . . PUNCT fumecheng-4967 501 1 the the DET fumecheng-4967 501 2 presence presence NOUN fumecheng-4967 501 3 of of ADP fumecheng-4967 501 4 a a DET fumecheng-4967 501 5 preferential preferential ADJ fumecheng-4967 501 6 direction direction NOUN fumecheng-4967 501 7 implies imply VERB fumecheng-4967 501 8 a a DET fumecheng-4967 501 9 stress stress NOUN fumecheng-4967 501 10 enhancement enhancement NOUN fumecheng-4967 501 11 in in ADP fumecheng-4967 501 12 some some DET fumecheng-4967 501 13 direction direction NOUN fumecheng-4967 501 14 , , PUNCT fumecheng-4967 501 15 and and CCONJ fumecheng-4967 501 16 , , PUNCT fumecheng-4967 501 17 therefore therefore ADV fumecheng-4967 501 18 , , PUNCT fumecheng-4967 501 19 material material ADJ fumecheng-4967 501 20 failure failure NOUN fumecheng-4967 501 21 facilitation facilitation NOUN fumecheng-4967 501 22 , , PUNCT fumecheng-4967 501 23 as as ADV fumecheng-4967 501 24 well well ADV fumecheng-4967 501 25 as as ADP fumecheng-4967 501 26 stronger strong ADJ fumecheng-4967 501 27 abrasion abrasion NOUN fumecheng-4967 501 28 . . PUNCT fumecheng-4967 502 1 standard standard ADJ fumecheng-4967 502 2 approach approach NOUN fumecheng-4967 502 3 to to ADP fumecheng-4967 502 4 weakly weakly ADJ fumecheng-4967 502 5 disordered disordered ADJ fumecheng-4967 502 6 hexagonal hexagonal ADJ fumecheng-4967 502 7 systems system NOUN fumecheng-4967 502 8 normally normally ADV fumecheng-4967 502 9 supposes suppose VERB fumecheng-4967 502 10 application application NOUN fumecheng-4967 502 11 of of ADP fumecheng-4967 502 12 the the DET fumecheng-4967 502 13 directly directly ADV fumecheng-4967 502 14 prescribed prescribe VERB fumecheng-4967 502 15 hexagonal hexagonal ADJ fumecheng-4967 502 16 arrangement arrangement NOUN fumecheng-4967 502 17 , , PUNCT fumecheng-4967 502 18 which which PRON fumecheng-4967 502 19 is be AUX fumecheng-4967 502 20 slightly slightly ADV fumecheng-4967 502 21 perturbed perturb VERB fumecheng-4967 502 22 from from ADP fumecheng-4967 502 23 the the DET fumecheng-4967 502 24 originally originally ADV fumecheng-4967 502 25 perfect perfect ADJ fumecheng-4967 502 26 positions position NOUN fumecheng-4967 502 27 by by ADP fumecheng-4967 502 28 a a DET fumecheng-4967 502 29 random random ADJ fumecheng-4967 502 30 noise noise NOUN fumecheng-4967 502 31 of of ADP fumecheng-4967 502 32 the the DET fumecheng-4967 502 33 displacements displacement NOUN fumecheng-4967 502 34 . . PUNCT fumecheng-4967 503 1 in in ADP fumecheng-4967 503 2 this this DET fumecheng-4967 503 3 approach approach NOUN fumecheng-4967 503 4 , , PUNCT fumecheng-4967 503 5 the the DET fumecheng-4967 503 6 particular particular ADJ fumecheng-4967 503 7 amplitude amplitude NOUN fumecheng-4967 503 8 of of ADP fumecheng-4967 503 9 gaussian gaussian ADJ fumecheng-4967 503 10 random random ADJ fumecheng-4967 503 11 shifts shift NOUN fumecheng-4967 503 12 might might AUX fumecheng-4967 503 13 be be AUX fumecheng-4967 503 14 appropriately appropriately ADV fumecheng-4967 503 15 adjusted adjust VERB fumecheng-4967 503 16 to to PART fumecheng-4967 503 17 fit fit VERB fumecheng-4967 503 18 numerically numerically ADV fumecheng-4967 503 19 found find VERB fumecheng-4967 503 20 distribution distribution NOUN fumecheng-4967 503 21 of of ADP fumecheng-4967 503 22 the the DET fumecheng-4967 503 23 distances distance NOUN fumecheng-4967 503 24 close close ADV fumecheng-4967 503 25 to to ADP fumecheng-4967 503 26 the the DET fumecheng-4967 503 27 experimentally experimentally ADV fumecheng-4967 503 28 observed observe VERB fumecheng-4967 503 29 in in ADP fumecheng-4967 503 30 real real ADJ fumecheng-4967 503 31 snakeskin snakeskin NOUN fumecheng-4967 503 32 . . PUNCT fumecheng-4967 504 1 despite despite SCONJ fumecheng-4967 504 2 this this PRON fumecheng-4967 504 3 , , PUNCT fumecheng-4967 504 4 the the DET fumecheng-4967 504 5 arrangement arrangement NOUN fumecheng-4967 504 6 of of ADP fumecheng-4967 504 7 the the DET fumecheng-4967 504 8 snake snake NOUN fumecheng-4967 504 9 nano nano NOUN fumecheng-4967 504 10 - - PUNCT fumecheng-4967 504 11 dimples dimple NOUN fumecheng-4967 504 12 has have VERB fumecheng-4967 504 13 obviously obviously ADV fumecheng-4967 504 14 different different ADJ fumecheng-4967 504 15 symmetry symmetry NOUN fumecheng-4967 504 16 of of ADP fumecheng-4967 504 17 its its PRON fumecheng-4967 504 18 power power NOUN fumecheng-4967 504 19 spectrum spectrum NOUN fumecheng-4967 504 20 compared compare VERB fumecheng-4967 504 21 to to ADP fumecheng-4967 504 22 the the DET fumecheng-4967 504 23 simulated simulated ADJ fumecheng-4967 504 24 one one NUM fumecheng-4967 504 25 . . PUNCT fumecheng-4967 505 1 this this DET fumecheng-4967 505 2 result result NOUN fumecheng-4967 505 3 means mean VERB fumecheng-4967 505 4 that that SCONJ fumecheng-4967 505 5 the the DET fumecheng-4967 505 6 nano nano NOUN fumecheng-4967 505 7 - - PUNCT fumecheng-4967 505 8 dimple dimple ADJ fumecheng-4967 505 9 spatial spatial ADJ fumecheng-4967 505 10 distribution distribution NOUN fumecheng-4967 505 11 can can AUX fumecheng-4967 505 12 not not PART fumecheng-4967 505 13 be be AUX fumecheng-4967 505 14 simulated simulate VERB fumecheng-4967 505 15 by by ADP fumecheng-4967 505 16 such such ADJ fumecheng-4967 505 17 naive naive ADJ fumecheng-4967 505 18 slightlyrandomized slightlyrandomize VERB fumecheng-4967 505 19 hexagonal hexagonal ADJ fumecheng-4967 505 20 configuration configuration NOUN fumecheng-4967 505 21 . . PUNCT fumecheng-4967 506 1 thus thus ADV fumecheng-4967 506 2 , , PUNCT fumecheng-4967 506 3 real real ADJ fumecheng-4967 506 4 arrangement arrangement NOUN fumecheng-4967 506 5 appears appear VERB fumecheng-4967 506 6 to to PART fumecheng-4967 506 7 be be AUX fumecheng-4967 506 8 a a DET fumecheng-4967 506 9 result result NOUN fumecheng-4967 506 10 of of ADP fumecheng-4967 506 11 some some DET fumecheng-4967 506 12 self self NOUN fumecheng-4967 506 13 - - PUNCT fumecheng-4967 506 14 organization organization NOUN fumecheng-4967 506 15 process process NOUN fumecheng-4967 506 16 caused cause VERB fumecheng-4967 506 17 by by ADP fumecheng-4967 506 18 an an DET fumecheng-4967 506 19 interaction interaction NOUN fumecheng-4967 506 20 between between ADP fumecheng-4967 506 21 nanostructures nanostructure NOUN fumecheng-4967 506 22 . . PUNCT fumecheng-4967 507 1 in in ADP fumecheng-4967 507 2 spirit spirit NOUN fumecheng-4967 507 3 of of ADP fumecheng-4967 507 4 the the DET fumecheng-4967 507 5 approach approach NOUN fumecheng-4967 507 6 presented present VERB fumecheng-4967 507 7 here here ADV fumecheng-4967 507 8 , , PUNCT fumecheng-4967 507 9 one one PRON fumecheng-4967 507 10 can can AUX fumecheng-4967 507 11 perform perform VERB fumecheng-4967 507 12 generate generate NOUN fumecheng-4967 507 13 , , PUNCT fumecheng-4967 507 14 as as ADP fumecheng-4967 507 15 an an DET fumecheng-4967 507 16 initial initial ADJ fumecheng-4967 507 17 condition condition NOUN fumecheng-4967 507 18 , , PUNCT fumecheng-4967 507 19 an an DET fumecheng-4967 507 20 array array NOUN fumecheng-4967 507 21 of of ADP fumecheng-4967 507 22 the the DET fumecheng-4967 507 23 randomly randomly ADV fumecheng-4967 507 24 distributed distribute VERB fumecheng-4967 507 25 dimples dimple NOUN fumecheng-4967 507 26 and and CCONJ fumecheng-4967 507 27 apply apply VERB fumecheng-4967 507 28 short short ADJ fumecheng-4967 507 29 range range NOUN fumecheng-4967 507 30 repulsion repulsion NOUN fumecheng-4967 507 31 between between ADP fumecheng-4967 507 32 them they PRON fumecheng-4967 507 33 with with ADP fumecheng-4967 507 34 some some DET fumecheng-4967 507 35 potential potential NOUN fumecheng-4967 507 36 . . PUNCT fumecheng-4967 508 1 system system NOUN fumecheng-4967 508 2 of of ADP fumecheng-4967 508 3 the the DET fumecheng-4967 508 4 dimples dimple NOUN fumecheng-4967 508 5 evolves evolve NOUN fumecheng-4967 508 6 according accord VERB fumecheng-4967 508 7 to to ADP fumecheng-4967 508 8 the the DET fumecheng-4967 508 9 standard standard ADJ fumecheng-4967 508 10 equation equation NOUN fumecheng-4967 508 11 of of ADP fumecheng-4967 508 12 motion motion NOUN fumecheng-4967 508 13 for for ADP fumecheng-4967 508 14 their their PRON fumecheng-4967 508 15 centers center NOUN fumecheng-4967 508 16 : : PUNCT fumecheng-4967 508 17 / / SYM fumecheng-4967 508 18 /i /i PUNCT fumecheng-4967 508 19 ij ij INTJ fumecheng-4967 508 20 j j PROPN fumecheng-4967 508 21 r r NOUN fumecheng-4967 508 22 t t PROPN fumecheng-4967 508 23 u u NOUN fumecheng-4967 508 24 r r ADJ fumecheng-4967 508 25   ADJ fumecheng-4967 508 26   PROPN fumecheng-4967 508 27   PROPN fumecheng-4967 508 28   PROPN fumecheng-4967 508 29   PROPN fumecheng-4967 508 30 . . PUNCT fumecheng-4967 509 1 but but CCONJ fumecheng-4967 509 2 , , PUNCT fumecheng-4967 509 3 here here ADV fumecheng-4967 509 4 we we PRON fumecheng-4967 509 5 are be AUX fumecheng-4967 509 6 actually actually ADV fumecheng-4967 509 7 interested interested ADJ fumecheng-4967 509 8 not not PART fumecheng-4967 509 9 in in ADP fumecheng-4967 509 10 an an DET fumecheng-4967 509 11 exact exact ADJ fumecheng-4967 509 12 pattern pattern NOUN fumecheng-4967 509 13 , , PUNCT fumecheng-4967 509 14 but but CCONJ fumecheng-4967 509 15 rather rather ADV fumecheng-4967 509 16 in in ADP fumecheng-4967 509 17 the the DET fumecheng-4967 509 18 shape shape NOUN fumecheng-4967 509 19 of of ADP fumecheng-4967 509 20 the the DET fumecheng-4967 509 21 distribution distribution NOUN fumecheng-4967 509 22 of of ADP fumecheng-4967 509 23 distances distance NOUN fumecheng-4967 509 24 and and CCONJ fumecheng-4967 509 25 in in ADP fumecheng-4967 509 26 the the DET fumecheng-4967 509 27 symmetry symmetry NOUN fumecheng-4967 509 28 of of ADP fumecheng-4967 509 29 the the DET fumecheng-4967 509 30 correlation correlation NOUN fumecheng-4967 509 31 function function NOUN fumecheng-4967 509 32 . . PUNCT fumecheng-4967 510 1 they they PRON fumecheng-4967 510 2 can can AUX fumecheng-4967 510 3 be be AUX fumecheng-4967 510 4 easily easily ADV fumecheng-4967 510 5 calculated calculate VERB fumecheng-4967 510 6 at at ADP fumecheng-4967 510 7 every every DET fumecheng-4967 510 8 single single ADJ fumecheng-4967 510 9 step step NOUN fumecheng-4967 510 10 of of ADP fumecheng-4967 510 11 the the DET fumecheng-4967 510 12 simulation simulation NOUN fumecheng-4967 510 13 . . PUNCT fumecheng-4967 511 1 the the DET fumecheng-4967 511 2 total total ADJ fumecheng-4967 511 3 number number NOUN fumecheng-4967 511 4 of of ADP fumecheng-4967 511 5 dimples dimple NOUN fumecheng-4967 511 6 in in ADP fumecheng-4967 511 7 numerical numerical ADJ fumecheng-4967 511 8 array array NOUN fumecheng-4967 511 9 is be AUX fumecheng-4967 511 10 completely completely ADV fumecheng-4967 511 11 predefined predefine VERB fumecheng-4967 511 12 by by ADP fumecheng-4967 511 13 the the DET fumecheng-4967 511 14 dimple dimple ADJ fumecheng-4967 511 15 number number NOUN fumecheng-4967 511 16 in in ADP fumecheng-4967 511 17 a a DET fumecheng-4967 511 18 given give VERB fumecheng-4967 511 19 observation observation NOUN fumecheng-4967 511 20 area area NOUN fumecheng-4967 511 21 of of ADP fumecheng-4967 511 22 the the DET fumecheng-4967 511 23 real real ADJ fumecheng-4967 511 24 system system NOUN fumecheng-4967 511 25 . . PUNCT fumecheng-4967 512 1 as as ADP fumecheng-4967 512 2 result result NOUN fumecheng-4967 512 3 , , PUNCT fumecheng-4967 512 4 in in ADP fumecheng-4967 512 5 the the DET fumecheng-4967 512 6 course course NOUN fumecheng-4967 512 7 of of ADP fumecheng-4967 512 8 kinetic kinetic ADJ fumecheng-4967 512 9 process process NOUN fumecheng-4967 512 10 , , PUNCT fumecheng-4967 512 11 the the DET fumecheng-4967 512 12 mean mean ADJ fumecheng-4967 512 13 distance distance NOUN fumecheng-4967 512 14 between between ADP fumecheng-4967 512 15 the the DET fumecheng-4967 512 16 dimples dimple NOUN fumecheng-4967 512 17 remains remains AUX fumecheng-4967 512 18 fixed fix VERB fumecheng-4967 512 19 by by ADP fumecheng-4967 512 20 the the DET fumecheng-4967 512 21 restricted restricted ADJ fumecheng-4967 512 22 size size NOUN fumecheng-4967 512 23 of of ADP fumecheng-4967 512 24 the the DET fumecheng-4967 512 25 observation observation NOUN fumecheng-4967 512 26 area area NOUN fumecheng-4967 512 27 and and CCONJ fumecheng-4967 512 28 the the DET fumecheng-4967 512 29 only only ADJ fumecheng-4967 512 30 parameters parameter NOUN fumecheng-4967 512 31 that that PRON fumecheng-4967 512 32 change change VERB fumecheng-4967 512 33 during during ADP fumecheng-4967 512 34 the the DET fumecheng-4967 512 35 relaxation relaxation NOUN fumecheng-4967 512 36 are be AUX fumecheng-4967 512 37 the the DET fumecheng-4967 512 38 symmetry symmetry NOUN fumecheng-4967 512 39 and and CCONJ fumecheng-4967 512 40 shape shape NOUN fumecheng-4967 512 41 of of ADP fumecheng-4967 512 42 the the DET fumecheng-4967 512 43 distribution distribution NOUN fumecheng-4967 512 44 of of ADP fumecheng-4967 512 45 distances distance NOUN fumecheng-4967 512 46 . . PUNCT fumecheng-4967 513 1 from from ADP fumecheng-4967 513 2 the the DET fumecheng-4967 513 3 mathematical mathematical ADJ fumecheng-4967 513 4 point point NOUN fumecheng-4967 513 5 of of ADP fumecheng-4967 513 6 view view NOUN fumecheng-4967 513 7 , , PUNCT fumecheng-4967 513 8 it it PRON fumecheng-4967 513 9 means mean VERB fumecheng-4967 513 10 that that SCONJ fumecheng-4967 513 11 the the DET fumecheng-4967 513 12 only only ADJ fumecheng-4967 513 13 one one NUM fumecheng-4967 513 14 fitting fitting ADJ fumecheng-4967 513 15 parameter parameter NOUN fumecheng-4967 513 16 remains remain VERB fumecheng-4967 513 17 in in ADP fumecheng-4967 513 18 the the DET fumecheng-4967 513 19 simulation simulation NOUN fumecheng-4967 513 20 . . PUNCT fumecheng-4967 514 1 it it PRON fumecheng-4967 514 2 is be AUX fumecheng-4967 514 3 the the DET fumecheng-4967 514 4 width width NOUN fumecheng-4967 514 5 of of ADP fumecheng-4967 514 6 the the DET fumecheng-4967 514 7 final final ADJ fumecheng-4967 514 8 distribution distribution NOUN fumecheng-4967 514 9 of of ADP fumecheng-4967 514 10 distances distance NOUN fumecheng-4967 514 11 . . PUNCT fumecheng-4967 515 1 relaxation relaxation NOUN fumecheng-4967 515 2 process process NOUN fumecheng-4967 515 3 runs run VERB fumecheng-4967 515 4 up up ADP fumecheng-4967 515 5 to to ADP fumecheng-4967 515 6 the the DET fumecheng-4967 515 7 moment moment NOUN fumecheng-4967 515 8 , , PUNCT fumecheng-4967 515 9 when when SCONJ fumecheng-4967 515 10 its its PRON fumecheng-4967 515 11 width width NOUN fumecheng-4967 515 12 coincides coincide VERB fumecheng-4967 515 13 with with ADP fumecheng-4967 515 14 the the DET fumecheng-4967 515 15 experimental experimental ADJ fumecheng-4967 515 16 one one NUM fumecheng-4967 515 17 . . PUNCT fumecheng-4967 516 1 it it PRON fumecheng-4967 516 2 automatically automatically ADV fumecheng-4967 516 3 defines define VERB fumecheng-4967 516 4 a a DET fumecheng-4967 516 5 time time NOUN fumecheng-4967 516 6 moment moment NOUN fumecheng-4967 516 7 , , PUNCT fumecheng-4967 516 8 when when SCONJ fumecheng-4967 516 9 the the DET fumecheng-4967 516 10 simulation simulation NOUN fumecheng-4967 516 11 has have VERB fumecheng-4967 516 12 to to PART fumecheng-4967 516 13 be be AUX fumecheng-4967 516 14 terminated terminate VERB fumecheng-4967 516 15 . . PUNCT fumecheng-4967 517 1 this this DET fumecheng-4967 517 2 stop stop AUX fumecheng-4967 517 3 immediately immediately ADV fumecheng-4967 517 4 freezes freeze VERB fumecheng-4967 517 5 the the DET fumecheng-4967 517 6 final final ADJ fumecheng-4967 517 7 configuration configuration NOUN fumecheng-4967 517 8 that that PRON fumecheng-4967 517 9 is be AUX fumecheng-4967 517 10 statistically statistically ADV fumecheng-4967 517 11 close close ADJ fumecheng-4967 517 12 to to ADP fumecheng-4967 517 13 the the DET fumecheng-4967 517 14 one one NUM fumecheng-4967 517 15 observed observe VERB fumecheng-4967 517 16 in in ADP fumecheng-4967 517 17 the the DET fumecheng-4967 517 18 real real ADJ fumecheng-4967 517 19 system system NOUN fumecheng-4967 517 20 . . PUNCT fumecheng-4967 518 1 other other ADJ fumecheng-4967 518 2 well well ADV fumecheng-4967 518 3 - - PUNCT fumecheng-4967 518 4 known know VERB fumecheng-4967 518 5 example example NOUN fumecheng-4967 518 6 of of ADP fumecheng-4967 518 7 biologicalу biologicalу PROPN fumecheng-4967 518 8 produced produce VERB fumecheng-4967 518 9 structured structured ADJ fumecheng-4967 518 10 surfaces surface NOUN fumecheng-4967 518 11 are be AUX fumecheng-4967 518 12 superhydrophobic superhydrophobic ADJ fumecheng-4967 518 13 surfaces surface NOUN fumecheng-4967 518 14 that that PRON fumecheng-4967 518 15 gain gain VERB fumecheng-4967 518 16 this this DET fumecheng-4967 518 17 functional functional ADJ fumecheng-4967 518 18 feature feature NOUN fumecheng-4967 518 19 due due ADJ fumecheng-4967 518 20 to to ADP fumecheng-4967 518 21 nano nano NOUN fumecheng-4967 518 22 - - PUNCT fumecheng-4967 518 23 structures structure NOUN fumecheng-4967 518 24 of of ADP fumecheng-4967 518 25 the the DET fumecheng-4967 518 26 surface surface NOUN fumecheng-4967 518 27 , , PUNCT fumecheng-4967 518 28 often often ADV fumecheng-4967 518 29 due due ADP fumecheng-4967 518 30 to to ADP fumecheng-4967 518 31 the the DET fumecheng-4967 518 32 surface surface NOUN fumecheng-4967 518 33 coatings coating NOUN fumecheng-4967 518 34 by by ADP fumecheng-4967 518 35 crystals crystal NOUN fumecheng-4967 518 36 or or CCONJ fumecheng-4967 518 37 particles particle NOUN fumecheng-4967 518 38 . . PUNCT fumecheng-4967 519 1 we we PRON fumecheng-4967 519 2 will will AUX fumecheng-4967 519 3 talk talk VERB fumecheng-4967 519 4 later later ADV fumecheng-4967 519 5 about about ADP fumecheng-4967 519 6 biological biological ADJ fumecheng-4967 519 7 inspirations inspiration NOUN fumecheng-4967 519 8 for for ADP fumecheng-4967 519 9 these these DET fumecheng-4967 519 10 kinds kind NOUN fumecheng-4967 519 11 of of ADP fumecheng-4967 519 12 technical technical ADJ fumecheng-4967 519 13 solutions solution NOUN fumecheng-4967 519 14 . . PUNCT fumecheng-4967 520 1 now now ADV fumecheng-4967 520 2 let let VERB fumecheng-4967 520 3 us we PRON fumecheng-4967 520 4 mention mention VERB fumecheng-4967 520 5 that that SCONJ fumecheng-4967 520 6 in in ADP fumecheng-4967 520 7 material material NOUN fumecheng-4967 520 8 240 240 NUM fumecheng-4967 520 9 a.e a.e PROPN fumecheng-4967 520 10 . . PROPN fumecheng-4967 520 11 filippov filippov PROPN fumecheng-4967 520 12 , , PUNCT fumecheng-4967 520 13 s.n s.n PROPN fumecheng-4967 520 14 . . PROPN fumecheng-4967 520 15 gorb gorb PROPN fumecheng-4967 520 16 science science PROPN fumecheng-4967 520 17 , , PUNCT fumecheng-4967 520 18 surface surface NOUN fumecheng-4967 520 19 coatings coating NOUN fumecheng-4967 520 20 with with ADP fumecheng-4967 520 21 regularly regularly ADV fumecheng-4967 520 22 arranged arrange VERB fumecheng-4967 520 23 globular globular ADJ fumecheng-4967 520 24 particles particle NOUN fumecheng-4967 520 25 have have AUX fumecheng-4967 520 26 been be AUX fumecheng-4967 520 27 produced produce VERB fumecheng-4967 520 28 by by ADP fumecheng-4967 520 29 so so ADV fumecheng-4967 520 30 - - PUNCT fumecheng-4967 520 31 called call VERB fumecheng-4967 520 32 colloidal colloidal NOUN fumecheng-4967 520 33 lithography lithography NOUN fumecheng-4967 520 34 , , PUNCT fumecheng-4967 520 35 a a DET fumecheng-4967 520 36 technique technique NOUN fumecheng-4967 520 37 utilizing utilize VERB fumecheng-4967 520 38 the the DET fumecheng-4967 520 39 self self NOUN fumecheng-4967 520 40 - - PUNCT fumecheng-4967 520 41 assembly assembly NOUN fumecheng-4967 520 42 of of ADP fumecheng-4967 520 43 nano nano NOUN fumecheng-4967 520 44 - - NOUN fumecheng-4967 520 45 particles particle NOUN fumecheng-4967 520 46 on on ADP fumecheng-4967 520 47 the the DET fumecheng-4967 520 48 substrate substrate NOUN fumecheng-4967 520 49 surface surface NOUN fumecheng-4967 520 50 . . PUNCT fumecheng-4967 521 1 however however ADV fumecheng-4967 521 2 , , PUNCT fumecheng-4967 521 3 the the DET fumecheng-4967 521 4 range range NOUN fumecheng-4967 521 5 of of ADP fumecheng-4967 521 6 producible producible ADJ fumecheng-4967 521 7 patterns pattern NOUN fumecheng-4967 521 8 and and CCONJ fumecheng-4967 521 9 properties property NOUN fumecheng-4967 521 10 of of ADP fumecheng-4967 521 11 these these DET fumecheng-4967 521 12 coatings coating NOUN fumecheng-4967 521 13 are be AUX fumecheng-4967 521 14 still still ADV fumecheng-4967 521 15 quite quite ADV fumecheng-4967 521 16 limited limited ADJ fumecheng-4967 521 17 , , PUNCT fumecheng-4967 521 18 as as ADV fumecheng-4967 521 19 well well ADV fumecheng-4967 521 20 as as ADP fumecheng-4967 521 21 their their PRON fumecheng-4967 521 22 durability durability NOUN fumecheng-4967 521 23 . . PUNCT fumecheng-4967 522 1 therefore therefore ADV fumecheng-4967 522 2 , , PUNCT fumecheng-4967 522 3 the the DET fumecheng-4967 522 4 study study NOUN fumecheng-4967 522 5 of of ADP fumecheng-4967 522 6 the the DET fumecheng-4967 522 7 close close ADJ fumecheng-4967 522 8 problems problem NOUN fumecheng-4967 522 9 by by ADP fumecheng-4967 522 10 numerical numerical ADJ fumecheng-4967 522 11 modeling modeling NOUN fumecheng-4967 522 12 seems seem VERB fumecheng-4967 522 13 to to PART fumecheng-4967 522 14 be be AUX fumecheng-4967 522 15 promising promise VERB fumecheng-4967 522 16 for for ADP fumecheng-4967 522 17 generating generate VERB fumecheng-4967 522 18 new new ADJ fumecheng-4967 522 19 solutions solution NOUN fumecheng-4967 522 20 . . PUNCT fumecheng-4967 523 1 a a DET fumecheng-4967 523 2 very very ADV fumecheng-4967 523 3 interesting interesting ADJ fumecheng-4967 523 4 and and CCONJ fumecheng-4967 523 5 non non ADJ fumecheng-4967 523 6 - - ADJ fumecheng-4967 523 7 trivial trivial ADJ fumecheng-4967 523 8 problem problem NOUN fumecheng-4967 523 9 , , PUNCT fumecheng-4967 523 10 in in ADP fumecheng-4967 523 11 particular particular ADJ fumecheng-4967 523 12 , , PUNCT fumecheng-4967 523 13 was be AUX fumecheng-4967 523 14 raised raise VERB fumecheng-4967 523 15 by by ADP fumecheng-4967 523 16 the the DET fumecheng-4967 523 17 study study NOUN fumecheng-4967 523 18 of of ADP fumecheng-4967 523 19 water water NOUN fumecheng-4967 523 20 repellence repellence NOUN fumecheng-4967 523 21 and and CCONJ fumecheng-4967 523 22 the the DET fumecheng-4967 523 23 ultrastructure ultrastructure NOUN fumecheng-4967 523 24 of of ADP fumecheng-4967 523 25 covering covering NOUN fumecheng-4967 523 26 granules granule NOUN fumecheng-4967 523 27 . . PUNCT fumecheng-4967 524 1 here here ADV fumecheng-4967 524 2 we we PRON fumecheng-4967 524 3 will will AUX fumecheng-4967 524 4 be be AUX fumecheng-4967 524 5 just just ADV fumecheng-4967 524 6 interested interested ADJ fumecheng-4967 524 7 in in ADP fumecheng-4967 524 8 complex complex ADJ fumecheng-4967 524 9 patterns pattern NOUN fumecheng-4967 524 10 , , PUNCT fumecheng-4967 524 11 which which PRON fumecheng-4967 524 12 can can AUX fumecheng-4967 524 13 self self NOUN fumecheng-4967 524 14 - - PUNCT fumecheng-4967 524 15 organize organize VERB fumecheng-4967 524 16 from from ADP fumecheng-4967 524 17 frozen frozen ADJ fumecheng-4967 524 18 kinetics kinetic NOUN fumecheng-4967 524 19 on on ADP fumecheng-4967 524 20 the the DET fumecheng-4967 524 21 spherical spherical ADJ fumecheng-4967 524 22 surfaces surface NOUN fumecheng-4967 524 23 of of ADP fumecheng-4967 524 24 colloidal colloidal NOUN fumecheng-4967 524 25 particles particle NOUN fumecheng-4967 524 26 . . PUNCT fumecheng-4967 525 1 direct direct ADJ fumecheng-4967 525 2 observation observation NOUN fumecheng-4967 525 3 shows show VERB fumecheng-4967 525 4 that that SCONJ fumecheng-4967 525 5 fine fine ADJ fumecheng-4967 525 6 structure structure NOUN fumecheng-4967 525 7 of of ADP fumecheng-4967 525 8 distribution distribution NOUN fumecheng-4967 525 9 of of ADP fumecheng-4967 525 10 asperities asperity NOUN fumecheng-4967 525 11 on on ADP fumecheng-4967 525 12 the the DET fumecheng-4967 525 13 surface surface NOUN fumecheng-4967 525 14 of of ADP fumecheng-4967 525 15 spheres sphere NOUN fumecheng-4967 525 16 is be AUX fumecheng-4967 525 17 species specie NOUN fumecheng-4967 525 18 - - PUNCT fumecheng-4967 525 19 specific specific ADJ fumecheng-4967 525 20 and and CCONJ fumecheng-4967 525 21 probably probably ADV fumecheng-4967 525 22 depends depend VERB fumecheng-4967 525 23 on on ADP fumecheng-4967 525 24 the the DET fumecheng-4967 525 25 interactions interaction NOUN fumecheng-4967 525 26 responsible responsible ADJ fumecheng-4967 525 27 for for ADP fumecheng-4967 525 28 the the DET fumecheng-4967 525 29 appearance appearance NOUN fumecheng-4967 525 30 of of ADP fumecheng-4967 525 31 these these DET fumecheng-4967 525 32 structures structure NOUN fumecheng-4967 525 33 . . PUNCT fumecheng-4967 526 1 in in ADP fumecheng-4967 526 2 order order NOUN fumecheng-4967 526 3 to to PART fumecheng-4967 526 4 gain gain VERB fumecheng-4967 526 5 a a DET fumecheng-4967 526 6 better well ADJ fumecheng-4967 526 7 understanding understanding NOUN fumecheng-4967 526 8 of of ADP fumecheng-4967 526 9 the the DET fumecheng-4967 526 10 process process NOUN fumecheng-4967 526 11 of of ADP fumecheng-4967 526 12 self self NOUN fumecheng-4967 526 13 - - PUNCT fumecheng-4967 526 14 assembly assembly NOUN fumecheng-4967 526 15 and and CCONJ fumecheng-4967 526 16 selfarrangement selfarrangement NOUN fumecheng-4967 526 17 of of ADP fumecheng-4967 526 18 nano nano NOUN fumecheng-4967 526 19 - - NOUN fumecheng-4967 526 20 particles particle NOUN fumecheng-4967 526 21 on on ADP fumecheng-4967 526 22 spherical spherical ADJ fumecheng-4967 526 23 microstructures microstructure NOUN fumecheng-4967 526 24 , , PUNCT fumecheng-4967 526 25 we we PRON fumecheng-4967 526 26 here here ADV fumecheng-4967 526 27 apply apply VERB fumecheng-4967 526 28 a a DET fumecheng-4967 526 29 theoretical theoretical ADJ fumecheng-4967 526 30 approach approach NOUN fumecheng-4967 526 31 . . PUNCT fumecheng-4967 527 1 in in ADP fumecheng-4967 527 2 the the DET fumecheng-4967 527 3 spirit spirit NOUN fumecheng-4967 527 4 of of ADP fumecheng-4967 527 5 previously previously ADV fumecheng-4967 527 6 described describe VERB fumecheng-4967 527 7 kinetic kinetic ADJ fumecheng-4967 527 8 approach approach NOUN fumecheng-4967 527 9 , , PUNCT fumecheng-4967 527 10 we we PRON fumecheng-4967 527 11 introduce introduce VERB fumecheng-4967 527 12 a a DET fumecheng-4967 527 13 numerical numerical ADJ fumecheng-4967 527 14 model model NOUN fumecheng-4967 527 15 that that PRON fumecheng-4967 527 16 allows allow VERB fumecheng-4967 527 17 us we PRON fumecheng-4967 527 18 to to PART fumecheng-4967 527 19 test test VERB fumecheng-4967 527 20 the the DET fumecheng-4967 527 21 effect effect NOUN fumecheng-4967 527 22 of of ADP fumecheng-4967 527 23 different different ADJ fumecheng-4967 527 24 interaction interaction NOUN fumecheng-4967 527 25 properties property NOUN fumecheng-4967 527 26 between between ADP fumecheng-4967 527 27 the the DET fumecheng-4967 527 28 particles particle NOUN fumecheng-4967 527 29 on on ADP fumecheng-4967 527 30 the the DET fumecheng-4967 527 31 morphology morphology NOUN fumecheng-4967 527 32 of of ADP fumecheng-4967 527 33 the the DET fumecheng-4967 527 34 eventual eventual ADJ fumecheng-4967 527 35 structure structure NOUN fumecheng-4967 527 36 . . PUNCT fumecheng-4967 528 1 our our PRON fumecheng-4967 528 2 results result NOUN fumecheng-4967 528 3 show show VERB fumecheng-4967 528 4 good good ADJ fumecheng-4967 528 5 mutual mutual ADJ fumecheng-4967 528 6 correspondence correspondence NOUN fumecheng-4967 528 7 with with ADP fumecheng-4967 528 8 numerically numerically ADV fumecheng-4967 528 9 found find VERB fumecheng-4967 528 10 structures structure NOUN fumecheng-4967 528 11 . . PUNCT fumecheng-4967 529 1 as as ADP fumecheng-4967 529 2 in in ADP fumecheng-4967 529 3 the the DET fumecheng-4967 529 4 previous previous ADJ fumecheng-4967 529 5 example example NOUN fumecheng-4967 529 6 ( ( PUNCT fumecheng-4967 529 7 snakeskin snakeskin NOUN fumecheng-4967 529 8 ) ) PUNCT fumecheng-4967 529 9 , , PUNCT fumecheng-4967 529 10 the the DET fumecheng-4967 529 11 model model NOUN fumecheng-4967 529 12 of of ADP fumecheng-4967 529 13 the the DET fumecheng-4967 529 14 systems system NOUN fumecheng-4967 529 15 under under ADP fumecheng-4967 529 16 consideration consideration NOUN fumecheng-4967 529 17 is be AUX fumecheng-4967 529 18 organized organize VERB fumecheng-4967 529 19 as as ADP fumecheng-4967 529 20 a a DET fumecheng-4967 529 21 combination combination NOUN fumecheng-4967 529 22 of of ADP fumecheng-4967 529 23 both both CCONJ fumecheng-4967 529 24 discrete discrete ADJ fumecheng-4967 529 25 and and CCONJ fumecheng-4967 529 26 continuous continuous ADJ fumecheng-4967 529 27 approaches approach NOUN fumecheng-4967 529 28 . . PUNCT fumecheng-4967 530 1 from from ADP fumecheng-4967 530 2 a a DET fumecheng-4967 530 3 general general ADJ fumecheng-4967 530 4 ( ( PUNCT fumecheng-4967 530 5 physical physical ADJ fumecheng-4967 530 6 , , PUNCT fumecheng-4967 530 7 chemical chemical NOUN fumecheng-4967 530 8 and and CCONJ fumecheng-4967 530 9 biological biological ADJ fumecheng-4967 530 10 ) ) PUNCT fumecheng-4967 530 11 point point NOUN fumecheng-4967 530 12 of of ADP fumecheng-4967 530 13 view view NOUN fumecheng-4967 530 14 , , PUNCT fumecheng-4967 530 15 one one PRON fumecheng-4967 530 16 can can AUX fumecheng-4967 530 17 expect expect VERB fumecheng-4967 530 18 that that SCONJ fumecheng-4967 530 19 the the DET fumecheng-4967 530 20 observed observed ADJ fumecheng-4967 530 21 structures structure NOUN fumecheng-4967 530 22 appear appear VERB fumecheng-4967 530 23 in in ADP fumecheng-4967 530 24 some some DET fumecheng-4967 530 25 kinetic kinetic ADJ fumecheng-4967 530 26 process process NOUN fumecheng-4967 530 27 during during ADP fumecheng-4967 530 28 which which PRON fumecheng-4967 530 29 continuously continuously ADV fumecheng-4967 530 30 an an DET fumecheng-4967 530 31 initially initially ADV fumecheng-4967 530 32 more more ADV fumecheng-4967 530 33 or or CCONJ fumecheng-4967 530 34 less less ADV fumecheng-4967 530 35 uniformly uniformly ADV fumecheng-4967 530 36 distributed distribute VERB fumecheng-4967 530 37 substance substance NOUN fumecheng-4967 530 38 redistributes redistribute NOUN fumecheng-4967 530 39 and and CCONJ fumecheng-4967 530 40 solidifies solidify VERB fumecheng-4967 530 41 in in ADP fumecheng-4967 530 42 a a DET fumecheng-4967 530 43 3 3 NUM fumecheng-4967 530 44 - - PUNCT fumecheng-4967 530 45 dimensional dimensional ADJ fumecheng-4967 530 46 space space NOUN fumecheng-4967 530 47 . . PUNCT fumecheng-4967 531 1 as as ADP fumecheng-4967 531 2 always always ADV fumecheng-4967 531 3 , , PUNCT fumecheng-4967 531 4 our our PRON fumecheng-4967 531 5 goal goal NOUN fumecheng-4967 531 6 is be AUX fumecheng-4967 531 7 to to PART fumecheng-4967 531 8 minimize minimize VERB fumecheng-4967 531 9 calculation calculation NOUN fumecheng-4967 531 10 time time NOUN fumecheng-4967 531 11 , , PUNCT fumecheng-4967 531 12 from from ADP fumecheng-4967 531 13 one one NUM fumecheng-4967 531 14 side side NOUN fumecheng-4967 531 15 , , PUNCT fumecheng-4967 531 16 and and CCONJ fumecheng-4967 531 17 to to PART fumecheng-4967 531 18 get get VERB fumecheng-4967 531 19 transparent transparent ADJ fumecheng-4967 531 20 understanding understanding NOUN fumecheng-4967 531 21 of of ADP fumecheng-4967 531 22 the the DET fumecheng-4967 531 23 process process NOUN fumecheng-4967 531 24 in in ADP fumecheng-4967 531 25 the the DET fumecheng-4967 531 26 frame frame NOUN fumecheng-4967 531 27 of of ADP fumecheng-4967 531 28 relatively relatively ADV fumecheng-4967 531 29 simple simple ADJ fumecheng-4967 531 30 model model NOUN fumecheng-4967 531 31 . . PUNCT fumecheng-4967 532 1 in in ADP fumecheng-4967 532 2 the the DET fumecheng-4967 532 3 particular particular ADJ fumecheng-4967 532 4 case case NOUN fumecheng-4967 532 5 of of ADP fumecheng-4967 532 6 the the DET fumecheng-4967 532 7 structuralized structuralize VERB fumecheng-4967 532 8 colloidal colloidal NOUN fumecheng-4967 532 9 particles particle NOUN fumecheng-4967 532 10 , , PUNCT fumecheng-4967 532 11 the the DET fumecheng-4967 532 12 problem problem NOUN fumecheng-4967 532 13 is be AUX fumecheng-4967 532 14 complicated complicate VERB fumecheng-4967 532 15 by by ADP fumecheng-4967 532 16 the the DET fumecheng-4967 532 17 specific specific ADJ fumecheng-4967 532 18 topology topology NOUN fumecheng-4967 532 19 of of ADP fumecheng-4967 532 20 the the DET fumecheng-4967 532 21 surface surface NOUN fumecheng-4967 532 22 , , PUNCT fumecheng-4967 532 23 on on ADP fumecheng-4967 532 24 which which PRON fumecheng-4967 532 25 the the DET fumecheng-4967 532 26 process process NOUN fumecheng-4967 532 27 runs run VERB fumecheng-4967 532 28 , , PUNCT fumecheng-4967 532 29 because because SCONJ fumecheng-4967 532 30 the the DET fumecheng-4967 532 31 redistribution redistribution NOUN fumecheng-4967 532 32 of of ADP fumecheng-4967 532 33 the the DET fumecheng-4967 532 34 densities density NOUN fumecheng-4967 532 35 and and CCONJ fumecheng-4967 532 36 their their PRON fumecheng-4967 532 37 further further ADJ fumecheng-4967 532 38 solidification solidification NOUN fumecheng-4967 532 39 takes take VERB fumecheng-4967 532 40 place place NOUN fumecheng-4967 532 41 directly directly ADV fumecheng-4967 532 42 on on ADP fumecheng-4967 532 43 spheres sphere NOUN fumecheng-4967 532 44 [ [ X fumecheng-4967 532 45 16 16 NUM fumecheng-4967 532 46 ] ] PUNCT fumecheng-4967 532 47 . . PUNCT fumecheng-4967 533 1 here here ADV fumecheng-4967 533 2 , , PUNCT fumecheng-4967 533 3 one one PRON fumecheng-4967 533 4 has have VERB fumecheng-4967 533 5 to to PART fumecheng-4967 533 6 deal deal VERB fumecheng-4967 533 7 with with ADP fumecheng-4967 533 8 a a DET fumecheng-4967 533 9 kind kind NOUN fumecheng-4967 533 10 of of ADP fumecheng-4967 533 11 phase phase NOUN fumecheng-4967 533 12 transition transition NOUN fumecheng-4967 533 13 ( ( PUNCT fumecheng-4967 533 14 or or CCONJ fumecheng-4967 533 15 phase phase NOUN fumecheng-4967 533 16 separation separation NOUN fumecheng-4967 533 17 ) ) PUNCT fumecheng-4967 533 18 inside inside ADP fumecheng-4967 533 19 a a DET fumecheng-4967 533 20 spherical spherical ADJ fumecheng-4967 533 21 layer layer NOUN fumecheng-4967 533 22 . . PUNCT fumecheng-4967 534 1 as as ADV fumecheng-4967 534 2 far far ADV fumecheng-4967 534 3 as as SCONJ fumecheng-4967 534 4 we we PRON fumecheng-4967 534 5 know know VERB fumecheng-4967 534 6 , , PUNCT fumecheng-4967 534 7 such such DET fumecheng-4967 534 8 a a DET fumecheng-4967 534 9 problem problem NOUN fumecheng-4967 534 10 with with ADP fumecheng-4967 534 11 geometrically geometrically ADV fumecheng-4967 534 12 frustrated frustrate VERB fumecheng-4967 534 13 assemblies assembly NOUN fumecheng-4967 534 14 was be AUX fumecheng-4967 534 15 not not PART fumecheng-4967 534 16 widely widely ADV fumecheng-4967 534 17 studied study VERB fumecheng-4967 534 18 in in ADP fumecheng-4967 534 19 conventional conventional ADJ fumecheng-4967 534 20 physics physics NOUN fumecheng-4967 534 21 and and CCONJ fumecheng-4967 534 22 chemistry chemistry NOUN fumecheng-4967 534 23 . . PUNCT fumecheng-4967 535 1 however however ADV fumecheng-4967 535 2 , , PUNCT fumecheng-4967 535 3 in in ADP fumecheng-4967 535 4 biological biological ADJ fumecheng-4967 535 5 systems system NOUN fumecheng-4967 535 6 , , PUNCT fumecheng-4967 535 7 such such ADJ fumecheng-4967 535 8 geometry geometry NOUN fumecheng-4967 535 9 is be AUX fumecheng-4967 535 10 widespread widespread ADJ fumecheng-4967 535 11 , , PUNCT fumecheng-4967 535 12 and and CCONJ fumecheng-4967 535 13 therefore therefore ADV fumecheng-4967 535 14 must must AUX fumecheng-4967 535 15 be be AUX fumecheng-4967 535 16 properly properly ADV fumecheng-4967 535 17 studied study VERB fumecheng-4967 535 18 . . PUNCT fumecheng-4967 536 1 topological topological ADJ fumecheng-4967 536 2 complexity complexity NOUN fumecheng-4967 536 3 of of ADP fumecheng-4967 536 4 the the DET fumecheng-4967 536 5 problem problem NOUN fumecheng-4967 536 6 forces force VERB fumecheng-4967 536 7 us we PRON fumecheng-4967 536 8 to to ADP fumecheng-4967 536 9 as as ADV fumecheng-4967 536 10 simple simple ADJ fumecheng-4967 536 11 as as ADP fumecheng-4967 536 12 possible possible ADJ fumecheng-4967 536 13 reduction reduction NOUN fumecheng-4967 536 14 of of ADP fumecheng-4967 536 15 the the DET fumecheng-4967 536 16 numerical numerical ADJ fumecheng-4967 536 17 model model NOUN fumecheng-4967 536 18 , , PUNCT fumecheng-4967 536 19 namely namely ADV fumecheng-4967 536 20 substitute substitute VERB fumecheng-4967 536 21 an an DET fumecheng-4967 536 22 original original ADJ fumecheng-4967 536 23 continuous continuous ADJ fumecheng-4967 536 24 problem problem NOUN fumecheng-4967 536 25 by by ADP fumecheng-4967 536 26 a a DET fumecheng-4967 536 27 combination combination NOUN fumecheng-4967 536 28 of of ADP fumecheng-4967 536 29 discrete discrete ADJ fumecheng-4967 536 30 model model NOUN fumecheng-4967 536 31 to to PART fumecheng-4967 536 32 find find VERB fumecheng-4967 536 33 almost almost ADV fumecheng-4967 536 34 stationary stationary ADJ fumecheng-4967 536 35 configuration configuration NOUN fumecheng-4967 536 36 and and CCONJ fumecheng-4967 536 37 further far ADV fumecheng-4967 536 38 continues continue VERB fumecheng-4967 536 39 density density NOUN fumecheng-4967 536 40 calculation calculation NOUN fumecheng-4967 536 41 . . PUNCT fumecheng-4967 537 1 let let VERB fumecheng-4967 537 2 us we PRON fumecheng-4967 537 3 mention mention VERB fumecheng-4967 537 4 that that SCONJ fumecheng-4967 537 5 such such DET fumecheng-4967 537 6 an an DET fumecheng-4967 537 7 approach approach NOUN fumecheng-4967 537 8 is be AUX fumecheng-4967 537 9 also also ADV fumecheng-4967 537 10 applicable applicable ADJ fumecheng-4967 537 11 for for ADP fumecheng-4967 537 12 the the DET fumecheng-4967 537 13 tamme‟s tamme‟s NOUN fumecheng-4967 537 14 problem problem NOUN fumecheng-4967 537 15 , , PUNCT fumecheng-4967 537 16 where where SCONJ fumecheng-4967 537 17 the the DET fumecheng-4967 537 18 study study NOUN fumecheng-4967 537 19 of of ADP fumecheng-4967 537 20 kinetic kinetic ADJ fumecheng-4967 537 21 ordering ordering NOUN fumecheng-4967 537 22 on on ADP fumecheng-4967 537 23 a a DET fumecheng-4967 537 24 sphere sphere NOUN fumecheng-4967 537 25 can can AUX fumecheng-4967 537 26 be be AUX fumecheng-4967 537 27 substituted substitute VERB fumecheng-4967 537 28 by by ADP fumecheng-4967 537 29 a a DET fumecheng-4967 537 30 finding finding NOUN fumecheng-4967 537 31 of of ADP fumecheng-4967 537 32 equilibrium equilibrium NOUN fumecheng-4967 537 33 ordering ordering NOUN fumecheng-4967 537 34 of of ADP fumecheng-4967 537 35 “ " PUNCT fumecheng-4967 537 36 n n CCONJ fumecheng-4967 537 37 equal equal ADJ fumecheng-4967 537 38 charges charge NOUN fumecheng-4967 537 39 ” " PUNCT fumecheng-4967 537 40 on on ADP fumecheng-4967 537 41 the the DET fumecheng-4967 537 42 sphere sphere NOUN fumecheng-4967 537 43 . . PUNCT fumecheng-4967 538 1 in in ADP fumecheng-4967 538 2 all all DET fumecheng-4967 538 3 these these DET fumecheng-4967 538 4 cases case NOUN fumecheng-4967 538 5 , , PUNCT fumecheng-4967 538 6 it it PRON fumecheng-4967 538 7 is be AUX fumecheng-4967 538 8 important important ADJ fumecheng-4967 538 9 that that SCONJ fumecheng-4967 538 10 , , PUNCT fumecheng-4967 538 11 in in ADP fumecheng-4967 538 12 the the DET fumecheng-4967 538 13 used used ADJ fumecheng-4967 538 14 approach approach NOUN fumecheng-4967 538 15 , , PUNCT fumecheng-4967 538 16 one one PRON fumecheng-4967 538 17 can can AUX fumecheng-4967 538 18 finalize finalize VERB fumecheng-4967 538 19 a a DET fumecheng-4967 538 20 discrete discrete ADJ fumecheng-4967 538 21 distribution distribution NOUN fumecheng-4967 538 22 of of ADP fumecheng-4967 538 23 the the DET fumecheng-4967 538 24 maximums maximum NOUN fumecheng-4967 538 25 or or CCONJ fumecheng-4967 538 26 minimums minimum NOUN fumecheng-4967 538 27 of of ADP fumecheng-4967 538 28 the the DET fumecheng-4967 538 29 densities density NOUN fumecheng-4967 538 30 , , PUNCT fumecheng-4967 538 31 and and CCONJ fumecheng-4967 538 32 only only ADV fumecheng-4967 538 33 after after ADP fumecheng-4967 538 34 getting get VERB fumecheng-4967 538 35 the the DET fumecheng-4967 538 36 distributions distribution NOUN fumecheng-4967 538 37 to to PART fumecheng-4967 538 38 “ " PUNCT fumecheng-4967 538 39 dress dress VERB fumecheng-4967 538 40 ” " PUNCT fumecheng-4967 538 41 them they PRON fumecheng-4967 538 42 by by ADP fumecheng-4967 538 43 the the DET fumecheng-4967 538 44 continuous continuous ADJ fumecheng-4967 538 45 field field NOUN fumecheng-4967 538 46 with with ADP fumecheng-4967 538 47 an an DET fumecheng-4967 538 48 expected expect VERB fumecheng-4967 538 49 density density NOUN fumecheng-4967 538 50 distribution distribution NOUN fumecheng-4967 538 51 . . PUNCT fumecheng-4967 539 1 however however ADV fumecheng-4967 539 2 , , PUNCT fumecheng-4967 539 3 it it PRON fumecheng-4967 539 4 is be AUX fumecheng-4967 539 5 important important ADJ fumecheng-4967 539 6 to to PART fumecheng-4967 539 7 note note VERB fumecheng-4967 539 8 that that SCONJ fumecheng-4967 539 9 in in ADP fumecheng-4967 539 10 its its PRON fumecheng-4967 539 11 classical classical ADJ fumecheng-4967 539 12 mathematical mathematical ADJ fumecheng-4967 539 13 form form NOUN fumecheng-4967 539 14 tammes tamme NOUN fumecheng-4967 539 15 problem problem NOUN fumecheng-4967 539 16 is be AUX fumecheng-4967 539 17 treated treat VERB fumecheng-4967 539 18 as as ADP fumecheng-4967 539 19 an an DET fumecheng-4967 539 20 optimization optimization NOUN fumecheng-4967 539 21 problem problem NOUN fumecheng-4967 539 22 which which PRON fumecheng-4967 539 23 can can AUX fumecheng-4967 539 24 be be AUX fumecheng-4967 539 25 formulated formulate VERB fumecheng-4967 539 26 as as ADP fumecheng-4967 539 27 follows follow VERB fumecheng-4967 539 28 : : PUNCT fumecheng-4967 539 29 given give VERB fumecheng-4967 539 30 a a DET fumecheng-4967 539 31 natural natural ADJ fumecheng-4967 539 32 number number NOUN fumecheng-4967 539 33 n n CCONJ fumecheng-4967 539 34 , , PUNCT fumecheng-4967 539 35 place place NOUN fumecheng-4967 539 36 n n PRON fumecheng-4967 539 37 points point VERB fumecheng-4967 539 38 on on ADP fumecheng-4967 539 39 the the DET fumecheng-4967 539 40 surface surface NOUN fumecheng-4967 539 41 of of ADP fumecheng-4967 539 42 a a DET fumecheng-4967 539 43 sphere sphere NOUN fumecheng-4967 539 44 in in ADP fumecheng-4967 539 45 a a DET fumecheng-4967 539 46 way way NOUN fumecheng-4967 539 47 that that PRON fumecheng-4967 539 48 maximizes maximize VERB fumecheng-4967 539 49 the the DET fumecheng-4967 539 50 shortest short ADJ fumecheng-4967 539 51 distance distance NOUN fumecheng-4967 539 52 between between ADP fumecheng-4967 539 53 any any DET fumecheng-4967 539 54 two two NUM fumecheng-4967 539 55 points point NOUN fumecheng-4967 539 56 . . PUNCT fumecheng-4967 540 1 this this DET fumecheng-4967 540 2 question question NOUN fumecheng-4967 540 3 normally normally ADV fumecheng-4967 540 4 dictates dictate VERB fumecheng-4967 540 5 maximal maximal ADJ fumecheng-4967 540 6 simplification simplification NOUN fumecheng-4967 540 7 of of ADP fumecheng-4967 540 8 the the DET fumecheng-4967 540 9 problem problem NOUN fumecheng-4967 540 10 ( ( PUNCT fumecheng-4967 540 11 like like ADP fumecheng-4967 540 12 limiting limit VERB fumecheng-4967 540 13 a a DET fumecheng-4967 540 14 number number NOUN fumecheng-4967 540 15 of of ADP fumecheng-4967 540 16 points point NOUN fumecheng-4967 540 17 by by ADP fumecheng-4967 540 18 special special ADJ fumecheng-4967 540 19 cases case NOUN fumecheng-4967 540 20 , , PUNCT fumecheng-4967 540 21 which which PRON fumecheng-4967 540 22 allow allow VERB fumecheng-4967 540 23 analytical analytical ADJ fumecheng-4967 540 24 solution solution NOUN fumecheng-4967 540 25 , , PUNCT fumecheng-4967 540 26 or or CCONJ fumecheng-4967 540 27 limiting limiting NOUN fumecheng-4967 540 28 of of ADP fumecheng-4967 540 29 their their PRON fumecheng-4967 540 30 interaction interaction NOUN fumecheng-4967 540 31 by by ADP fumecheng-4967 540 32 the the DET fumecheng-4967 540 33 simple simple ADJ fumecheng-4967 540 34 coulomb coulomb NOUN fumecheng-4967 540 35 one one NUM fumecheng-4967 540 36 ) ) PUNCT fumecheng-4967 540 37 . . PUNCT fumecheng-4967 541 1 our our PRON fumecheng-4967 541 2 goal goal NOUN fumecheng-4967 541 3 here here ADV fumecheng-4967 541 4 is be AUX fumecheng-4967 541 5 almost almost ADV fumecheng-4967 541 6 an an DET fumecheng-4967 541 7 opposite opposite ADJ fumecheng-4967 541 8 one one NUM fumecheng-4967 541 9 . . PUNCT fumecheng-4967 542 1 we we PRON fumecheng-4967 542 2 study study VERB fumecheng-4967 542 3 which which PRON fumecheng-4967 542 4 particular particular ADJ fumecheng-4967 542 5 structures structure NOUN fumecheng-4967 542 6 can can AUX fumecheng-4967 542 7 appear appear VERB fumecheng-4967 542 8 at at ADP fumecheng-4967 542 9 different different ADJ fumecheng-4967 542 10 interactions interaction NOUN fumecheng-4967 542 11 and and CCONJ fumecheng-4967 542 12 how how SCONJ fumecheng-4967 542 13 they they PRON fumecheng-4967 542 14 reproduce reproduce VERB fumecheng-4967 542 15 the the DET fumecheng-4967 542 16 observed observed ADJ fumecheng-4967 542 17 ones one NOUN fumecheng-4967 542 18 . . PUNCT fumecheng-4967 543 1 these these DET fumecheng-4967 543 2 methods method NOUN fumecheng-4967 543 3 of of ADP fumecheng-4967 543 4 the the DET fumecheng-4967 543 5 pattern pattern NOUN fumecheng-4967 543 6 formation formation NOUN fumecheng-4967 543 7 in in ADP fumecheng-4967 543 8 numerical numerical ADJ fumecheng-4967 543 9 modeling modeling NOUN fumecheng-4967 543 10 of of ADP fumecheng-4967 543 11 biological biological ADJ fumecheng-4967 543 12 problems problem NOUN fumecheng-4967 543 13 241 241 NUM fumecheng-4967 543 14 structures structure NOUN fumecheng-4967 543 15 are be AUX fumecheng-4967 543 16 certainly certainly ADV fumecheng-4967 543 17 not not PART fumecheng-4967 543 18 optimal optimal ADJ fumecheng-4967 543 19 , , PUNCT fumecheng-4967 543 20 and and CCONJ fumecheng-4967 543 21 in in ADP fumecheng-4967 543 22 many many ADJ fumecheng-4967 543 23 cases case NOUN fumecheng-4967 543 24 , , PUNCT fumecheng-4967 543 25 the the DET fumecheng-4967 543 26 distribution distribution NOUN fumecheng-4967 543 27 of of ADP fumecheng-4967 543 28 final final ADJ fumecheng-4967 543 29 densities density NOUN fumecheng-4967 543 30 , , PUNCT fumecheng-4967 543 31 being be AUX fumecheng-4967 543 32 generated generate VERB fumecheng-4967 543 33 by by ADP fumecheng-4967 543 34 frozen frozen ADJ fumecheng-4967 543 35 kinetics kinetic NOUN fumecheng-4967 543 36 , , PUNCT fumecheng-4967 543 37 is be AUX fumecheng-4967 543 38 even even ADV fumecheng-4967 543 39 extremely extremely ADV fumecheng-4967 543 40 inhomogeneous inhomogeneous ADJ fumecheng-4967 543 41 . . PUNCT fumecheng-4967 544 1 it it PRON fumecheng-4967 544 2 rather rather ADV fumecheng-4967 544 3 reminds remind VERB fumecheng-4967 544 4 study study NOUN fumecheng-4967 544 5 of of ADP fumecheng-4967 544 6 structural structural ADJ fumecheng-4967 544 7 phase phase NOUN fumecheng-4967 544 8 transitions transition NOUN fumecheng-4967 544 9 between between ADP fumecheng-4967 544 10 different different ADJ fumecheng-4967 544 11 phases phase NOUN fumecheng-4967 544 12 in in ADP fumecheng-4967 544 13 solid solid ADJ fumecheng-4967 544 14 state state NOUN fumecheng-4967 544 15 physics physics NOUN fumecheng-4967 544 16 depending depend VERB fumecheng-4967 544 17 on on ADP fumecheng-4967 544 18 the the DET fumecheng-4967 544 19 relations relation NOUN fumecheng-4967 544 20 between between ADP fumecheng-4967 544 21 the the DET fumecheng-4967 544 22 interactions interaction NOUN fumecheng-4967 544 23 . . PUNCT fumecheng-4967 545 1 however however ADV fumecheng-4967 545 2 , , PUNCT fumecheng-4967 545 3 it it PRON fumecheng-4967 545 4 differs differ VERB fumecheng-4967 545 5 from from ADP fumecheng-4967 545 6 the the DET fumecheng-4967 545 7 standard standard ADJ fumecheng-4967 545 8 physical physical ADJ fumecheng-4967 545 9 studies study NOUN fumecheng-4967 545 10 due due ADJ fumecheng-4967 545 11 to to ADP fumecheng-4967 545 12 new new ADJ fumecheng-4967 545 13 atypical atypical ADJ fumecheng-4967 545 14 confinement confinement NOUN fumecheng-4967 545 15 of of ADP fumecheng-4967 545 16 the the DET fumecheng-4967 545 17 geometrically geometrically ADV fumecheng-4967 545 18 frustrated frustrated ADJ fumecheng-4967 545 19 assemblies assembly NOUN fumecheng-4967 545 20 of of ADP fumecheng-4967 545 21 particles particle NOUN fumecheng-4967 545 22 on on ADP fumecheng-4967 545 23 the the DET fumecheng-4967 545 24 spherical spherical ADJ fumecheng-4967 545 25 surface surface NOUN fumecheng-4967 545 26 . . PUNCT fumecheng-4967 546 1 according accord VERB fumecheng-4967 546 2 to to ADP fumecheng-4967 546 3 these these DET fumecheng-4967 546 4 ideas idea NOUN fumecheng-4967 546 5 , , PUNCT fumecheng-4967 546 6 we we PRON fumecheng-4967 546 7 organize organize VERB fumecheng-4967 546 8 the the DET fumecheng-4967 546 9 procedure procedure NOUN fumecheng-4967 546 10 as as SCONJ fumecheng-4967 546 11 follows follow VERB fumecheng-4967 546 12 . . PUNCT fumecheng-4967 547 1 at at ADP fumecheng-4967 547 2 the the DET fumecheng-4967 547 3 first first ADJ fumecheng-4967 547 4 stage stage NOUN fumecheng-4967 547 5 , , PUNCT fumecheng-4967 547 6 we we PRON fumecheng-4967 547 7 randomly randomly ADV fumecheng-4967 547 8 distribute distribute VERB fumecheng-4967 547 9 some some DET fumecheng-4967 547 10 number number NOUN fumecheng-4967 547 11 of of ADP fumecheng-4967 547 12 particles particle NOUN fumecheng-4967 547 13 ( ( PUNCT fumecheng-4967 547 14 further further ADJ fumecheng-4967 547 15 nucleation nucleation NOUN fumecheng-4967 547 16 centers center NOUN fumecheng-4967 547 17 for for ADP fumecheng-4967 547 18 the the DET fumecheng-4967 547 19 densities density NOUN fumecheng-4967 547 20 ) ) PUNCT fumecheng-4967 547 21 on on ADP fumecheng-4967 547 22 the the DET fumecheng-4967 547 23 surface surface NOUN fumecheng-4967 547 24 of of ADP fumecheng-4967 547 25 the the DET fumecheng-4967 547 26 sphere sphere NOUN fumecheng-4967 547 27 . . PUNCT fumecheng-4967 548 1 at at ADP fumecheng-4967 548 2 this this DET fumecheng-4967 548 3 stage stage NOUN fumecheng-4967 548 4 , , PUNCT fumecheng-4967 548 5 the the DET fumecheng-4967 548 6 most most ADV fumecheng-4967 548 7 important important ADJ fumecheng-4967 548 8 parameters parameter NOUN fumecheng-4967 548 9 are be AUX fumecheng-4967 548 10 the the DET fumecheng-4967 548 11 relationships relationship NOUN fumecheng-4967 548 12 between between ADP fumecheng-4967 548 13 the the DET fumecheng-4967 548 14 sphere sphere NOUN fumecheng-4967 548 15 with with ADP fumecheng-4967 548 16 radius radius NOUN fumecheng-4967 548 17 rs rs NOUN fumecheng-4967 548 18 , , PUNCT fumecheng-4967 548 19 number number NOUN fumecheng-4967 548 20 of of ADP fumecheng-4967 548 21 particles particle NOUN fumecheng-4967 548 22 n n CCONJ fumecheng-4967 548 23 , , PUNCT fumecheng-4967 548 24 and and CCONJ fumecheng-4967 548 25 the the DET fumecheng-4967 548 26 characteristic characteristic ADJ fumecheng-4967 548 27 distance distance NOUN fumecheng-4967 548 28 of of ADP fumecheng-4967 548 29 repulsion repulsion NOUN fumecheng-4967 548 30 interactionr0 interactionr0 NOUN fumecheng-4967 548 31 between between ADP fumecheng-4967 548 32 them they PRON fumecheng-4967 548 33 . . PUNCT fumecheng-4967 549 1 more more ADV fumecheng-4967 549 2 specifically specifically ADV fumecheng-4967 549 3 , , PUNCT fumecheng-4967 549 4 the the DET fumecheng-4967 549 5 model model NOUN fumecheng-4967 549 6 and and CCONJ fumecheng-4967 549 7 the the DET fumecheng-4967 549 8 numerical numerical ADJ fumecheng-4967 549 9 procedure procedure NOUN fumecheng-4967 549 10 was be AUX fumecheng-4967 549 11 described describe VERB fumecheng-4967 549 12 earlier early ADV fumecheng-4967 549 13 in in ADP fumecheng-4967 549 14 one one NUM fumecheng-4967 549 15 of of ADP fumecheng-4967 549 16 the the DET fumecheng-4967 549 17 previous previous ADJ fumecheng-4967 549 18 papers paper NOUN fumecheng-4967 549 19 [ [ X fumecheng-4967 549 20 16 16 NUM fumecheng-4967 549 21 ] ] PUNCT fumecheng-4967 549 22 . . PUNCT fumecheng-4967 550 1 here here ADV fumecheng-4967 550 2 we we PRON fumecheng-4967 550 3 mention mention VERB fumecheng-4967 550 4 only only ADV fumecheng-4967 550 5 that that PRON fumecheng-4967 550 6 total total ADJ fumecheng-4967 550 7 interaction interaction NOUN fumecheng-4967 550 8 can can AUX fumecheng-4967 550 9 be be AUX fumecheng-4967 550 10 chosen choose VERB fumecheng-4967 550 11 alternatively alternatively ADV fumecheng-4967 550 12 as as ADP fumecheng-4967 550 13 just just ADV fumecheng-4967 550 14 a a DET fumecheng-4967 550 15 pure pure ADJ fumecheng-4967 550 16 short short ADJ fumecheng-4967 550 17 range range NOUN fumecheng-4967 550 18 repulsion repulsion NOUN fumecheng-4967 550 19 : : PUNCT fumecheng-4967 550 20 1(| 1(| NUM fumecheng-4967 550 21 |)j |)j SYM fumecheng-4967 550 22 ku ku PROPN fumecheng-4967 550 23 r r NOUN fumecheng-4967 550 24 r r NOUN fumecheng-4967 550 25 , , PUNCT fumecheng-4967 550 26 or or CCONJ fumecheng-4967 550 27 as as ADP fumecheng-4967 550 28 a a DET fumecheng-4967 550 29 combination combination NOUN fumecheng-4967 550 30 of of ADP fumecheng-4967 550 31 both both DET fumecheng-4967 550 32 repulsion repulsion NOUN fumecheng-4967 550 33 and and CCONJ fumecheng-4967 550 34 attraction attraction NOUN fumecheng-4967 550 35 2 2 NUM fumecheng-4967 550 36 ( ( PUNCT fumecheng-4967 550 37 | | ADV fumecheng-4967 550 38 |)j |)j SYM fumecheng-4967 550 39 ku ku PROPN fumecheng-4967 550 40 r r NOUN fumecheng-4967 550 41 r r NOUN fumecheng-4967 550 42 terms term NOUN fumecheng-4967 550 43 . . PUNCT fumecheng-4967 551 1 the the DET fumecheng-4967 551 2 second second ADJ fumecheng-4967 551 3 variant variant NOUN fumecheng-4967 551 4 leads lead VERB fumecheng-4967 551 5 to to ADP fumecheng-4967 551 6 a a DET fumecheng-4967 551 7 typical typical ADJ fumecheng-4967 551 8 effective effective ADJ fumecheng-4967 551 9 potential potential NOUN fumecheng-4967 551 10 with with ADP fumecheng-4967 551 11 minimum minimum ADJ fumecheng-4967 551 12 1 1 NUM fumecheng-4967 551 13 2(| 2(| NUM fumecheng-4967 551 14 | | NOUN fumecheng-4967 551 15 ) ) PUNCT fumecheng-4967 551 16 ( ( PUNCT fumecheng-4967 551 17 | | ADV fumecheng-4967 551 18 | | ADV fumecheng-4967 551 19 ) ) PUNCT fumecheng-4967 551 20 ( ( PUNCT fumecheng-4967 551 21 | | ADV fumecheng-4967 551 22 |)interaction |)interaction NOUN fumecheng-4967 551 23 j j PROPN fumecheng-4967 552 1 k k PROPN fumecheng-4967 552 2 j j PROPN fumecheng-4967 552 3 k k PROPN fumecheng-4967 552 4 j j PROPN fumecheng-4967 552 5 ku ku PROPN fumecheng-4967 552 6 r r PROPN fumecheng-4967 552 7 r r NOUN fumecheng-4967 552 8 u u NOUN fumecheng-4967 552 9 r r NOUN fumecheng-4967 552 10 r r NOUN fumecheng-4967 552 11 u u NOUN fumecheng-4967 552 12 r r NOUN fumecheng-4967 552 13 r r NOUN fumecheng-4967 552 14   PROPN fumecheng-4967 552 15   PROPN fumecheng-4967 552 16   VERB fumecheng-4967 552 17   PROPN fumecheng-4967 552 18 , , PUNCT fumecheng-4967 552 19 which which PRON fumecheng-4967 552 20 determines determine VERB fumecheng-4967 552 21 an an DET fumecheng-4967 552 22 equilibrium equilibrium NOUN fumecheng-4967 552 23 distance distance NOUN fumecheng-4967 552 24 between between ADP fumecheng-4967 552 25 the the DET fumecheng-4967 552 26 particles particle NOUN fumecheng-4967 552 27 reachable reachable VERB fumecheng-4967 552 28 in in ADP fumecheng-4967 552 29 long long ADJ fumecheng-4967 552 30 time time NOUN fumecheng-4967 552 31 asymptotics asymptotic NOUN fumecheng-4967 552 32 . . PUNCT fumecheng-4967 553 1 the the DET fumecheng-4967 553 2 mostly mostly ADV fumecheng-4967 553 3 nontrivial nontrivial ADJ fumecheng-4967 553 4 aspect aspect NOUN fumecheng-4967 553 5 of of ADP fumecheng-4967 553 6 the the DET fumecheng-4967 553 7 situation situation NOUN fumecheng-4967 553 8 here here ADV fumecheng-4967 553 9 is be AUX fumecheng-4967 553 10 that that SCONJ fumecheng-4967 553 11 the the DET fumecheng-4967 553 12 particles particle NOUN fumecheng-4967 553 13 have have VERB fumecheng-4967 553 14 to to PART fumecheng-4967 553 15 move move VERB fumecheng-4967 553 16 confined confine VERB fumecheng-4967 553 17 to to ADP fumecheng-4967 553 18 the the DET fumecheng-4967 553 19 sphere sphere NOUN fumecheng-4967 553 20 . . PUNCT fumecheng-4967 554 1 from from ADP fumecheng-4967 554 2 the the DET fumecheng-4967 554 3 mathematical mathematical ADJ fumecheng-4967 554 4 point point NOUN fumecheng-4967 554 5 of of ADP fumecheng-4967 554 6 view view NOUN fumecheng-4967 554 7 , , PUNCT fumecheng-4967 554 8 it it PRON fumecheng-4967 554 9 means mean VERB fumecheng-4967 554 10 that that SCONJ fumecheng-4967 554 11 we we PRON fumecheng-4967 554 12 apply apply VERB fumecheng-4967 554 13 a a DET fumecheng-4967 554 14 strong strong ADJ fumecheng-4967 554 15 potential potential NOUN fumecheng-4967 554 16 , , PUNCT fumecheng-4967 554 17 ( ( PUNCT fumecheng-4967 554 18 | | ADV fumecheng-4967 554 19 |)sphere |)sphere ADP fumecheng-4967 554 20 j j PROPN fumecheng-4967 554 21 su su PROPN fumecheng-4967 554 22 r r NOUN fumecheng-4967 554 23 r r NOUN fumecheng-4967 554 24 which which PRON fumecheng-4967 554 25 attracts attract VERB fumecheng-4967 554 26 them they PRON fumecheng-4967 554 27 to to ADP fumecheng-4967 554 28 the the DET fumecheng-4967 554 29 surface surface NOUN fumecheng-4967 554 30 of of ADP fumecheng-4967 554 31 given give VERB fumecheng-4967 554 32 radius radius NOUN fumecheng-4967 554 33 rs rs NOUN fumecheng-4967 554 34 . . PUNCT fumecheng-4967 555 1 if if SCONJ fumecheng-4967 555 2 this this DET fumecheng-4967 555 3 potential potential NOUN fumecheng-4967 555 4 is be AUX fumecheng-4967 555 5 strong strong ADJ fumecheng-4967 555 6 enough enough ADV fumecheng-4967 555 7 , , PUNCT fumecheng-4967 555 8 despite despite SCONJ fumecheng-4967 555 9 of of ADP fumecheng-4967 555 10 ( ( PUNCT fumecheng-4967 555 11 relatively relatively ADV fumecheng-4967 555 12 weak weak ADJ fumecheng-4967 555 13 ) ) PUNCT fumecheng-4967 555 14 repulsion repulsion NOUN fumecheng-4967 555 15 usphere≫u1 usphere≫u1 PROPN fumecheng-4967 555 16 between between ADP fumecheng-4967 555 17 the the DET fumecheng-4967 555 18 particles particle NOUN fumecheng-4967 555 19 , , PUNCT fumecheng-4967 555 20 they they PRON fumecheng-4967 555 21 practically practically ADV fumecheng-4967 555 22 can can AUX fumecheng-4967 555 23 not not PART fumecheng-4967 555 24 leave leave VERB fumecheng-4967 555 25 the the DET fumecheng-4967 555 26 spherical spherical ADJ fumecheng-4967 555 27 surface surface NOUN fumecheng-4967 555 28 . . PUNCT fumecheng-4967 556 1 the the DET fumecheng-4967 556 2 equation equation NOUN fumecheng-4967 556 3 of of ADP fumecheng-4967 556 4 motion motion NOUN fumecheng-4967 556 5 for for ADP fumecheng-4967 556 6 the the DET fumecheng-4967 556 7 “ " PUNCT fumecheng-4967 556 8 particles particle NOUN fumecheng-4967 556 9 ” " PUNCT fumecheng-4967 556 10 takes take VERB fumecheng-4967 556 11 the the DET fumecheng-4967 556 12 form form NOUN fumecheng-4967 556 13 : : PUNCT fumecheng-4967 556 14 /jr /jr X fumecheng-4967 557 1 t t NUM fumecheng-4967 557 2   ADJ fumecheng-4967 557 3   PRON fumecheng-4967 558 1 [ [ PUNCT fumecheng-4967 558 2 | | ADV fumecheng-4967 558 3 | | ADV fumecheng-4967 558 4 | | INTJ fumecheng-4967 558 5 |]/interaction |]/interaction NOUN fumecheng-4967 558 6 j j PROPN fumecheng-4967 558 7 k k PROPN fumecheng-4967 558 8 sphere sphere PROPN fumecheng-4967 558 9 j j PROPN fumecheng-4967 559 1 k k PROPN fumecheng-4967 559 2 k k PROPN fumecheng-4967 559 3 k k PROPN fumecheng-4967 559 4 u u NOUN fumecheng-4967 559 5 r r NOUN fumecheng-4967 559 6 r r NOUN fumecheng-4967 559 7 u u NOUN fumecheng-4967 559 8 r r NOUN fumecheng-4967 559 9 r r NOUN fumecheng-4967 559 10 r r NOUN fumecheng-4967 559 11   ADJ fumecheng-4967 559 12   PROPN fumecheng-4967 559 13   ADV fumecheng-4967 559 14   PROPN fumecheng-4967 559 15   PROPN fumecheng-4967 559 16 . . PUNCT fumecheng-4967 560 1 during during ADP fumecheng-4967 560 2 the the DET fumecheng-4967 560 3 routine routine NOUN fumecheng-4967 560 4 , , PUNCT fumecheng-4967 560 5 the the DET fumecheng-4967 560 6 particles particle NOUN fumecheng-4967 560 7 dynamically dynamically ADV fumecheng-4967 560 8 rearrange rearrange VERB fumecheng-4967 560 9 with with ADP fumecheng-4967 560 10 a a DET fumecheng-4967 560 11 rate rate NOUN fumecheng-4967 560 12 , , PUNCT fumecheng-4967 560 13 which which PRON fumecheng-4967 560 14 gradually gradually ADV fumecheng-4967 560 15 goes go VERB fumecheng-4967 560 16 down down ADP fumecheng-4967 560 17 with with ADP fumecheng-4967 560 18 time time NOUN fumecheng-4967 560 19 . . PUNCT fumecheng-4967 561 1 it it PRON fumecheng-4967 561 2 is be AUX fumecheng-4967 561 3 one one NUM fumecheng-4967 561 4 of of ADP fumecheng-4967 561 5 the the DET fumecheng-4967 561 6 particular particular ADJ fumecheng-4967 561 7 implementation implementation NOUN fumecheng-4967 561 8 of of ADP fumecheng-4967 561 9 the the DET fumecheng-4967 561 10 so so ADV fumecheng-4967 561 11 - - PUNCT fumecheng-4967 561 12 called call VERB fumecheng-4967 561 13 “ " PUNCT fumecheng-4967 561 14 a a DET fumecheng-4967 561 15 large large ADJ fumecheng-4967 561 16 river river NOUN fumecheng-4967 561 17 effect effect NOUN fumecheng-4967 561 18 ” " PUNCT fumecheng-4967 561 19 . . PUNCT fumecheng-4967 562 1 a a DET fumecheng-4967 562 2 particular particular ADJ fumecheng-4967 562 3 realization realization NOUN fumecheng-4967 562 4 of of ADP fumecheng-4967 562 5 this this DET fumecheng-4967 562 6 procedure procedure NOUN fumecheng-4967 562 7 is be AUX fumecheng-4967 562 8 shown show VERB fumecheng-4967 562 9 in in ADP fumecheng-4967 562 10 fig fig NOUN fumecheng-4967 562 11 . . PUNCT fumecheng-4967 563 1 12 12 NUM fumecheng-4967 563 2 . . PUNCT fumecheng-4967 564 1 as as ADP fumecheng-4967 564 2 usual usual ADJ fumecheng-4967 564 3 , , PUNCT fumecheng-4967 564 4 one one PRON fumecheng-4967 564 5 can can AUX fumecheng-4967 564 6 control control VERB fumecheng-4967 564 7 this this DET fumecheng-4967 564 8 slow slow ADJ fumecheng-4967 564 9 - - PUNCT fumecheng-4967 564 10 down down NOUN fumecheng-4967 564 11 calculating calculate VERB fumecheng-4967 564 12 mean mean NOUN fumecheng-4967 564 13 velocity velocity NOUN fumecheng-4967 564 14 of of ADP fumecheng-4967 564 15 the the DET fumecheng-4967 564 16 particles particle NOUN fumecheng-4967 564 17 and and CCONJ fumecheng-4967 564 18 stop stop VERB fumecheng-4967 564 19 the the DET fumecheng-4967 564 20 procedure procedure NOUN fumecheng-4967 564 21 , , PUNCT fumecheng-4967 564 22 when when SCONJ fumecheng-4967 564 23 velocity velocity NOUN fumecheng-4967 564 24 becomes become VERB fumecheng-4967 564 25 negligible negligible ADJ fumecheng-4967 564 26 . . PUNCT fumecheng-4967 565 1 certainly certainly ADV fumecheng-4967 565 2 , , PUNCT fumecheng-4967 565 3 as as SCONJ fumecheng-4967 565 4 we we PRON fumecheng-4967 565 5 already already ADV fumecheng-4967 565 6 discussed discuss VERB fumecheng-4967 565 7 before before ADV fumecheng-4967 565 8 , , PUNCT fumecheng-4967 565 9 the the DET fumecheng-4967 565 10 particles particle NOUN fumecheng-4967 565 11 can can AUX fumecheng-4967 565 12 never never ADV fumecheng-4967 565 13 reach reach VERB fumecheng-4967 565 14 real real ADJ fumecheng-4967 565 15 “ " PUNCT fumecheng-4967 565 16 ground ground NOUN fumecheng-4967 565 17 state state NOUN fumecheng-4967 565 18 ” " PUNCT fumecheng-4967 565 19 . . PUNCT fumecheng-4967 566 1 especially especially ADV fumecheng-4967 566 2 , , PUNCT fumecheng-4967 566 3 it it PRON fumecheng-4967 566 4 is be AUX fumecheng-4967 566 5 correct correct ADJ fumecheng-4967 566 6 for for ADP fumecheng-4967 566 7 the the DET fumecheng-4967 566 8 spherical spherical ADJ fumecheng-4967 566 9 surface surface NOUN fumecheng-4967 566 10 . . PUNCT fumecheng-4967 567 1 but but CCONJ fumecheng-4967 567 2 , , PUNCT fumecheng-4967 567 3 at at ADP fumecheng-4967 567 4 long long ADJ fumecheng-4967 567 5 time time NOUN fumecheng-4967 567 6 run run NOUN fumecheng-4967 567 7 , , PUNCT fumecheng-4967 567 8 they they PRON fumecheng-4967 567 9 get get VERB fumecheng-4967 567 10 some some DET fumecheng-4967 567 11 stationary stationary ADJ fumecheng-4967 567 12 distribution distribution NOUN fumecheng-4967 567 13 which which PRON fumecheng-4967 567 14 looks look VERB fumecheng-4967 567 15 quite quite ADV fumecheng-4967 567 16 realistically realistically ADV fumecheng-4967 567 17 . . PUNCT fumecheng-4967 568 1 it it PRON fumecheng-4967 568 2 is be AUX fumecheng-4967 568 3 what what PRON fumecheng-4967 568 4 we we PRON fumecheng-4967 568 5 expect expect VERB fumecheng-4967 568 6 for for ADP fumecheng-4967 568 7 the the DET fumecheng-4967 568 8 “ " PUNCT fumecheng-4967 568 9 large large ADJ fumecheng-4967 568 10 river river NOUN fumecheng-4967 568 11 ” " PUNCT fumecheng-4967 568 12 ( ( PUNCT fumecheng-4967 568 13 or or CCONJ fumecheng-4967 568 14 frozen frozen ADJ fumecheng-4967 568 15 kinetics kinetic NOUN fumecheng-4967 568 16 ) ) PUNCT fumecheng-4967 568 17 in in ADP fumecheng-4967 568 18 a a DET fumecheng-4967 568 19 real real ADJ fumecheng-4967 568 20 system system NOUN fumecheng-4967 568 21 . . PUNCT fumecheng-4967 569 1 the the DET fumecheng-4967 569 2 final final ADJ fumecheng-4967 569 3 stage stage NOUN fumecheng-4967 569 4 of of ADP fumecheng-4967 569 5 the the DET fumecheng-4967 569 6 simulation simulation NOUN fumecheng-4967 569 7 is be AUX fumecheng-4967 569 8 to to PART fumecheng-4967 569 9 “ " PUNCT fumecheng-4967 569 10 dress dress VERB fumecheng-4967 569 11 ” " PUNCT fumecheng-4967 569 12 the the DET fumecheng-4967 569 13 spherical spherical ADJ fumecheng-4967 569 14 surface surface NOUN fumecheng-4967 569 15 ( ( PUNCT fumecheng-4967 569 16 ) ) PUNCT fumecheng-4967 569 17 j j PROPN fumecheng-4967 569 18 r r ADJ fumecheng-4967 569 19 and and CCONJ fumecheng-4967 569 20 nucleation nucleation NOUN fumecheng-4967 569 21 centers center NOUN fumecheng-4967 569 22 ( ( PUNCT fumecheng-4967 569 23 particles particle NOUN fumecheng-4967 569 24 ) ) PUNCT fumecheng-4967 569 25 by by ADP fumecheng-4967 569 26 the the DET fumecheng-4967 569 27 continuous continuous ADJ fumecheng-4967 569 28 density density NOUN fumecheng-4967 569 29 distributions distribution NOUN fumecheng-4967 569 30 . . PUNCT fumecheng-4967 570 1 fig fig NOUN fumecheng-4967 570 2 . . PUNCT fumecheng-4967 571 1 12 12 NUM fumecheng-4967 571 2 combination combination NOUN fumecheng-4967 571 3 of of ADP fumecheng-4967 571 4 the the DET fumecheng-4967 571 5 discrete discrete ADJ fumecheng-4967 571 6 and and CCONJ fumecheng-4967 571 7 continual continual ADJ fumecheng-4967 571 8 approaches approach NOUN fumecheng-4967 571 9 in in ADP fumecheng-4967 571 10 a a DET fumecheng-4967 571 11 single single ADJ fumecheng-4967 571 12 model model NOUN fumecheng-4967 571 13 . . PUNCT fumecheng-4967 572 1 at at ADP fumecheng-4967 572 2 the the DET fumecheng-4967 572 3 first first ADJ fumecheng-4967 572 4 stage stage NOUN fumecheng-4967 572 5 of of ADP fumecheng-4967 572 6 the the DET fumecheng-4967 572 7 calculation calculation NOUN fumecheng-4967 572 8 , , PUNCT fumecheng-4967 572 9 a a DET fumecheng-4967 572 10 discrete discrete ADJ fumecheng-4967 572 11 array array NOUN fumecheng-4967 572 12 of of ADP fumecheng-4967 572 13 the the DET fumecheng-4967 572 14 interacting interact VERB fumecheng-4967 572 15 points point NOUN fumecheng-4967 572 16 , , PUNCT fumecheng-4967 572 17 randomly randomly ADV fumecheng-4967 572 18 242 242 NUM fumecheng-4967 572 19 a.e a.e PROPN fumecheng-4967 572 20 . . PROPN fumecheng-4967 572 21 filippov filippov PROPN fumecheng-4967 572 22 , , PUNCT fumecheng-4967 572 23 s.n s.n PROPN fumecheng-4967 572 24 . . PROPN fumecheng-4967 572 25 gorb gorb PROPN fumecheng-4967 572 26 placed place VERB fumecheng-4967 572 27 on on ADP fumecheng-4967 572 28 the the DET fumecheng-4967 572 29 sphere sphere NOUN fumecheng-4967 572 30 ( ( PUNCT fumecheng-4967 572 31 a a X fumecheng-4967 572 32 ) ) PUNCT fumecheng-4967 572 33 , , PUNCT fumecheng-4967 572 34 dynamically dynamically ADV fumecheng-4967 572 35 orders order VERB fumecheng-4967 572 36 itself itself PRON fumecheng-4967 572 37 into into ADP fumecheng-4967 572 38 a a DET fumecheng-4967 572 39 frozen frozen ADJ fumecheng-4967 572 40 , , PUNCT fumecheng-4967 572 41 almost almost ADV fumecheng-4967 572 42 static static ADJ fumecheng-4967 572 43 configuration configuration NOUN fumecheng-4967 572 44 ( ( PUNCT fumecheng-4967 572 45 b b NOUN fumecheng-4967 572 46 ) ) PUNCT fumecheng-4967 572 47 , , PUNCT fumecheng-4967 572 48 which which PRON fumecheng-4967 572 49 is be AUX fumecheng-4967 572 50 “ " PUNCT fumecheng-4967 572 51 dressed dressed ADJ fumecheng-4967 572 52 ” " PUNCT fumecheng-4967 572 53 by by ADP fumecheng-4967 572 54 the the DET fumecheng-4967 572 55 continuous continuous ADJ fumecheng-4967 572 56 density density NOUN fumecheng-4967 572 57 ( ( PUNCT fumecheng-4967 572 58 c c X fumecheng-4967 572 59 ) ) PUNCT fumecheng-4967 572 60 the the DET fumecheng-4967 572 61 total total ADJ fumecheng-4967 572 62 density density NOUN fumecheng-4967 572 63 around around ADP fumecheng-4967 572 64 the the DET fumecheng-4967 572 65 nucleation nucleation NOUN fumecheng-4967 572 66 centers center NOUN fumecheng-4967 572 67 should should AUX fumecheng-4967 572 68 be be AUX fumecheng-4967 572 69 accumulated accumulate VERB fumecheng-4967 572 70 by by ADP fumecheng-4967 572 71 a a DET fumecheng-4967 572 72 summation summation NOUN fumecheng-4967 572 73 of of ADP fumecheng-4967 572 74 all all DET fumecheng-4967 572 75 the the DET fumecheng-4967 572 76 particles particle NOUN fumecheng-4967 572 77 ( ( PUNCT fumecheng-4967 572 78 ) ) PUNCT fumecheng-4967 572 79 ( ( PUNCT fumecheng-4967 572 80 ) ) PUNCT fumecheng-4967 572 81 ( ( PUNCT fumecheng-4967 572 82 ) ) PUNCT fumecheng-4967 572 83 total total PROPN fumecheng-4967 573 1 j j PROPN fumecheng-4967 573 2 s s PROPN fumecheng-4967 573 3 j j PROPN fumecheng-4967 573 4 r r NOUN fumecheng-4967 573 5 r r NOUN fumecheng-4967 573 6 r r NOUN fumecheng-4967 573 7   NOUN fumecheng-4967 573 8   ADP fumecheng-4967 573 9   NOUN fumecheng-4967 573 10 . . PUNCT fumecheng-4967 574 1 it it PRON fumecheng-4967 574 2 can can AUX fumecheng-4967 574 3 be be AUX fumecheng-4967 574 4 proven prove VERB fumecheng-4967 574 5 that that SCONJ fumecheng-4967 574 6 each each DET fumecheng-4967 574 7 numerically numerically ADV fumecheng-4967 574 8 found find VERB fumecheng-4967 574 9 pattern pattern NOUN fumecheng-4967 574 10 is be AUX fumecheng-4967 574 11 determined determine VERB fumecheng-4967 574 12 by by ADP fumecheng-4967 574 13 a a DET fumecheng-4967 574 14 relation relation NOUN fumecheng-4967 574 15 between between ADP fumecheng-4967 574 16 the the DET fumecheng-4967 574 17 area area NOUN fumecheng-4967 574 18 of of ADP fumecheng-4967 574 19 the the DET fumecheng-4967 574 20 sphere sphere NOUN fumecheng-4967 574 21 and and CCONJ fumecheng-4967 574 22 the the DET fumecheng-4967 574 23 size size NOUN fumecheng-4967 574 24 of of ADP fumecheng-4967 574 25 the the DET fumecheng-4967 574 26 particles particle NOUN fumecheng-4967 574 27 on on ADP fumecheng-4967 574 28 one one NUM fumecheng-4967 574 29 side side NOUN fumecheng-4967 574 30 ( ( PUNCT fumecheng-4967 574 31 or or CCONJ fumecheng-4967 574 32 density density NOUN fumecheng-4967 574 33 of of ADP fumecheng-4967 574 34 them they PRON fumecheng-4967 574 35 on on ADP fumecheng-4967 574 36 the the DET fumecheng-4967 574 37 surface surface NOUN fumecheng-4967 574 38 ) ) PUNCT fumecheng-4967 574 39 , , PUNCT fumecheng-4967 574 40 and and CCONJ fumecheng-4967 574 41 the the DET fumecheng-4967 574 42 interaction interaction NOUN fumecheng-4967 574 43 between between ADP fumecheng-4967 574 44 the the DET fumecheng-4967 574 45 particles particle NOUN fumecheng-4967 574 46 on on ADP fumecheng-4967 574 47 the the DET fumecheng-4967 574 48 other other ADJ fumecheng-4967 574 49 side side NOUN fumecheng-4967 574 50 . . PUNCT fumecheng-4967 575 1 according accord VERB fumecheng-4967 575 2 to to ADP fumecheng-4967 575 3 general general ADJ fumecheng-4967 575 4 discussion discussion NOUN fumecheng-4967 575 5 , , PUNCT fumecheng-4967 575 6 we we PRON fumecheng-4967 575 7 can can AUX fumecheng-4967 575 8 not not PART fumecheng-4967 575 9 directly directly ADV fumecheng-4967 575 10 visualize visualize VERB fumecheng-4967 575 11 obtained obtain VERB fumecheng-4967 575 12 continuous continuous ADJ fumecheng-4967 575 13 density density NOUN fumecheng-4967 575 14 distributions distribution NOUN fumecheng-4967 575 15 as as ADP fumecheng-4967 575 16 a a DET fumecheng-4967 575 17 projection projection NOUN fumecheng-4967 575 18 on on ADP fumecheng-4967 575 19 the the DET fumecheng-4967 575 20 2d 2d NUM fumecheng-4967 575 21 surface surface NOUN fumecheng-4967 575 22 of of ADP fumecheng-4967 575 23 the the DET fumecheng-4967 575 24 plots plot NOUN fumecheng-4967 575 25 . . PUNCT fumecheng-4967 576 1 but but CCONJ fumecheng-4967 576 2 , , PUNCT fumecheng-4967 576 3 in in ADP fumecheng-4967 576 4 standard standard ADJ fumecheng-4967 576 5 manner manner NOUN fumecheng-4967 576 6 , , PUNCT fumecheng-4967 576 7 we we PRON fumecheng-4967 576 8 can can AUX fumecheng-4967 576 9 plot plot VERB fumecheng-4967 576 10 the the DET fumecheng-4967 576 11 surfaces surface NOUN fumecheng-4967 576 12 corresponding correspond VERB fumecheng-4967 576 13 to to ADP fumecheng-4967 576 14 any any DET fumecheng-4967 576 15 constant constant ADJ fumecheng-4967 576 16 density density NOUN fumecheng-4967 576 17 and and CCONJ fumecheng-4967 576 18 compare compare VERB fumecheng-4967 576 19 them they PRON fumecheng-4967 576 20 with with ADP fumecheng-4967 576 21 the the DET fumecheng-4967 576 22 data datum NOUN fumecheng-4967 576 23 of of ADP fumecheng-4967 576 24 real real ADJ fumecheng-4967 576 25 structures structure NOUN fumecheng-4967 576 26 . . PUNCT fumecheng-4967 577 1 acknowledgments acknowledgment NOUN fumecheng-4967 577 2 : : PUNCT fumecheng-4967 577 3 this this DET fumecheng-4967 577 4 work work NOUN fumecheng-4967 577 5 was be AUX fumecheng-4967 577 6 supported support VERB fumecheng-4967 577 7 by by ADP fumecheng-4967 577 8 the the DET fumecheng-4967 577 9 georg georg NOUN fumecheng-4967 577 10 forster forster PROPN fumecheng-4967 577 11 research research PROPN fumecheng-4967 577 12 award award PROPN fumecheng-4967 577 13 ( ( PUNCT fumecheng-4967 577 14 alexander alexander PROPN fumecheng-4967 577 15 von von PROPN fumecheng-4967 577 16 humboldt humboldt PROPN fumecheng-4967 577 17 foundation foundation PROPN fumecheng-4967 577 18 , , PUNCT fumecheng-4967 577 19 germany germany PROPN fumecheng-4967 577 20 ) ) PUNCT fumecheng-4967 577 21 ukr ukr PROPN fumecheng-4967 577 22 1118826 1118826 NUM fumecheng-4967 577 23 to to ADP fumecheng-4967 577 24 a.e.f a.e.f PROPN fumecheng-4967 577 25 . . PUNCT fumecheng-4967 578 1 renate renate PROPN fumecheng-4967 578 2 schilling schilling NOUN fumecheng-4967 578 3 is be AUX fumecheng-4967 578 4 greatly greatly ADV fumecheng-4967 578 5 acknowledged acknowledge VERB fumecheng-4967 578 6 for for ADP fumecheng-4967 578 7 the the DET fumecheng-4967 578 8 linguistic linguistic ADJ fumecheng-4967 578 9 corrections correction NOUN fumecheng-4967 578 10 of of ADP fumecheng-4967 578 11 the the DET fumecheng-4967 578 12 manuscript manuscript NOUN fumecheng-4967 578 13 . . PUNCT fumecheng-4967 579 1 references reference NOUN fumecheng-4967 579 2 1 1 NUM fumecheng-4967 579 3 . . PUNCT fumecheng-4967 580 1 popov popov PROPN fumecheng-4967 580 2 , , PUNCT fumecheng-4967 580 3 v.l v.l PROPN fumecheng-4967 580 4 . . PROPN fumecheng-4967 580 5 , , PUNCT fumecheng-4967 580 6 heß heß PROPN fumecheng-4967 580 7 m. m. NOUN fumecheng-4967 580 8 , , PUNCT fumecheng-4967 580 9 2015 2015 NUM fumecheng-4967 580 10 , , PUNCT fumecheng-4967 580 11 method method NOUN fumecheng-4967 580 12 of of ADP fumecheng-4967 580 13 dimensionality dimensionality NOUN fumecheng-4967 580 14 reduction reduction NOUN fumecheng-4967 580 15 in in ADP fumecheng-4967 580 16 contact contact NOUN fumecheng-4967 580 17 mechanics mechanic NOUN fumecheng-4967 580 18 and and CCONJ fumecheng-4967 580 19 friction friction NOUN fumecheng-4967 580 20 , , PUNCT fumecheng-4967 580 21 springer springer NOUN fumecheng-4967 580 22 de de PROPN fumecheng-4967 580 23 . . PROPN fumecheng-4967 580 24 2 2 NUM fumecheng-4967 580 25 . . NUM fumecheng-4967 580 26 landau landau NOUN fumecheng-4967 580 27 , , PUNCT fumecheng-4967 580 28 l.d l.d PROPN fumecheng-4967 580 29 . . PROPN fumecheng-4967 580 30 , , PUNCT fumecheng-4967 580 31 1937 1937 NUM fumecheng-4967 580 32 , , PUNCT fumecheng-4967 580 33 theory theory NOUN fumecheng-4967 580 34 of of ADP fumecheng-4967 580 35 phase phase NOUN fumecheng-4967 580 36 transitions transition NOUN fumecheng-4967 580 37 , , PUNCT fumecheng-4967 580 38 zh zh PROPN fumecheng-4967 580 39 . . PUNCT fumecheng-4967 580 40 eksp eksp PROPN fumecheng-4967 580 41 . . PUNCT fumecheng-4967 581 1 teor teor PROPN fumecheng-4967 581 2 . . PUNCT fumecheng-4967 582 1 fiz fiz PROPN fumecheng-4967 582 2 . . PUNCT fumecheng-4967 583 1 pp pp ADJ fumecheng-4967 583 2 . . PUNCT fumecheng-4967 584 1 19–32 19–32 NUM fumecheng-4967 584 2 . . PUNCT fumecheng-4967 585 1 3 3 X fumecheng-4967 585 2 . . X fumecheng-4967 585 3 patashinskii patashinskii PROPN fumecheng-4967 585 4 , , PUNCT fumecheng-4967 585 5 a. a. PROPN fumecheng-4967 585 6 z. z. PROPN fumecheng-4967 585 7 , , PUNCT fumecheng-4967 585 8 pokrovskii pokrovskii ADJ fumecheng-4967 585 9 , , PUNCT fumecheng-4967 585 10 v.l v.l PROPN fumecheng-4967 585 11 . . PROPN fumecheng-4967 585 12 , , PUNCT fumecheng-4967 585 13 1979 1979 NUM fumecheng-4967 585 14 , , PUNCT fumecheng-4967 585 15 fluctuarion fluctuarion NOUN fumecheng-4967 585 16 theory theory NOUN fumecheng-4967 585 17 of of ADP fumecheng-4967 585 18 phase phase NOUN fumecheng-4967 585 19 transitions transition NOUN fumecheng-4967 585 20 , , PUNCT fumecheng-4967 585 21 pergamon pergamon PROPN fumecheng-4967 585 22 press press PROPN fumecheng-4967 585 23 , , PUNCT fumecheng-4967 585 24 oxford oxford NOUN fumecheng-4967 585 25 . . PUNCT fumecheng-4967 586 1 4 4 NUM fumecheng-4967 586 2 . . X fumecheng-4967 586 3 landau landau NOUN fumecheng-4967 586 4 , , PUNCT fumecheng-4967 586 5 l.d l.d PROPN fumecheng-4967 586 6 . . PROPN fumecheng-4967 586 7 , , PUNCT fumecheng-4967 586 8 khalatnikov khalatnikov PROPN fumecheng-4967 586 9 i.m i.m PROPN fumecheng-4967 586 10 . . PROPN fumecheng-4967 586 11 , , PUNCT fumecheng-4967 586 12 1965 1965 NUM fumecheng-4967 586 13 , , PUNCT fumecheng-4967 586 14 on on ADP fumecheng-4967 586 15 the the DET fumecheng-4967 586 16 anomalous anomalous ADJ fumecheng-4967 586 17 absorption absorption NOUN fumecheng-4967 586 18 of of ADP fumecheng-4967 586 19 sound sound NOUN fumecheng-4967 586 20 near near ADP fumecheng-4967 586 21 a a DET fumecheng-4967 586 22 second second ADJ fumecheng-4967 586 23 order order NOUN fumecheng-4967 586 24 phase phase NOUN fumecheng-4967 586 25 transition transition NOUN fumecheng-4967 586 26 point point NOUN fumecheng-4967 586 27 , , PUNCT fumecheng-4967 586 28 in in ADP fumecheng-4967 586 29 collected collect VERB fumecheng-4967 586 30 papers paper NOUN fumecheng-4967 586 31 of of ADP fumecheng-4967 586 32 l.d l.d PROPN fumecheng-4967 586 33 . . PROPN fumecheng-4967 586 34 landau landau NOUN fumecheng-4967 586 35 , , PUNCT fumecheng-4967 586 36 edited edit VERB fumecheng-4967 586 37 by by ADP fumecheng-4967 586 38 d. d. PROPN fumecheng-4967 586 39 ter ter PROPN fumecheng-4967 586 40 haar haar PROPN fumecheng-4967 586 41 , , PUNCT fumecheng-4967 586 42 elsevier elsevier PROPN fumecheng-4967 586 43 inc inc PROPN fumecheng-4967 586 44 . . PROPN fumecheng-4967 586 45 , , PUNCT fumecheng-4967 586 46 pp pp PROPN fumecheng-4967 586 47 . . PUNCT fumecheng-4967 587 1 626 626 NUM fumecheng-4967 587 2 - - SYM fumecheng-4967 587 3 629 629 NUM fumecheng-4967 587 4 . . NOUN fumecheng-4967 588 1 5 5 NUM fumecheng-4967 588 2 . . PUNCT fumecheng-4967 588 3 kuzovlev kuzovlev PROPN fumecheng-4967 588 4 , , PUNCT fumecheng-4967 588 5 yu.e yu.e NOUN fumecheng-4967 588 6 . . PROPN fumecheng-4967 588 7 , , PUNCT fumecheng-4967 588 8 soboleva soboleva PROPN fumecheng-4967 588 9 , , PUNCT fumecheng-4967 588 10 t.k t.k PROPN fumecheng-4967 588 11 . . PROPN fumecheng-4967 588 12 , , PUNCT fumecheng-4967 588 13 filippov filippov NOUN fumecheng-4967 588 14 , , PUNCT fumecheng-4967 588 15 a.e a.e PROPN fumecheng-4967 588 16 . . PROPN fumecheng-4967 588 17 , , PUNCT fumecheng-4967 588 18 1993 1993 NUM fumecheng-4967 588 19 , , PUNCT fumecheng-4967 588 20 structure structure NOUN fumecheng-4967 588 21 and and CCONJ fumecheng-4967 588 22 evolution evolution NOUN fumecheng-4967 588 23 of of ADP fumecheng-4967 588 24 new new ADJ fumecheng-4967 588 25 phase phase NOUN fumecheng-4967 588 26 nuclea nuclea ADV fumecheng-4967 588 27 at at ADP fumecheng-4967 588 28 first first ADJ fumecheng-4967 588 29 order order NOUN fumecheng-4967 588 30 phase phase NOUN fumecheng-4967 588 31 transitions transition NOUN fumecheng-4967 588 32 , , PUNCT fumecheng-4967 588 33 journ.exp journ.exp PROPN fumecheng-4967 588 34 . . PUNCT fumecheng-4967 588 35 and and CCONJ fumecheng-4967 588 36 theor.phys theor.phy NOUN fumecheng-4967 588 37 . . PUNCT fumecheng-4967 588 38 , , PUNCT fumecheng-4967 588 39 76 76 NUM fumecheng-4967 588 40 , , PUNCT fumecheng-4967 588 41 pp pp ADJ fumecheng-4967 588 42 . . PUNCT fumecheng-4967 589 1 858 858 NUM fumecheng-4967 589 2 - - SYM fumecheng-4967 589 3 867 867 NUM fumecheng-4967 589 4 . . PUNCT fumecheng-4967 590 1 6 6 NUM fumecheng-4967 590 2 . . X fumecheng-4967 590 3 kuzovlev kuzovlev PROPN fumecheng-4967 590 4 , , PUNCT fumecheng-4967 590 5 yu.e yu.e NOUN fumecheng-4967 590 6 . . PROPN fumecheng-4967 590 7 , , PUNCT fumecheng-4967 590 8 soboleva soboleva PROPN fumecheng-4967 590 9 , , PUNCT fumecheng-4967 590 10 t.k t.k PROPN fumecheng-4967 590 11 . . PROPN fumecheng-4967 590 12 , , PUNCT fumecheng-4967 590 13 filippov filippov PROPN fumecheng-4967 590 14 a.e a.e PROPN fumecheng-4967 590 15 . . PROPN fumecheng-4967 590 16 , , PUNCT fumecheng-4967 590 17 1993 1993 NUM fumecheng-4967 590 18 , , PUNCT fumecheng-4967 590 19 formation formation NOUN fumecheng-4967 590 20 of of ADP fumecheng-4967 590 21 the the DET fumecheng-4967 590 22 filli filli PROPN fumecheng-4967 590 23 structure structure NOUN fumecheng-4967 590 24 at at ADP fumecheng-4967 590 25 nucleation nucleation NOUN fumecheng-4967 590 26 processes process NOUN fumecheng-4967 590 27 , , PUNCT fumecheng-4967 590 28 j. j. PROPN fumecheng-4967 590 29 exp exp PROPN fumecheng-4967 590 30 . . PUNCT fumecheng-4967 590 31 theor theor PROPN fumecheng-4967 590 32 . . PUNCT fumecheng-4967 591 1 phys phy NOUN fumecheng-4967 591 2 . . PUNCT fumecheng-4967 592 1 lett lett PROPN fumecheng-4967 592 2 . . PROPN fumecheng-4967 592 3 , , PUNCT fumecheng-4967 592 4 58 58 NUM fumecheng-4967 592 5 , , PUNCT fumecheng-4967 592 6 pp pp ADJ fumecheng-4967 592 7 . . PUNCT fumecheng-4967 593 1 357 357 NUM fumecheng-4967 593 2 - - SYM fumecheng-4967 593 3 362 362 NUM fumecheng-4967 593 4 . . PUNCT fumecheng-4967 594 1 7 7 NUM fumecheng-4967 594 2 . . X fumecheng-4967 594 3 zeltser zeltser PROPN fumecheng-4967 594 4 , , PUNCT fumecheng-4967 594 5 a.s a.s PROPN fumecheng-4967 594 6 . . PROPN fumecheng-4967 594 7 , , PUNCT fumecheng-4967 594 8 soboleva soboleva PROPN fumecheng-4967 594 9 , , PUNCT fumecheng-4967 594 10 t.k t.k PROPN fumecheng-4967 594 11 . . PROPN fumecheng-4967 594 12 , , PUNCT fumecheng-4967 594 13 filippov filippov NOUN fumecheng-4967 594 14 , , PUNCT fumecheng-4967 594 15 a.e a.e PROPN fumecheng-4967 594 16 . . PROPN fumecheng-4967 594 17 , , PUNCT fumecheng-4967 594 18 1995 1995 NUM fumecheng-4967 594 19 , , PUNCT fumecheng-4967 594 20 automatic automatic ADJ fumecheng-4967 594 21 blocking blocking NOUN fumecheng-4967 594 22 of of ADP fumecheng-4967 594 23 the the DET fumecheng-4967 594 24 nucleation nucleation NOUN fumecheng-4967 594 25 and and CCONJ fumecheng-4967 594 26 universality universality NOUN fumecheng-4967 594 27 of of ADP fumecheng-4967 594 28 kinetic kinetic ADJ fumecheng-4967 594 29 phenomena phenomenon NOUN fumecheng-4967 594 30 at at ADP fumecheng-4967 594 31 first first ADJ fumecheng-4967 594 32 order order NOUN fumecheng-4967 594 33 phase phase NOUN fumecheng-4967 594 34 transitions transition NOUN fumecheng-4967 594 35 , , PUNCT fumecheng-4967 594 36 j. j. PROPN fumecheng-4967 594 37 exp exp PROPN fumecheng-4967 594 38 . . PUNCT fumecheng-4967 595 1 theor theor PROPN fumecheng-4967 595 2 . . PUNCT fumecheng-4967 596 1 phys phy NOUN fumecheng-4967 596 2 . . PUNCT fumecheng-4967 596 3 , , PUNCT fumecheng-4967 596 4 81 81 NUM fumecheng-4967 596 5 , , PUNCT fumecheng-4967 596 6 pp pp ADJ fumecheng-4967 596 7 . . PUNCT fumecheng-4967 597 1 193 193 NUM fumecheng-4967 597 2 - - SYM fumecheng-4967 597 3 201 201 NUM fumecheng-4967 597 4 . . NOUN fumecheng-4967 598 1 8 8 NUM fumecheng-4967 598 2 . . X fumecheng-4967 599 1 filippov filippov PROPN fumecheng-4967 599 2 , , PUNCT fumecheng-4967 599 3 a.e a.e PROPN fumecheng-4967 599 4 . . PROPN fumecheng-4967 599 5 , , PUNCT fumecheng-4967 599 6 1994 1994 NUM fumecheng-4967 599 7 , , PUNCT fumecheng-4967 599 8 large large ADJ fumecheng-4967 599 9 scale scale NOUN fumecheng-4967 599 10 structure structure NOUN fumecheng-4967 599 11 of of ADP fumecheng-4967 599 12 fluctuating fluctuate VERB fumecheng-4967 599 13 order order NOUN fumecheng-4967 599 14 parameter parameter NOUN fumecheng-4967 599 15 field field NOUN fumecheng-4967 599 16 , , PUNCT fumecheng-4967 599 17 j. j. PROPN fumecheng-4967 599 18 stat stat PROPN fumecheng-4967 599 19 . . PUNCT fumecheng-4967 600 1 phys phy NOUN fumecheng-4967 600 2 . . PUNCT fumecheng-4967 600 3 , , PUNCT fumecheng-4967 600 4 75 75 NUM fumecheng-4967 600 5 , , PUNCT fumecheng-4967 600 6 pp pp ADJ fumecheng-4967 600 7 . . PUNCT fumecheng-4967 601 1 241 241 NUM fumecheng-4967 601 2 - - PUNCT fumecheng-4967 601 3 252 252 NUM fumecheng-4967 601 4 . . PUNCT fumecheng-4967 602 1 9 9 X fumecheng-4967 602 2 . . X fumecheng-4967 603 1 filippov filippov NOUN fumecheng-4967 603 2 , , PUNCT fumecheng-4967 603 3 a.e a.e PROPN fumecheng-4967 603 4 . . PROPN fumecheng-4967 603 5 , , PUNCT fumecheng-4967 603 6 1998 1998 NUM fumecheng-4967 603 7 , , PUNCT fumecheng-4967 603 8 two two NUM fumecheng-4967 603 9 - - PUNCT fumecheng-4967 603 10 component component NOUN fumecheng-4967 603 11 model model NOUN fumecheng-4967 603 12 for for ADP fumecheng-4967 603 13 the the DET fumecheng-4967 603 14 growth growth NOUN fumecheng-4967 603 15 of of ADP fumecheng-4967 603 16 porous porous ADJ fumecheng-4967 603 17 surface surface NOUN fumecheng-4967 603 18 layers layer NOUN fumecheng-4967 603 19 , , PUNCT fumecheng-4967 603 20 j. j. PROPN fumecheng-4967 603 21 exp exp PROPN fumecheng-4967 603 22 . . PUNCT fumecheng-4967 603 23 theor theor PROPN fumecheng-4967 603 24 . . PUNCT fumecheng-4967 604 1 phys phy NOUN fumecheng-4967 604 2 . . PUNCT fumecheng-4967 604 3 , , PUNCT fumecheng-4967 604 4 87 87 NUM fumecheng-4967 604 5 , , PUNCT fumecheng-4967 604 6 pp.814 pp.814 PROPN fumecheng-4967 604 7 – – PUNCT fumecheng-4967 604 8 822 822 NUM fumecheng-4967 604 9 . . PUNCT fumecheng-4967 604 10 10 10 NUM fumecheng-4967 604 11 . . PUNCT fumecheng-4967 605 1 filippov filippov NOUN fumecheng-4967 605 2 , , PUNCT fumecheng-4967 605 3 a.e a.e PROPN fumecheng-4967 605 4 . . PROPN fumecheng-4967 605 5 , , PUNCT fumecheng-4967 605 6 popov popov PROPN fumecheng-4967 605 7 , , PUNCT fumecheng-4967 605 8 v.l v.l PROPN fumecheng-4967 605 9 , , PUNCT fumecheng-4967 605 10 2007 2007 NUM fumecheng-4967 605 11 , , PUNCT fumecheng-4967 605 12 fractal fractal PROPN fumecheng-4967 605 13 tomlinson tomlinson PROPN fumecheng-4967 605 14 model model NOUN fumecheng-4967 605 15 for for ADP fumecheng-4967 605 16 mesoscopic mesoscopic NOUN fumecheng-4967 605 17 friction friction NOUN fumecheng-4967 605 18 : : PUNCT fumecheng-4967 605 19 from from ADP fumecheng-4967 605 20 microscopic microscopic ADJ fumecheng-4967 605 21 velocity velocity NOUN fumecheng-4967 605 22 - - PUNCT fumecheng-4967 605 23 dependent dependent ADJ fumecheng-4967 605 24 damping damp VERB fumecheng-4967 605 25 to to ADP fumecheng-4967 605 26 macroscopic macroscopic ADJ fumecheng-4967 605 27 coulomb coulomb NOUN fumecheng-4967 605 28 friction friction NOUN fumecheng-4967 605 29 , , PUNCT fumecheng-4967 605 30 phys phy NOUN fumecheng-4967 605 31 . . PUNCT fumecheng-4967 606 1 rev rev PROPN fumecheng-4967 606 2 . . PROPN fumecheng-4967 606 3 , , PUNCT fumecheng-4967 606 4 e e PROPN fumecheng-4967 606 5 75 75 NUM fumecheng-4967 606 6 27103 27103 NUM fumecheng-4967 606 7 . . PUNCT fumecheng-4967 607 1 11 11 NUM fumecheng-4967 607 2 . . X fumecheng-4967 608 1 filippov filippov NOUN fumecheng-4967 608 2 , , PUNCT fumecheng-4967 608 3 a.e a.e PROPN fumecheng-4967 608 4 . . PROPN fumecheng-4967 608 5 , , PUNCT fumecheng-4967 608 6 popov popov PROPN fumecheng-4967 608 7 , , PUNCT fumecheng-4967 608 8 v.l v.l PROPN fumecheng-4967 608 9 . . PROPN fumecheng-4967 608 10 , , PUNCT fumecheng-4967 608 11 gorb gorb PROPN fumecheng-4967 608 12 , , PUNCT fumecheng-4967 608 13 s.n s.n PROPN fumecheng-4967 608 14 . . PROPN fumecheng-4967 608 15 , , PUNCT fumecheng-4967 608 16 2011 2011 NUM fumecheng-4967 608 17 , , PUNCT fumecheng-4967 608 18 shear shear NOUN fumecheng-4967 608 19 induced induce VERB fumecheng-4967 608 20 adhesion adhesion NOUN fumecheng-4967 608 21 : : PUNCT fumecheng-4967 608 22 contact contact NOUN fumecheng-4967 608 23 mechanics mechanic NOUN fumecheng-4967 608 24 of of ADP fumecheng-4967 608 25 biological biological ADJ fumecheng-4967 608 26 spatula spatula NOUN fumecheng-4967 608 27 - - PUNCT fumecheng-4967 608 28 like like ADJ fumecheng-4967 608 29 attachment attachment NOUN fumecheng-4967 608 30 devices device NOUN fumecheng-4967 608 31 , , PUNCT fumecheng-4967 608 32 j. j. PROPN fumecheng-4967 608 33 theor theor PROPN fumecheng-4967 608 34 . . PUNCT fumecheng-4967 609 1 biol biol PROPN fumecheng-4967 609 2 . . PUNCT fumecheng-4967 609 3 , , PUNCT fumecheng-4967 609 4 276 276 NUM fumecheng-4967 609 5 , , PUNCT fumecheng-4967 609 6 pp pp ADJ fumecheng-4967 609 7 . . PUNCT fumecheng-4967 610 1 126 126 NUM fumecheng-4967 610 2 - - SYM fumecheng-4967 610 3 131 131 NUM fumecheng-4967 610 4 . . PUNCT fumecheng-4967 611 1 12 12 NUM fumecheng-4967 611 2 . . PUNCT fumecheng-4967 612 1 starcevic starcevic PROPN fumecheng-4967 612 2 j. j. PROPN fumecheng-4967 612 3 , , PUNCT fumecheng-4967 612 4 popov popov PROPN fumecheng-4967 612 5 , , PUNCT fumecheng-4967 612 6 v.l v.l PROPN fumecheng-4967 612 7 . . PROPN fumecheng-4967 612 8 , , PUNCT fumecheng-4967 612 9 filippov filippov PROPN fumecheng-4967 612 10 , , PUNCT fumecheng-4967 612 11 a.e a.e PROPN fumecheng-4967 612 12 . . PROPN fumecheng-4967 612 13 , , PUNCT fumecheng-4967 612 14 2007 2007 NUM fumecheng-4967 612 15 , , PUNCT fumecheng-4967 612 16 reconstruction reconstruction NOUN fumecheng-4967 612 17 of of ADP fumecheng-4967 612 18 potential potential NOUN fumecheng-4967 612 19 from from ADP fumecheng-4967 612 20 dynamic dynamic ADJ fumecheng-4967 612 21 experiments experiment NOUN fumecheng-4967 612 22 , , PUNCT fumecheng-4967 612 23 phys phy NOUN fumecheng-4967 612 24 . . PUNCT fumecheng-4967 612 25 rev rev PROPN fumecheng-4967 612 26 . . PUNCT fumecheng-4967 613 1 e e PROPN fumecheng-4967 613 2 75 75 NUM fumecheng-4967 613 3 , , PUNCT fumecheng-4967 613 4 066104 066104 NUM fumecheng-4967 613 5 . . PUNCT fumecheng-4967 614 1 13 13 NUM fumecheng-4967 614 2 . . X fumecheng-4967 615 1 soboleva soboleva PROPN fumecheng-4967 615 2 , , PUNCT fumecheng-4967 615 3 t.k t.k PROPN fumecheng-4967 615 4 . . PROPN fumecheng-4967 615 5 , , PUNCT fumecheng-4967 615 6 wedderburn wedderburn PROPN fumecheng-4967 615 7 , , PUNCT fumecheng-4967 615 8 m.e m.e PROPN fumecheng-4967 615 9 . . PROPN fumecheng-4967 615 10 , , PUNCT fumecheng-4967 615 11 filippov filippov PROPN fumecheng-4967 615 12 , , PUNCT fumecheng-4967 615 13 a.e a.e PROPN fumecheng-4967 615 14 . . PROPN fumecheng-4967 615 15 , , PUNCT fumecheng-4967 615 16 2000 2000 NUM fumecheng-4967 615 17 , , PUNCT fumecheng-4967 615 18 a a DET fumecheng-4967 615 19 mathematical mathematical ADJ fumecheng-4967 615 20 model model NOUN fumecheng-4967 615 21 of of ADP fumecheng-4967 615 22 competitive competitive ADJ fumecheng-4967 615 23 selforganization selforganization NOUN fumecheng-4967 615 24 , , PUNCT fumecheng-4967 615 25 j. j. PROPN fumecheng-4967 615 26 complexity complexity PROPN fumecheng-4967 615 27 int int PROPN fumecheng-4967 615 28 . . PUNCT fumecheng-4967 616 1 , , PUNCT fumecheng-4967 616 2 8 8 NUM fumecheng-4967 616 3 , , PUNCT fumecheng-4967 616 4 pp pp ADJ fumecheng-4967 616 5 . . PUNCT fumecheng-4967 617 1 1 1 NUM fumecheng-4967 617 2 - - SYM fumecheng-4967 617 3 10 10 NUM fumecheng-4967 617 4 . . PUNCT fumecheng-4967 618 1 14 14 NUM fumecheng-4967 618 2 . . PUNCT fumecheng-4967 619 1 kosterlitz kosterlitz PROPN fumecheng-4967 619 2 , , PUNCT fumecheng-4967 619 3 j.m j.m PROPN fumecheng-4967 619 4 . . PROPN fumecheng-4967 619 5 , , PUNCT fumecheng-4967 619 6 thouless thouless NOUN fumecheng-4967 619 7 , , PUNCT fumecheng-4967 619 8 d.j d.j PROPN fumecheng-4967 619 9 . . PROPN fumecheng-4967 619 10 , , PUNCT fumecheng-4967 619 11 1973 1973 NUM fumecheng-4967 619 12 , , PUNCT fumecheng-4967 619 13 ordering ordering NOUN fumecheng-4967 619 14 , , PUNCT fumecheng-4967 619 15 metastability metastability NOUN fumecheng-4967 619 16 and and CCONJ fumecheng-4967 619 17 phase phase NOUN fumecheng-4967 619 18 transitions transition NOUN fumecheng-4967 619 19 in in ADP fumecheng-4967 619 20 two two NUM fumecheng-4967 619 21 - - PUNCT fumecheng-4967 619 22 dimensional dimensional ADJ fumecheng-4967 619 23 systems system NOUN fumecheng-4967 619 24 , , PUNCT fumecheng-4967 619 25 j. j. PROPN fumecheng-4967 619 26 phys phys PROPN fumecheng-4967 619 27 . . PUNCT fumecheng-4967 620 1 c c X fumecheng-4967 620 2 : : PUNCT fumecheng-4967 620 3 solid solid ADJ fumecheng-4967 620 4 state state NOUN fumecheng-4967 620 5 physics physics NOUN fumecheng-4967 620 6 , , PUNCT fumecheng-4967 620 7 6 6 NUM fumecheng-4967 620 8 , , PUNCT fumecheng-4967 620 9 pp pp ADJ fumecheng-4967 620 10 . . PUNCT fumecheng-4967 621 1 1181–1203 1181–1203 NUM fumecheng-4967 621 2 . . PUNCT fumecheng-4967 622 1 15 15 NUM fumecheng-4967 622 2 . . PUNCT fumecheng-4967 623 1 kovalev kovalev PROPN fumecheng-4967 623 2 , , PUNCT fumecheng-4967 623 3 a a PRON fumecheng-4967 623 4 , , PUNCT fumecheng-4967 623 5 filippov filippov NOUN fumecheng-4967 623 6 , , PUNCT fumecheng-4967 623 7 a.e a.e PROPN fumecheng-4967 623 8 . . PROPN fumecheng-4967 623 9 , , PUNCT fumecheng-4967 623 10 gorb gorb PROPN fumecheng-4967 623 11 , , PUNCT fumecheng-4967 623 12 s.n s.n PROPN fumecheng-4967 623 13 . . PROPN fumecheng-4967 623 14 , , PUNCT fumecheng-4967 623 15 2016 2016 NUM fumecheng-4967 623 16 , , PUNCT fumecheng-4967 623 17 correlation correlation NOUN fumecheng-4967 623 18 analysis analysis NOUN fumecheng-4967 623 19 of of ADP fumecheng-4967 623 20 symmetry symmetry NOUN fumecheng-4967 623 21 breaking break VERB fumecheng-4967 623 22 in in ADP fumecheng-4967 623 23 the the DET fumecheng-4967 623 24 surface surface NOUN fumecheng-4967 623 25 nanostructure nanostructure NOUN fumecheng-4967 623 26 ordering ordering NOUN fumecheng-4967 623 27 : : PUNCT fumecheng-4967 623 28 case case NOUN fumecheng-4967 623 29 study study NOUN fumecheng-4967 623 30 of of ADP fumecheng-4967 623 31 the the DET fumecheng-4967 623 32 ventral ventral ADJ fumecheng-4967 623 33 scale scale NOUN fumecheng-4967 623 34 of of ADP fumecheng-4967 623 35 the the DET fumecheng-4967 623 36 snake snake NOUN fumecheng-4967 623 37 morelia morelia PROPN fumecheng-4967 623 38 viridis viridis PROPN fumecheng-4967 623 39 , , PUNCT fumecheng-4967 623 40 appl appl PROPN fumecheng-4967 623 41 . . PUNCT fumecheng-4967 624 1 phys phy NOUN fumecheng-4967 624 2 . . PUNCT fumecheng-4967 625 1 a a DET fumecheng-4967 625 2 , , PUNCT fumecheng-4967 625 3 122(253 122(253 NUM fumecheng-4967 625 4 ) ) PUNCT fumecheng-4967 625 5 , , PUNCT fumecheng-4967 626 1 pp pp ADP fumecheng-4967 626 2 . . PUNCT fumecheng-4967 627 1 3 3 NUM fumecheng-4967 627 2 - - SYM fumecheng-4967 627 3 6 6 NUM fumecheng-4967 627 4 . . NOUN fumecheng-4967 627 5 16 16 NUM fumecheng-4967 627 6 . . PUNCT fumecheng-4967 628 1 filippov filippov NOUN fumecheng-4967 628 2 , , PUNCT fumecheng-4967 628 3 a.e a.e PROPN fumecheng-4967 628 4 , , PUNCT fumecheng-4967 628 5 wolff wolff PROPN fumecheng-4967 628 6 , , PUNCT fumecheng-4967 628 7 j.o j.o PROPN fumecheng-4967 628 8 . . PROPN fumecheng-4967 628 9 , , PUNCT fumecheng-4967 628 10 seiter seiter NOUN fumecheng-4967 628 11 , , PUNCT fumecheng-4967 628 12 m. m. NOUN fumecheng-4967 628 13 , , PUNCT fumecheng-4967 628 14 gorb gorb PROPN fumecheng-4967 628 15 , , PUNCT fumecheng-4967 628 16 s.n s.n PROPN fumecheng-4967 628 17 . . PROPN fumecheng-4967 628 18 , , PUNCT fumecheng-4967 628 19 2017 2017 NUM fumecheng-4967 628 20 , , PUNCT fumecheng-4967 628 21 numerical numerical ADJ fumecheng-4967 628 22 simulation simulation NOUN fumecheng-4967 628 23 of of ADP fumecheng-4967 628 24 colloidal colloidal NOUN fumecheng-4967 628 25 self self NOUN fumecheng-4967 628 26 - - PUNCT fumecheng-4967 628 27 assembly assembly NOUN fumecheng-4967 628 28 of of ADP fumecheng-4967 628 29 super super ADJ fumecheng-4967 628 30 - - ADJ fumecheng-4967 628 31 hydrophobic hydrophobic ADJ fumecheng-4967 628 32 arachnid arachnid NOUN fumecheng-4967 628 33 cerotegument cerotegument NOUN fumecheng-4967 628 34 structures structure NOUN fumecheng-4967 628 35 , , PUNCT fumecheng-4967 628 36 j. j. PROPN fumecheng-4967 628 37 theor theor PROPN fumecheng-4967 628 38 . . PUNCT fumecheng-4967 629 1 biol biol PROPN fumecheng-4967 629 2 . . PUNCT fumecheng-4967 629 3 , , PUNCT fumecheng-4967 629 4 430 430 NUM fumecheng-4967 629 5 , , PUNCT fumecheng-4967 629 6 pp pp ADJ fumecheng-4967 629 7 . . PUNCT fumecheng-4967 630 1 1 1 NUM fumecheng-4967 630 2 - - SYM fumecheng-4967 630 3 8 8 NUM fumecheng-4967 630 4 . . PUNCT