id sid tid token lemma pos cana-6326 1 1 communications communication NOUN cana-6326 1 2 on on ADP cana-6326 1 3 applied apply VERB cana-6326 1 4 nonlinear nonlinear ADJ cana-6326 1 5 analysis analysis NOUN cana-6326 1 6 issn issn NOUN cana-6326 1 7 : : PUNCT cana-6326 1 8 1074 1074 NUM cana-6326 1 9 - - PUNCT cana-6326 1 10 133x 133x NUM cana-6326 1 11 vol vol VERB cana-6326 1 12 32 32 NUM cana-6326 1 13 no no NOUN cana-6326 1 14 . . PUNCT cana-6326 2 1 10s 10 NOUN cana-6326 2 2 ( ( PUNCT cana-6326 2 3 2025 2025 NUM cana-6326 2 4 ) ) PUNCT cana-6326 2 5 3715 3715 NUM cana-6326 2 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 2 7 effect effect NOUN cana-6326 2 8 of of ADP cana-6326 2 9 linearly linearly ADV cana-6326 2 10 distributed distribute VERB cana-6326 2 11 sources source NOUN cana-6326 2 12 in in ADP cana-6326 2 13 normal normal ADJ cana-6326 2 14 loading loading NOUN cana-6326 2 15 of of ADP cana-6326 2 16 a a DET cana-6326 2 17 dualphase dualphase NOUN cana-6326 2 18 - - PUNCT cana-6326 2 19 lag lag NOUN cana-6326 2 20 thermoelastic thermoelastic ADJ cana-6326 2 21 diffusion diffusion NOUN cana-6326 2 22 with with ADP cana-6326 2 23 non non ADJ cana-6326 2 24 - - ADJ cana-6326 2 25 local local ADJ cana-6326 2 26 formulation formulation NOUN cana-6326 2 27 rajneesh rajneesh PROPN cana-6326 2 28 kumar1 kumar1 PROPN cana-6326 2 29 , , PUNCT cana-6326 2 30 pawan pawan PROPN cana-6326 2 31 kumari2 kumari2 PROPN cana-6326 2 32 , , PUNCT cana-6326 2 33 kavita kavita PROPN cana-6326 2 34 rani3 rani3 PROPN cana-6326 2 35 , , PUNCT cana-6326 2 36 seetu seetu VERB cana-6326 2 37 rana4 rana4 NOUN cana-6326 3 1 1department 1department NUM cana-6326 3 2 of of ADP cana-6326 3 3 mathematics mathematics PROPN cana-6326 3 4 , , PUNCT cana-6326 3 5 kurukshetra kurukshetra PROPN cana-6326 3 6 university university PROPN cana-6326 3 7 , , PUNCT cana-6326 3 8 kurukshetra kurukshetra PROPN cana-6326 3 9 136119 136119 NUM cana-6326 3 10 , , PUNCT cana-6326 3 11 india india PROPN cana-6326 3 12 email email NOUN cana-6326 3 13 : : PUNCT cana-6326 3 14 rajneeshkuk@rediffmail.com rajneeshkuk@rediffmail.com X cana-6326 3 15 2 2 NUM cana-6326 3 16 associate associate NOUN cana-6326 3 17 professor professor NOUN cana-6326 3 18 , , PUNCT cana-6326 3 19 department department NOUN cana-6326 3 20 of of ADP cana-6326 3 21 mathematics mathematic NOUN cana-6326 3 22 , , PUNCT cana-6326 3 23 govt govt NOUN cana-6326 3 24 . . PUNCT cana-6326 4 1 college college PROPN cana-6326 4 2 , , PUNCT cana-6326 4 3 hisar hisar PROPN cana-6326 4 4 , , PUNCT cana-6326 4 5 haryana,125001 haryana,125001 PROPN cana-6326 4 6 india india PROPN cana-6326 4 7 email email NOUN cana-6326 4 8 : : PUNCT cana-6326 4 9 pawankumarigawarya@gmail.com pawankumarigawarya@gmail.com X cana-6326 4 10 3associate 3associate NUM cana-6326 4 11 professor professor NOUN cana-6326 4 12 , , PUNCT cana-6326 4 13 department department NOUN cana-6326 4 14 of of ADP cana-6326 4 15 mathematics mathematics PROPN cana-6326 4 16 , , PUNCT cana-6326 4 17 cmg cmg PROPN cana-6326 4 18 gcw gcw PROPN cana-6326 4 19 , , PUNCT cana-6326 4 20 bhodia bhodia NOUN cana-6326 4 21 khera khera PROPN cana-6326 4 22 , , PUNCT cana-6326 4 23 fatehabad fatehabad PROPN cana-6326 4 24 , , PUNCT cana-6326 4 25 haryana,125050 haryana,125050 PROPN cana-6326 4 26 , , PUNCT cana-6326 4 27 india india PROPN cana-6326 4 28 email email NOUN cana-6326 4 29 : : PUNCT cana-6326 4 30 karya4@gmail.com karya4@gmail.com X cana-6326 4 31 4 4 NUM cana-6326 4 32 assistant assistant NOUN cana-6326 4 33 professor professor NOUN cana-6326 4 34 , , PUNCT cana-6326 4 35 department department NOUN cana-6326 4 36 of of ADP cana-6326 4 37 mathematics mathematic NOUN cana-6326 4 38 , , PUNCT cana-6326 4 39 govt govt NOUN cana-6326 4 40 . . PUNCT cana-6326 5 1 college college PROPN cana-6326 5 2 , , PUNCT cana-6326 5 3 hisar hisar PROPN cana-6326 5 4 , , PUNCT cana-6326 5 5 haryana,125001 haryana,125001 PROPN cana-6326 5 6 india india PROPN cana-6326 5 7 email email NOUN cana-6326 5 8 : : PUNCT cana-6326 5 9 rana.seetu@gmail.com rana.seetu@gmail.com X cana-6326 5 10 article article NOUN cana-6326 5 11 history history NOUN cana-6326 5 12 : : PUNCT cana-6326 5 13 received receive VERB cana-6326 5 14 : : PUNCT cana-6326 5 15 04 04 NUM cana-6326 5 16 - - SYM cana-6326 5 17 10 10 NUM cana-6326 5 18 - - PUNCT cana-6326 5 19 2025 2025 NUM cana-6326 5 20 revised revise VERB cana-6326 5 21 : : PUNCT cana-6326 5 22 23 23 NUM cana-6326 5 23 - - SYM cana-6326 5 24 11 11 NUM cana-6326 5 25 - - PUNCT cana-6326 5 26 2025 2025 NUM cana-6326 5 27 accepted accept VERB cana-6326 5 28 : : PUNCT cana-6326 5 29 14 14 NUM cana-6326 5 30 - - SYM cana-6326 5 31 12 12 NUM cana-6326 5 32 - - PUNCT cana-6326 5 33 2025 2025 NUM cana-6326 5 34 abstract abstract NOUN cana-6326 5 35 : : PUNCT cana-6326 5 36 the the DET cana-6326 5 37 present present ADJ cana-6326 5 38 study study NOUN cana-6326 5 39 aims aim VERB cana-6326 5 40 at at ADP cana-6326 5 41 exploring explore VERB cana-6326 5 42 the the DET cana-6326 5 43 effects effect NOUN cana-6326 5 44 of of ADP cana-6326 5 45 non non ADJ cana-6326 5 46 - - ADJ cana-6326 5 47 locality locality ADJ cana-6326 5 48 and and CCONJ cana-6326 5 49 dual dual ADJ cana-6326 5 50 - - PUNCT cana-6326 5 51 phase phase NOUN cana-6326 5 52 - - PUNCT cana-6326 5 53 lags lag NOUN cana-6326 5 54 in in ADP cana-6326 5 55 a a DET cana-6326 5 56 thermoelastic thermoelastic ADJ cana-6326 5 57 half half ADJ cana-6326 5 58 - - PUNCT cana-6326 5 59 space space NOUN cana-6326 5 60 subjected subject VERB cana-6326 5 61 to to ADP cana-6326 5 62 normal normal ADJ cana-6326 5 63 loading loading NOUN cana-6326 5 64 . . PUNCT cana-6326 6 1 the the DET cana-6326 6 2 governing govern VERB cana-6326 6 3 equations equation NOUN cana-6326 6 4 are be AUX cana-6326 6 5 solved solve VERB cana-6326 6 6 using use VERB cana-6326 6 7 harmonic harmonic ADJ cana-6326 6 8 vibration vibration NOUN cana-6326 6 9 analysis analysis NOUN cana-6326 6 10 coupled couple VERB cana-6326 6 11 with with ADP cana-6326 6 12 fourier fourier NOUN cana-6326 6 13 transform transform NOUN cana-6326 6 14 techniques technique NOUN cana-6326 6 15 . . PUNCT cana-6326 7 1 linearly linearly ADV cana-6326 7 2 distributed distribute VERB cana-6326 7 3 sources source NOUN cana-6326 7 4 are be AUX cana-6326 7 5 considered consider VERB cana-6326 7 6 to to PART cana-6326 7 7 demonstrate demonstrate VERB cana-6326 7 8 practical practical ADJ cana-6326 7 9 relevance relevance NOUN cana-6326 7 10 for for ADP cana-6326 7 11 mechanical mechanical ADJ cana-6326 7 12 excitations excitation NOUN cana-6326 7 13 . . PUNCT cana-6326 8 1 numerical numerical ADJ cana-6326 8 2 simulations simulation NOUN cana-6326 8 3 are be AUX cana-6326 8 4 performed perform VERB cana-6326 8 5 to to PART cana-6326 8 6 evaluate evaluate VERB cana-6326 8 7 displacements displacement NOUN cana-6326 8 8 , , PUNCT cana-6326 8 9 stresses stress NOUN cana-6326 8 10 , , PUNCT cana-6326 8 11 temperature temperature NOUN cana-6326 8 12 variations variation NOUN cana-6326 8 13 and and CCONJ cana-6326 8 14 chemical chemical NOUN cana-6326 8 15 potential potential NOUN cana-6326 8 16 , , PUNCT cana-6326 8 17 with with ADP cana-6326 8 18 results result NOUN cana-6326 8 19 presented present VERB cana-6326 8 20 graphically graphically ADV cana-6326 8 21 . . PUNCT cana-6326 9 1 the the DET cana-6326 9 2 study study NOUN cana-6326 9 3 is be AUX cana-6326 9 4 applicable applicable ADJ cana-6326 9 5 to to ADP cana-6326 9 6 predicting predict VERB cana-6326 9 7 the the DET cana-6326 9 8 mechanical mechanical ADJ cana-6326 9 9 responses response NOUN cana-6326 9 10 in in ADP cana-6326 9 11 electronics electronic NOUN cana-6326 9 12 devices device NOUN cana-6326 9 13 , , PUNCT cana-6326 9 14 aerospace aerospace NOUN cana-6326 9 15 components component NOUN cana-6326 9 16 , , PUNCT cana-6326 9 17 and and CCONJ cana-6326 9 18 energy energy NOUN cana-6326 9 19 systems system NOUN cana-6326 9 20 subjected subject VERB cana-6326 9 21 to to ADP cana-6326 9 22 time time NOUN cana-6326 9 23 - - PUNCT cana-6326 9 24 harmonic harmonic ADJ cana-6326 9 25 loads load NOUN cana-6326 9 26 . . PUNCT cana-6326 10 1 keywords keyword NOUN cana-6326 10 2 : : PUNCT cana-6326 10 3 thermoelasticity thermoelasticity NOUN cana-6326 10 4 , , PUNCT cana-6326 10 5 non non ADJ cana-6326 10 6 - - ADJ cana-6326 10 7 local local ADJ cana-6326 10 8 theory theory NOUN cana-6326 10 9 , , PUNCT cana-6326 10 10 dual dual ADJ cana-6326 10 11 - - PUNCT cana-6326 10 12 phase phase NOUN cana-6326 10 13 - - PUNCT cana-6326 10 14 lag lag NOUN cana-6326 10 15 , , PUNCT cana-6326 10 16 fourier fourier NOUN cana-6326 10 17 transform transform NOUN cana-6326 10 18 , , PUNCT cana-6326 10 19 time time NOUN cana-6326 10 20 harmonic harmonic ADJ cana-6326 10 21 sources source NOUN cana-6326 10 22 . . PUNCT cana-6326 11 1 1 1 X cana-6326 11 2 . . X cana-6326 11 3 introduction introduction NOUN cana-6326 11 4 in in ADP cana-6326 11 5 non non ADJ cana-6326 11 6 - - ADJ cana-6326 11 7 local local ADJ cana-6326 11 8 elasticity elasticity NOUN cana-6326 11 9 , , PUNCT cana-6326 11 10 the the DET cana-6326 11 11 stress stress NOUN cana-6326 11 12 at at ADP cana-6326 11 13 a a DET cana-6326 11 14 point point NOUN cana-6326 11 15 is be AUX cana-6326 11 16 affected affect VERB cana-6326 11 17 by by ADP cana-6326 11 18 both both CCONJ cana-6326 11 19 the the DET cana-6326 11 20 local local ADJ cana-6326 11 21 strain strain NOUN cana-6326 11 22 and and CCONJ cana-6326 11 23 the the DET cana-6326 11 24 strain strain ADJ cana-6326 11 25 distribution distribution NOUN cana-6326 11 26 throughout throughout ADP cana-6326 11 27 the the DET cana-6326 11 28 body body NOUN cana-6326 11 29 . . PUNCT cana-6326 12 1 this this PRON cana-6326 12 2 is be AUX cana-6326 12 3 different different ADJ cana-6326 12 4 from from ADP cana-6326 12 5 classical classical ADJ cana-6326 12 6 ( ( PUNCT cana-6326 12 7 local local ADJ cana-6326 12 8 ) ) PUNCT cana-6326 12 9 elasticity elasticity NOUN cana-6326 12 10 , , PUNCT cana-6326 12 11 which which PRON cana-6326 12 12 says say VERB cana-6326 12 13 that that SCONJ cana-6326 12 14 the the DET cana-6326 12 15 stress stress NOUN cana-6326 12 16 at at ADP cana-6326 12 17 a a DET cana-6326 12 18 point point NOUN cana-6326 12 19 is be AUX cana-6326 12 20 only only ADV cana-6326 12 21 affected affect VERB cana-6326 12 22 by by ADP cana-6326 12 23 the the DET cana-6326 12 24 strain strain NOUN cana-6326 12 25 at at ADP cana-6326 12 26 that that DET cana-6326 12 27 point point NOUN cana-6326 12 28 . . PUNCT cana-6326 13 1 researchers researcher NOUN cana-6326 13 2 like like ADP cana-6326 13 3 edelen edelen NOUN cana-6326 13 4 and and CCONJ cana-6326 13 5 laws law NOUN cana-6326 13 6 [ [ X cana-6326 13 7 1 1 NUM cana-6326 13 8 ] ] PUNCT cana-6326 13 9 , , PUNCT cana-6326 13 10 eringen eringen NOUN cana-6326 13 11 and and CCONJ cana-6326 13 12 edelen edelen ADJ cana-6326 13 13 [ [ X cana-6326 13 14 2 2 NUM cana-6326 13 15 ] ] PUNCT cana-6326 13 16 , , PUNCT cana-6326 13 17 and and CCONJ cana-6326 13 18 others other NOUN cana-6326 13 19 built build VERB cana-6326 13 20 on on ADP cana-6326 13 21 these these DET cana-6326 13 22 ideas idea NOUN cana-6326 13 23 to to PART cana-6326 13 24 find find VERB cana-6326 13 25 the the DET cana-6326 13 26 basics basic NOUN cana-6326 13 27 of of ADP cana-6326 13 28 non non ADJ cana-6326 13 29 - - ADJ cana-6326 13 30 local local ADJ cana-6326 13 31 elasticity elasticity NOUN cana-6326 13 32 . . PUNCT cana-6326 14 1 later later ADV cana-6326 14 2 , , PUNCT cana-6326 14 3 eringen eringen PROPN cana-6326 14 4 [ [ X cana-6326 14 5 3 3 NUM cana-6326 14 6 - - SYM cana-6326 14 7 8 8 NUM cana-6326 14 8 ] ] PUNCT cana-6326 14 9 , , PUNCT cana-6326 14 10 mccay mccay NOUN cana-6326 14 11 and and CCONJ cana-6326 14 12 narsimhan narsimhan ADV cana-6326 14 13 [ [ X cana-6326 14 14 9 9 NUM cana-6326 14 15 ] ] PUNCT cana-6326 14 16 , , PUNCT cana-6326 14 17 and and CCONJ cana-6326 14 18 narsimhan narsimhan ADV cana-6326 14 19 and and CCONJ cana-6326 14 20 mccay mccay VERB cana-6326 14 21 [ [ X cana-6326 14 22 10 10 NUM cana-6326 14 23 ] ] PUNCT cana-6326 14 24 added add VERB cana-6326 14 25 to to ADP cana-6326 14 26 these these DET cana-6326 14 27 ideas idea NOUN cana-6326 14 28 . . PUNCT cana-6326 15 1 eringen eringen PROPN cana-6326 15 2 's 's PART cana-6326 15 3 monograph monograph NOUN cana-6326 15 4 [ [ X cana-6326 15 5 11 11 NUM cana-6326 15 6 ] ] PUNCT cana-6326 15 7 goes go VERB cana-6326 15 8 into into ADP cana-6326 15 9 a a DET cana-6326 15 10 lot lot NOUN cana-6326 15 11 of of ADP cana-6326 15 12 detail detail NOUN cana-6326 15 13 about about ADP cana-6326 15 14 the the DET cana-6326 15 15 subject subject NOUN cana-6326 15 16 . . PUNCT cana-6326 16 1 non non ADJ cana-6326 16 2 - - ADJ cana-6326 16 3 local local ADJ cana-6326 16 4 response response NOUN cana-6326 16 5 and and CCONJ cana-6326 16 6 lagging lag VERB cana-6326 16 7 response response NOUN cana-6326 16 8 are be AUX cana-6326 16 9 related related ADJ cana-6326 16 10 ideas idea NOUN cana-6326 16 11 . . PUNCT cana-6326 17 1 non non ADJ cana-6326 17 2 - - ADJ cana-6326 17 3 local local ADJ cana-6326 17 4 response response NOUN cana-6326 17 5 is be AUX cana-6326 17 6 about about ADP cana-6326 17 7 effects effect NOUN cana-6326 17 8 in in ADP cana-6326 17 9 space space NOUN cana-6326 17 10 and and CCONJ cana-6326 17 11 lagging lag VERB cana-6326 17 12 response response NOUN cana-6326 17 13 is be AUX cana-6326 17 14 about about ADP cana-6326 17 15 delays delay NOUN cana-6326 17 16 in in ADP cana-6326 17 17 time time NOUN cana-6326 17 18 . . PUNCT cana-6326 18 1 the the DET cana-6326 18 2 results result NOUN cana-6326 18 3 were be AUX cana-6326 18 4 compared compare VERB cana-6326 18 5 with with ADP cana-6326 18 6 the the DET cana-6326 18 7 models model NOUN cana-6326 18 8 of of ADP cana-6326 18 9 cao cao PROPN cana-6326 18 10 and and CCONJ cana-6326 18 11 guo guo PROPN cana-6326 19 1 [ [ X cana-6326 19 2 13 13 NUM cana-6326 19 3 ] ] PUNCT cana-6326 19 4 and and CCONJ cana-6326 19 5 guo guo PROPN cana-6326 19 6 and and CCONJ cana-6326 19 7 hou hou NOUN cana-6326 20 1 [ [ X cana-6326 20 2 14 14 NUM cana-6326 20 3 ] ] PUNCT cana-6326 20 4 by by ADP cana-6326 20 5 tzou tzou NOUN cana-6326 20 6 [ [ X cana-6326 20 7 12 12 NUM cana-6326 20 8 ] ] PUNCT cana-6326 20 9 . . PUNCT cana-6326 21 1 he he PRON cana-6326 21 2 used use VERB cana-6326 21 3 the the DET cana-6326 21 4 non non ADJ cana-6326 21 5 - - ADJ cana-6326 21 6 local local ADJ cana-6326 21 7 formulation formulation NOUN cana-6326 21 8 and and CCONJ cana-6326 21 9 single single ADJ cana-6326 21 10 - - PUNCT cana-6326 21 11 phase phase NOUN cana-6326 21 12 - - PUNCT cana-6326 21 13 lag lag NOUN cana-6326 21 14 heat heat NOUN cana-6326 21 15 conduction conduction NOUN cana-6326 21 16 . . PUNCT cana-6326 22 1 later later ADV cana-6326 22 2 , , PUNCT cana-6326 22 3 tzou tzou NOUN cana-6326 22 4 and and CCONJ cana-6326 22 5 gao gao PROPN cana-6326 23 1 [ [ X cana-6326 23 2 15 15 NUM cana-6326 23 3 ] ] PUNCT cana-6326 23 4 built build VERB cana-6326 23 5 on on ADP cana-6326 23 6 this this DET cana-6326 23 7 idea idea NOUN cana-6326 23 8 by by ADP cana-6326 23 9 adding add VERB cana-6326 23 10 non non ADJ cana-6326 23 11 - - ADJ cana-6326 23 12 local local ADJ cana-6326 23 13 elasticity elasticity NOUN cana-6326 23 14 to to ADP cana-6326 23 15 the the DET cana-6326 23 16 dual dual ADJ cana-6326 23 17 - - PUNCT cana-6326 23 18 phase phase NOUN cana-6326 23 19 - - PUNCT cana-6326 23 20 lag lag NOUN cana-6326 23 21 model model NOUN cana-6326 23 22 that that PRON cana-6326 23 23 tzou tzou VERB cana-6326 23 24 [ [ X cana-6326 23 25 16,17 16,17 NUM cana-6326 23 26 ] ] PUNCT cana-6326 23 27 had have AUX cana-6326 23 28 first first ADV cana-6326 23 29 suggested suggest VERB cana-6326 23 30 . . PUNCT cana-6326 24 1 this this PRON cana-6326 24 2 created create VERB cana-6326 24 3 a a DET cana-6326 24 4 single single ADJ cana-6326 24 5 mailto:pawankumarigawarya@gmail.com mailto:pawankumarigawarya@gmail.com NOUN cana-6326 24 6 communications communication NOUN cana-6326 24 7 on on ADP cana-6326 24 8 applied apply VERB cana-6326 24 9 nonlinear nonlinear ADJ cana-6326 24 10 analysis analysis NOUN cana-6326 24 11 issn issn NOUN cana-6326 24 12 : : PUNCT cana-6326 24 13 1074 1074 NUM cana-6326 24 14 - - PUNCT cana-6326 24 15 133x 133x NUM cana-6326 24 16 vol vol VERB cana-6326 24 17 32 32 NUM cana-6326 24 18 no no NOUN cana-6326 24 19 . . PUNCT cana-6326 25 1 10s 10 NOUN cana-6326 25 2 ( ( PUNCT cana-6326 25 3 2025 2025 NUM cana-6326 25 4 ) ) PUNCT cana-6326 25 5 3716 3716 NUM cana-6326 25 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 25 7 framework framework NOUN cana-6326 25 8 that that PRON cana-6326 25 9 included include VERB cana-6326 25 10 both both DET cana-6326 25 11 effects effect NOUN cana-6326 25 12 . . PUNCT cana-6326 26 1 at at ADP cana-6326 26 2 the the DET cana-6326 26 3 same same ADJ cana-6326 26 4 time time NOUN cana-6326 26 5 , , PUNCT cana-6326 26 6 sherief sherief NOUN cana-6326 26 7 et et PROPN cana-6326 26 8 al al PROPN cana-6326 26 9 . . PUNCT cana-6326 27 1 [ [ X cana-6326 27 2 18 18 NUM cana-6326 27 3 ] ] PUNCT cana-6326 27 4 created create VERB cana-6326 27 5 a a DET cana-6326 27 6 thermoelastic thermoelastic ADJ cana-6326 27 7 diffusion diffusion NOUN cana-6326 27 8 theory theory NOUN cana-6326 27 9 with with ADP cana-6326 27 10 a a DET cana-6326 27 11 single single ADJ cana-6326 27 12 relaxation relaxation NOUN cana-6326 27 13 time time NOUN cana-6326 27 14 , , PUNCT cana-6326 27 15 and and CCONJ cana-6326 27 16 sherief sherief NOUN cana-6326 27 17 and and CCONJ cana-6326 27 18 saleh saleh NOUN cana-6326 27 19 [ [ X cana-6326 27 20 19 19 NUM cana-6326 27 21 ] ] PUNCT cana-6326 27 22 looked look VERB cana-6326 27 23 at at ADP cana-6326 27 24 the the DET cana-6326 27 25 half half ADJ cana-6326 27 26 - - PUNCT cana-6326 27 27 space space NOUN cana-6326 27 28 problem problem NOUN cana-6326 27 29 in in ADP cana-6326 27 30 this this DET cana-6326 27 31 context context NOUN cana-6326 27 32 . . PUNCT cana-6326 28 1 later later ADJ cana-6326 28 2 additions addition NOUN cana-6326 28 3 to to ADP cana-6326 28 4 these these DET cana-6326 28 5 theories theory NOUN cana-6326 28 6 made make VERB cana-6326 28 7 them they PRON cana-6326 28 8 more more ADV cana-6326 28 9 general general ADJ cana-6326 28 10 . . PUNCT cana-6326 29 1 in in ADP cana-6326 29 2 his his PRON cana-6326 29 3 work work NOUN cana-6326 29 4 [ [ X cana-6326 29 5 20,21 20,21 NUM cana-6326 29 6 ] ] PUNCT cana-6326 29 7 , , PUNCT cana-6326 29 8 sharma sharma PROPN cana-6326 29 9 looked look VERB cana-6326 29 10 into into ADP cana-6326 29 11 boundary boundary ADJ cana-6326 29 12 - - PUNCT cana-6326 29 13 value value NOUN cana-6326 29 14 problems problem NOUN cana-6326 29 15 in in ADP cana-6326 29 16 generalized generalize VERB cana-6326 29 17 thermodiffusive thermodiffusive PRON cana-6326 29 18 elastic elastic ADJ cana-6326 29 19 media medium NOUN cana-6326 29 20 and and CCONJ cana-6326 29 21 wave wave NOUN cana-6326 29 22 reflection reflection NOUN cana-6326 29 23 in in ADP cana-6326 29 24 thermodiffusive thermodiffusive ADJ cana-6326 29 25 elastic elastic ADJ cana-6326 29 26 half half ADJ cana-6326 29 27 - - PUNCT cana-6326 29 28 spaces space NOUN cana-6326 29 29 with with ADP cana-6326 29 30 holes hole NOUN cana-6326 29 31 . . PUNCT cana-6326 30 1 sharma sharma PROPN cana-6326 30 2 et et PROPN cana-6326 30 3 al al PROPN cana-6326 30 4 . . PUNCT cana-6326 31 1 [ [ X cana-6326 31 2 22 22 NUM cana-6326 31 3 ] ] PUNCT cana-6326 31 4 looked look VERB cana-6326 31 5 at at ADP cana-6326 31 6 how how SCONJ cana-6326 31 7 viscosity viscosity NOUN cana-6326 31 8 affects affect VERB cana-6326 31 9 wave wave NOUN cana-6326 31 10 propagation propagation NOUN cana-6326 31 11 in in ADP cana-6326 31 12 green green ADJ cana-6326 31 13 – – PUNCT cana-6326 31 14 naghdi naghdi NOUN cana-6326 31 15 type type NOUN cana-6326 31 16 - - PUNCT cana-6326 31 17 ii ii NOUN cana-6326 31 18 and and CCONJ cana-6326 31 19 type type NOUN cana-6326 31 20 - - PUNCT cana-6326 31 21 iii iii NOUN cana-6326 31 22 thermoelastic thermoelastic ADJ cana-6326 31 23 solids solid NOUN cana-6326 31 24 that that PRON cana-6326 31 25 are be AUX cana-6326 31 26 not not PART cana-6326 31 27 all all DET cana-6326 31 28 the the DET cana-6326 31 29 same same ADJ cana-6326 31 30 . . PUNCT cana-6326 32 1 sharma sharma PROPN cana-6326 32 2 and and CCONJ cana-6326 32 3 marin marin NOUN cana-6326 33 1 [ [ X cana-6326 33 2 23 23 NUM cana-6326 33 3 ] ] PUNCT cana-6326 33 4 studied study VERB cana-6326 33 5 the the DET cana-6326 33 6 problem problem NOUN cana-6326 33 7 of of ADP cana-6326 33 8 reflection reflection NOUN cana-6326 33 9 and and CCONJ cana-6326 33 10 transmission transmission NOUN cana-6326 33 11 of of ADP cana-6326 33 12 plane plane NOUN cana-6326 33 13 waves wave NOUN cana-6326 33 14 from from ADP cana-6326 33 15 imperfect imperfect ADJ cana-6326 33 16 boundary boundary NOUN cana-6326 33 17 between between ADP cana-6326 33 18 two two NUM cana-6326 33 19 heat heat NOUN cana-6326 33 20 conducting conduct VERB cana-6326 33 21 micropolar micropolar ADJ cana-6326 33 22 thermoelastic thermoelastic ADJ cana-6326 33 23 solids solid NOUN cana-6326 33 24 . . PUNCT cana-6326 34 1 abouelregal abouelregal ADJ cana-6326 34 2 and and CCONJ cana-6326 34 3 zenkour zenkour PRON cana-6326 35 1 [ [ X cana-6326 35 2 24 24 NUM cana-6326 35 3 ] ] PUNCT cana-6326 35 4 looked look VERB cana-6326 35 5 at at ADP cana-6326 35 6 phase phase NOUN cana-6326 35 7 - - PUNCT cana-6326 35 8 lag lag NOUN cana-6326 35 9 effects effect NOUN cana-6326 35 10 in in ADP cana-6326 35 11 functionally functionally ADV cana-6326 35 12 graded grade VERB cana-6326 35 13 thermoelastic thermoelastic ADJ cana-6326 35 14 microbeams microbeam NOUN cana-6326 35 15 that that PRON cana-6326 35 16 were be AUX cana-6326 35 17 heated heat VERB cana-6326 35 18 in in ADP cana-6326 35 19 a a DET cana-6326 35 20 ramp ramp NOUN cana-6326 35 21 - - PUNCT cana-6326 35 22 type type NOUN cana-6326 35 23 way way NOUN cana-6326 35 24 . . PUNCT cana-6326 36 1 sharma sharma PROPN cana-6326 36 2 and and CCONJ cana-6326 36 3 sharma sharma PROPN cana-6326 36 4 [ [ X cana-6326 36 5 25 25 NUM cana-6326 36 6 ] ] PUNCT cana-6326 36 7 looked look VERB cana-6326 36 8 at at ADP cana-6326 36 9 how how SCONJ cana-6326 36 10 heat heat NOUN cana-6326 36 11 sources source NOUN cana-6326 36 12 and and CCONJ cana-6326 36 13 relaxation relaxation NOUN cana-6326 36 14 time time NOUN cana-6326 36 15 affect affect VERB cana-6326 36 16 the the DET cana-6326 36 17 way way NOUN cana-6326 36 18 temperatures temperature NOUN cana-6326 36 19 are be AUX cana-6326 36 20 distributed distribute VERB cana-6326 36 21 in in ADP cana-6326 36 22 living live VERB cana-6326 36 23 things thing NOUN cana-6326 36 24 . . PUNCT cana-6326 37 1 marin marin NOUN cana-6326 37 2 et et PROPN cana-6326 37 3 al al PROPN cana-6326 37 4 . . PUNCT cana-6326 38 1 [ [ X cana-6326 38 2 26 26 NUM cana-6326 38 3 ] ] PUNCT cana-6326 38 4 looked look VERB cana-6326 38 5 at at ADP cana-6326 38 6 the the DET cana-6326 38 7 saint saint ADJ cana-6326 38 8 - - PUNCT cana-6326 38 9 venant venant NOUN cana-6326 38 10 principle principle NOUN cana-6326 38 11 in in ADP cana-6326 38 12 micropolar micropolar ADJ cana-6326 38 13 thermoelastic thermoelastic ADJ cana-6326 38 14 diffusion diffusion NOUN cana-6326 38 15 when when SCONJ cana-6326 38 16 it it PRON cana-6326 38 17 is be AUX cana-6326 38 18 relaxed relax VERB cana-6326 38 19 . . PUNCT cana-6326 39 1 yu yu PROPN cana-6326 39 2 et et PROPN cana-6326 39 3 al al PROPN cana-6326 39 4 . . PUNCT cana-6326 40 1 [ [ X cana-6326 40 2 27 27 NUM cana-6326 40 3 ] ] PUNCT cana-6326 40 4 suggested suggest VERB cana-6326 40 5 a a DET cana-6326 40 6 size size NOUN cana-6326 40 7 - - PUNCT cana-6326 40 8 dependent dependent ADJ cana-6326 40 9 thermoelastic thermoelastic ADJ cana-6326 40 10 model model NOUN cana-6326 40 11 for for ADP cana-6326 40 12 more more ADJ cana-6326 40 13 complex complex ADJ cana-6326 40 14 materials material NOUN cana-6326 40 15 . . PUNCT cana-6326 41 1 this this DET cana-6326 41 2 model model NOUN cana-6326 41 3 takes take VERB cana-6326 41 4 into into ADP cana-6326 41 5 account account NOUN cana-6326 41 6 size size NOUN cana-6326 41 7 effects effect NOUN cana-6326 41 8 in in ADP cana-6326 41 9 both both DET cana-6326 41 10 heat heat NOUN cana-6326 41 11 conduction conduction NOUN cana-6326 41 12 and and CCONJ cana-6326 41 13 elasticity elasticity NOUN cana-6326 41 14 . . PUNCT cana-6326 42 1 it it PRON cana-6326 42 2 does do VERB cana-6326 42 3 this this PRON cana-6326 42 4 by by ADP cana-6326 42 5 using use VERB cana-6326 42 6 generalized generalize VERB cana-6326 42 7 free free ADJ cana-6326 42 8 energy energy NOUN cana-6326 42 9 and and CCONJ cana-6326 42 10 extended extend VERB cana-6326 42 11 irreversible irreversible ADJ cana-6326 42 12 thermodynamics thermodynamic NOUN cana-6326 42 13 . . PUNCT cana-6326 43 1 there there PRON cana-6326 43 2 are be VERB cana-6326 43 3 also also ADV cana-6326 43 4 studies study NOUN cana-6326 43 5 by by ADP cana-6326 43 6 kumar kumar PROPN cana-6326 43 7 and and CCONJ cana-6326 43 8 abbas abbas PROPN cana-6326 43 9 [ [ X cana-6326 43 10 28 28 NUM cana-6326 43 11 ] ] PUNCT cana-6326 43 12 , , PUNCT cana-6326 43 13 who who PRON cana-6326 43 14 looked look VERB cana-6326 43 15 into into ADP cana-6326 43 16 how how SCONJ cana-6326 43 17 thermomechanical thermomechanical ADJ cana-6326 43 18 sources source NOUN cana-6326 43 19 can can AUX cana-6326 43 20 cause cause VERB cana-6326 43 21 disturbances disturbance NOUN cana-6326 43 22 in in ADP cana-6326 43 23 poro poro NOUN cana-6326 43 24 - - PUNCT cana-6326 43 25 thermoelastic thermoelastic ADJ cana-6326 43 26 media medium NOUN cana-6326 43 27 , , PUNCT cana-6326 43 28 and and CCONJ cana-6326 43 29 kumar kumar PROPN cana-6326 43 30 et et PROPN cana-6326 43 31 al al PROPN cana-6326 43 32 . . PUNCT cana-6326 44 1 [ [ X cana-6326 44 2 29 29 NUM cana-6326 44 3 ] ] PUNCT cana-6326 44 4 , , PUNCT cana-6326 44 5 who who PRON cana-6326 44 6 looked look VERB cana-6326 44 7 into into ADP cana-6326 44 8 how how SCONJ cana-6326 44 9 deformation deformation NOUN cana-6326 44 10 happens happen VERB cana-6326 44 11 in in ADP cana-6326 44 12 a a DET cana-6326 44 13 modified modify VERB cana-6326 44 14 couple couple NOUN cana-6326 44 15 stress stress NOUN cana-6326 44 16 thermoelastic thermoelastic ADJ cana-6326 44 17 rotating rotating NOUN cana-6326 44 18 medium medium NOUN cana-6326 44 19 when when SCONJ cana-6326 44 20 hall hall NOUN cana-6326 44 21 current current ADJ cana-6326 44 22 and and CCONJ cana-6326 44 23 magnetic magnetic ADJ cana-6326 44 24 field field NOUN cana-6326 44 25 influences influence NOUN cana-6326 44 26 happen happen VERB cana-6326 44 27 , , PUNCT cana-6326 44 28 using use VERB cana-6326 44 29 the the DET cana-6326 44 30 lord lord PROPN cana-6326 44 31 - - PUNCT cana-6326 44 32 shulman shulman PROPN cana-6326 44 33 and and CCONJ cana-6326 44 34 green green ADJ cana-6326 44 35 - - PUNCT cana-6326 44 36 lindsay lindsay PROPN cana-6326 44 37 theories theory NOUN cana-6326 44 38 with with ADP cana-6326 44 39 a a DET cana-6326 44 40 ramp ramp NOUN cana-6326 44 41 - - PUNCT cana-6326 44 42 type type NOUN cana-6326 44 43 thermal thermal ADJ cana-6326 44 44 source source NOUN cana-6326 44 45 . . PUNCT cana-6326 45 1 a a DET cana-6326 45 2 study study NOUN cana-6326 45 3 by by ADP cana-6326 45 4 kumar kumar PROPN cana-6326 45 5 et et PROPN cana-6326 45 6 al al PROPN cana-6326 45 7 . . PUNCT cana-6326 46 1 [ [ X cana-6326 46 2 30 30 NUM cana-6326 46 3 ] ] PUNCT cana-6326 46 4 looked look VERB cana-6326 46 5 at at ADP cana-6326 46 6 a a DET cana-6326 46 7 non non ADJ cana-6326 46 8 - - ADJ cana-6326 46 9 local local ADJ cana-6326 46 10 microstretch microstretch VERB cana-6326 46 11 thermoelastic thermoelastic ADJ cana-6326 46 12 thick thick ADJ cana-6326 46 13 circular circular ADJ cana-6326 46 14 plate plate NOUN cana-6326 46 15 that that PRON cana-6326 46 16 was be AUX cana-6326 46 17 subject subject ADJ cana-6326 46 18 to to ADP cana-6326 46 19 phase phase NOUN cana-6326 46 20 lags lag NOUN cana-6326 46 21 . . PUNCT cana-6326 47 1 kumar kumar PROPN cana-6326 47 2 et et PROPN cana-6326 47 3 al al PROPN cana-6326 47 4 . . PUNCT cana-6326 48 1 [ [ X cana-6326 48 2 31 31 NUM cana-6326 48 3 ] ] PUNCT cana-6326 48 4 looked look VERB cana-6326 48 5 at at ADP cana-6326 48 6 how how SCONJ cana-6326 48 7 thermal thermal ADJ cana-6326 48 8 and and CCONJ cana-6326 48 9 chemical chemical ADJ cana-6326 48 10 potential potential ADJ cana-6326 48 11 sources source NOUN cana-6326 48 12 affected affect VERB cana-6326 48 13 a a DET cana-6326 48 14 thin thin ADJ cana-6326 48 15 beam beam NOUN cana-6326 48 16 in in ADP cana-6326 48 17 a a DET cana-6326 48 18 modified modify VERB cana-6326 48 19 couple couple NOUN cana-6326 48 20 stress stress NOUN cana-6326 48 21 thermoelasticity thermoelasticity NOUN cana-6326 48 22 ( ( PUNCT cana-6326 48 23 mct mct PROPN cana-6326 48 24 ) ) PUNCT cana-6326 48 25 model model NOUN cana-6326 48 26 with with ADP cana-6326 48 27 a a DET cana-6326 48 28 three three NUM cana-6326 48 29 - - PUNCT cana-6326 48 30 phase phase NOUN cana-6326 48 31 - - PUNCT cana-6326 48 32 lag lag NOUN cana-6326 48 33 diffusion diffusion NOUN cana-6326 48 34 model model NOUN cana-6326 48 35 in in ADP cana-6326 48 36 a a DET cana-6326 48 37 different different ADJ cana-6326 48 38 study study NOUN cana-6326 48 39 . . PUNCT cana-6326 49 1 marin marin NOUN cana-6326 49 2 et et PROPN cana-6326 49 3 al al PROPN cana-6326 49 4 . . PUNCT cana-6326 50 1 [ [ X cana-6326 50 2 32 32 NUM cana-6326 50 3 ] ] PUNCT cana-6326 50 4 used use VERB cana-6326 50 5 the the DET cana-6326 50 6 moore moore PROPN cana-6326 50 7 - - PUNCT cana-6326 50 8 gibson gibson PROPN cana-6326 50 9 - - PUNCT cana-6326 50 10 thompson thompson PROPN cana-6326 50 11 ( ( PUNCT cana-6326 50 12 mgt mgt NOUN cana-6326 50 13 ) ) PUNCT cana-6326 50 14 heat heat NOUN cana-6326 50 15 equation equation NOUN cana-6326 50 16 to to PART cana-6326 50 17 come come VERB cana-6326 50 18 up up ADP cana-6326 50 19 with with ADP cana-6326 50 20 a a DET cana-6326 50 21 basic basic ADJ cana-6326 50 22 solution solution NOUN cana-6326 50 23 and and CCONJ cana-6326 50 24 green green NOUN cana-6326 50 25 's 's PART cana-6326 50 26 function function NOUN cana-6326 50 27 for for ADP cana-6326 50 28 a a DET cana-6326 50 29 semi semi ADJ cana-6326 50 30 - - ADJ cana-6326 50 31 infinite infinite ADJ cana-6326 50 32 orthotropic orthotropic ADJ cana-6326 50 33 photo photo NOUN cana-6326 50 34 - - PUNCT cana-6326 50 35 thermoelastic thermoelastic ADJ cana-6326 50 36 medium medium NOUN cana-6326 50 37 whose whose DET cana-6326 50 38 properties property NOUN cana-6326 50 39 change change VERB cana-6326 50 40 with with ADP cana-6326 50 41 temperature temperature NOUN cana-6326 50 42 . . PUNCT cana-6326 51 1 they they PRON cana-6326 51 2 used use VERB cana-6326 51 3 the the DET cana-6326 51 4 operator operator NOUN cana-6326 51 5 theory theory NOUN cana-6326 51 6 and and CCONJ cana-6326 51 7 the the DET cana-6326 51 8 superposition superposition NOUN cana-6326 51 9 principle principle NOUN cana-6326 51 10 to to PART cana-6326 51 11 come come VERB cana-6326 51 12 up up ADP cana-6326 51 13 with with ADP cana-6326 51 14 a a DET cana-6326 51 15 general general ADJ cana-6326 51 16 solution solution NOUN cana-6326 51 17 using use VERB cana-6326 51 18 harmonic harmonic ADJ cana-6326 51 19 functions function NOUN cana-6326 51 20 . . PUNCT cana-6326 52 1 this this DET cana-6326 52 2 solution solution NOUN cana-6326 52 3 was be AUX cana-6326 52 4 then then ADV cana-6326 52 5 used use VERB cana-6326 52 6 to to PART cana-6326 52 7 find find VERB cana-6326 52 8 specific specific ADJ cana-6326 52 9 solutions solution NOUN cana-6326 52 10 for for ADP cana-6326 52 11 sources source NOUN cana-6326 52 12 of of ADP cana-6326 52 13 steady steady ADJ cana-6326 52 14 point point NOUN cana-6326 52 15 heat heat NOUN cana-6326 52 16 at at ADP cana-6326 52 17 the the DET cana-6326 52 18 medium medium NOUN cana-6326 52 19 's 's PART cana-6326 52 20 surface surface NOUN cana-6326 52 21 and and CCONJ cana-6326 52 22 inside inside ADV cana-6326 52 23 . . PUNCT cana-6326 53 1 sharma sharma PROPN cana-6326 53 2 et et PROPN cana-6326 53 3 al al PROPN cana-6326 53 4 . . PUNCT cana-6326 54 1 [ [ X cana-6326 54 2 33 33 NUM cana-6326 54 3 ] ] PUNCT cana-6326 54 4 looked look VERB cana-6326 54 5 into into ADP cana-6326 54 6 how how SCONJ cana-6326 54 7 the the DET cana-6326 54 8 moore moore PROPN cana-6326 54 9 - - PUNCT cana-6326 54 10 gibson gibson PROPN cana-6326 54 11 - - PUNCT cana-6326 54 12 thompson thompson NOUN cana-6326 54 13 equation equation NOUN cana-6326 54 14 controls control VERB cana-6326 54 15 thermomechanical thermomechanical ADJ cana-6326 54 16 deformation deformation NOUN cana-6326 54 17 in in ADP cana-6326 54 18 a a DET cana-6326 54 19 micropolar micropolar ADJ cana-6326 54 20 thermoviscoelastic thermoviscoelastic ADJ cana-6326 54 21 solid solid NOUN cana-6326 54 22 . . PUNCT cana-6326 55 1 they they PRON cana-6326 55 2 found find VERB cana-6326 55 3 that that SCONJ cana-6326 55 4 the the DET cana-6326 55 5 twotemperature twotemperature NOUN cana-6326 55 6 effects effect NOUN cana-6326 55 7 were be AUX cana-6326 55 8 not not PART cana-6326 55 9 local local ADJ cana-6326 55 10 and and CCONJ cana-6326 55 11 were be AUX cana-6326 55 12 hyperbolic hyperbolic ADJ cana-6326 55 13 . . PUNCT cana-6326 56 1 in in ADP cana-6326 56 2 their their PRON cana-6326 56 3 study study NOUN cana-6326 56 4 [ [ X cana-6326 56 5 34 34 NUM cana-6326 56 6 ] ] PUNCT cana-6326 56 7 , , PUNCT cana-6326 56 8 abouelregal abouelregal PROPN cana-6326 56 9 et et PROPN cana-6326 56 10 al al PROPN cana-6326 56 11 . . PROPN cana-6326 56 12 created create VERB cana-6326 56 13 a a DET cana-6326 56 14 thermoviscoelastic thermoviscoelastic ADJ cana-6326 56 15 model model NOUN cana-6326 56 16 by by ADP cana-6326 56 17 combining combine VERB cana-6326 56 18 non non ADJ cana-6326 56 19 - - ADJ cana-6326 56 20 local local ADJ cana-6326 56 21 elasticity elasticity NOUN cana-6326 56 22 with with ADP cana-6326 56 23 the the DET cana-6326 56 24 kelvin kelvin PROPN cana-6326 56 25 - - PUNCT cana-6326 56 26 voigt voigt PROPN cana-6326 56 27 viscoelastic viscoelastic NOUN cana-6326 56 28 framework framework NOUN cana-6326 56 29 and and CCONJ cana-6326 56 30 a a DET cana-6326 56 31 klein klein PROPN cana-6326 56 32 – – PUNCT cana-6326 56 33 gordon gordon PROPN cana-6326 56 34 - - PUNCT cana-6326 56 35 type type NOUN cana-6326 56 36 non non ADJ cana-6326 56 37 - - ADJ cana-6326 56 38 local local ADJ cana-6326 56 39 elasticity elasticity NOUN cana-6326 56 40 formulation formulation NOUN cana-6326 56 41 . . PUNCT cana-6326 57 1 they they PRON cana-6326 57 2 then then ADV cana-6326 57 3 looked look VERB cana-6326 57 4 at at ADP cana-6326 57 5 a a DET cana-6326 57 6 one one NUM cana-6326 57 7 - - PUNCT cana-6326 57 8 dimensional dimensional ADJ cana-6326 57 9 half half ADJ cana-6326 57 10 - - PUNCT cana-6326 57 11 space space NOUN cana-6326 57 12 problem problem NOUN cana-6326 57 13 that that PRON cana-6326 57 14 was be AUX cana-6326 57 15 affected affect VERB cana-6326 57 16 by by ADP cana-6326 57 17 an an DET cana-6326 57 18 instantaneous instantaneous ADJ cana-6326 57 19 in in ADP cana-6326 57 20 - - PUNCT cana-6326 57 21 line line NOUN cana-6326 57 22 heat heat NOUN cana-6326 57 23 source source NOUN cana-6326 57 24 . . PUNCT cana-6326 58 1 communications communication NOUN cana-6326 58 2 on on ADP cana-6326 58 3 applied apply VERB cana-6326 58 4 nonlinear nonlinear ADJ cana-6326 58 5 analysis analysis NOUN cana-6326 58 6 issn issn NOUN cana-6326 58 7 : : PUNCT cana-6326 58 8 1074 1074 NUM cana-6326 58 9 - - PUNCT cana-6326 58 10 133x 133x NUM cana-6326 58 11 vol vol VERB cana-6326 58 12 32 32 NUM cana-6326 58 13 no no NOUN cana-6326 58 14 . . PUNCT cana-6326 59 1 10s 10 NOUN cana-6326 59 2 ( ( PUNCT cana-6326 59 3 2025 2025 NUM cana-6326 59 4 ) ) PUNCT cana-6326 59 5 3717 3717 NUM cana-6326 59 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 60 1 we we PRON cana-6326 60 2 look look VERB cana-6326 60 3 at at ADP cana-6326 60 4 how how SCONJ cana-6326 60 5 non non ADJ cana-6326 60 6 - - ADJ cana-6326 60 7 locality locality ADJ cana-6326 60 8 and and CCONJ cana-6326 60 9 phase phase NOUN cana-6326 60 10 lags lag VERB cana-6326 60 11 affect affect VERB cana-6326 60 12 thermoelastic thermoelastic ADJ cana-6326 60 13 diffusion diffusion NOUN cana-6326 60 14 when when SCONJ cana-6326 60 15 sources source NOUN cana-6326 60 16 are be AUX cana-6326 60 17 spread spread VERB cana-6326 60 18 out out ADP cana-6326 60 19 in in ADP cana-6326 60 20 a a DET cana-6326 60 21 time time NOUN cana-6326 60 22 - - PUNCT cana-6326 60 23 harmonic harmonic ADJ cana-6326 60 24 way way NOUN cana-6326 60 25 in in ADP cana-6326 60 26 this this DET cana-6326 60 27 study study NOUN cana-6326 60 28 . . PUNCT cana-6326 61 1 the the DET cana-6326 61 2 integral integral ADJ cana-6326 61 3 transform transform NOUN cana-6326 61 4 method method NOUN cana-6326 61 5 is be AUX cana-6326 61 6 used use VERB cana-6326 61 7 to to PART cana-6326 61 8 write write VERB cana-6326 61 9 the the DET cana-6326 61 10 problem problem NOUN cana-6326 61 11 which which PRON cana-6326 61 12 takes take VERB cana-6326 61 13 into into ADP cana-6326 61 14 account account NOUN cana-6326 61 15 different different ADJ cana-6326 61 16 kinds kind NOUN cana-6326 61 17 of of ADP cana-6326 61 18 excitations excitation NOUN cana-6326 61 19 such such ADJ cana-6326 61 20 as as ADP cana-6326 61 21 normal normal ADJ cana-6326 61 22 load load NOUN cana-6326 61 23 , , PUNCT cana-6326 61 24 thermal thermal ADJ cana-6326 61 25 sources source NOUN cana-6326 61 26 and and CCONJ cana-6326 61 27 chemical chemical ADJ cana-6326 61 28 potential potential ADJ cana-6326 61 29 sources source NOUN cana-6326 61 30 . . PUNCT cana-6326 62 1 2 2 X cana-6326 62 2 . . NUM cana-6326 62 3 basic basic ADJ cana-6326 62 4 equations equation NOUN cana-6326 62 5 based base VERB cana-6326 62 6 on on ADP cana-6326 62 7 the the DET cana-6326 62 8 work work NOUN cana-6326 62 9 by by ADP cana-6326 62 10 tzou tzou PROPN cana-6326 62 11 & & CCONJ cana-6326 62 12 gao gao PROPN cana-6326 63 1 [ [ X cana-6326 63 2 15 15 NUM cana-6326 63 3 ] ] PUNCT cana-6326 63 4 , , PUNCT cana-6326 63 5 sherief sherief NOUN cana-6326 63 6 et et PROPN cana-6326 63 7 al al PROPN cana-6326 63 8 . . PUNCT cana-6326 64 1 [ [ X cana-6326 64 2 18 18 NUM cana-6326 64 3 ] ] PUNCT cana-6326 64 4 , , PUNCT cana-6326 64 5 and and CCONJ cana-6326 64 6 yu yu PROPN cana-6326 64 7 et et PROPN cana-6326 64 8 al al PROPN cana-6326 64 9 . . PUNCT cana-6326 65 1 [ [ X cana-6326 65 2 27 27 NUM cana-6326 65 3 ] ] PUNCT cana-6326 65 4 , , PUNCT cana-6326 65 5 the the DET cana-6326 65 6 equations equation NOUN cana-6326 65 7 that that PRON cana-6326 65 8 describe describe VERB cana-6326 65 9 thermoelastic thermoelastic ADJ cana-6326 65 10 diffusion diffusion NOUN cana-6326 65 11 with with ADP cana-6326 65 12 dual dual ADJ cana-6326 65 13 - - PUNCT cana-6326 65 14 phase phase NOUN cana-6326 65 15 - - PUNCT cana-6326 65 16 lag lag NOUN cana-6326 65 17 and and CCONJ cana-6326 65 18 non non ADJ cana-6326 65 19 - - ADJ cana-6326 65 20 local local ADJ cana-6326 65 21 effects effect NOUN cana-6326 65 22 are be AUX cana-6326 65 23 : : PUNCT cana-6326 65 24 ( ( PUNCT cana-6326 65 25 i i NOUN cana-6326 65 26 ) ) PUNCT cana-6326 65 27 constitutive constitutive ADJ cana-6326 65 28 relations relation NOUN cana-6326 65 29 𝑑𝑖𝑗 𝑑𝑖𝑗 NOUN cana-6326 65 30 = = SYM cana-6326 65 31 2¡𝑒𝑖𝑗 2¡𝑒𝑖𝑗 NUM cana-6326 66 1 + + CCONJ cana-6326 66 2 𝛿𝑖𝑗 𝛿𝑖𝑗 NOUN cana-6326 67 1 [ [ X cana-6326 67 2 πœ†π‘œπ‘’π‘˜π‘˜ πœ†π‘œπ‘’π‘˜π‘˜ NOUN cana-6326 67 3 𝛾1 𝛾1 PROPN cana-6326 67 4 t t PROPN cana-6326 67 5 𝛾2p 𝛾2p PROPN cana-6326 67 6 ] ] PUNCT cana-6326 67 7 ( ( PUNCT cana-6326 67 8 1 1 NUM cana-6326 67 9 ) ) PUNCT cana-6326 67 10 ( ( PUNCT cana-6326 67 11 ii ii NOUN cana-6326 67 12 ) ) PUNCT cana-6326 67 13 equation equation NOUN cana-6326 67 14 of of ADP cana-6326 67 15 motion motion NOUN cana-6326 67 16 ( ( PUNCT cana-6326 67 17 πœ†π‘œ+ πœ†π‘œ+ NOUN cana-6326 67 18 Β΅ Β΅ X cana-6326 67 19 ) ) PUNCT cana-6326 67 20 βˆ‡ βˆ‡ X cana-6326 67 21 ( ( PUNCT cana-6326 67 22 βˆ‡.u βˆ‡.u NUM cana-6326 67 23 ) ) PUNCT cana-6326 67 24 + + CCONJ cana-6326 67 25 Β΅βˆ†u Β΅βˆ†u VERB cana-6326 67 26 𝛾1βˆ‡t 𝛾1βˆ‡t PROPN cana-6326 67 27 𝛾2βˆ‡p 𝛾2βˆ‡p PROPN cana-6326 67 28 = = SYM cana-6326 67 29 𝜌(1πœ‰2βˆ† 𝜌(1πœ‰2βˆ† PROPN cana-6326 67 30 ) ) PUNCT cana-6326 67 31 πœ•Β²π’– πœ•Β²π’– PROPN cana-6326 67 32 πœ•π‘‘Β² πœ•π‘‘Β² NOUN cana-6326 67 33 ( ( PUNCT cana-6326 67 34 2 2 NUM cana-6326 67 35 ) ) PUNCT cana-6326 67 36 ( ( PUNCT cana-6326 67 37 iii iii X cana-6326 67 38 ) ) PUNCT cana-6326 67 39 equation equation NOUN cana-6326 67 40 of of ADP cana-6326 67 41 heat heat NOUN cana-6326 67 42 conduction conduction NOUN cana-6326 67 43 ( ( PUNCT cana-6326 67 44 1 1 NUM cana-6326 67 45 βˆ’ΞΆ2βˆ† βˆ’ΞΆ2βˆ† NOUN cana-6326 67 46 + + CCONJ cana-6326 67 47 πœπ‘ž πœπ‘ž PROPN cana-6326 67 48 πœ• πœ• PROPN cana-6326 67 49 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 67 50 + + CCONJ cana-6326 67 51 1 1 NUM cana-6326 67 52 2 2 NUM cana-6326 67 53 πœπ‘ž πœπ‘ž NOUN cana-6326 67 54 2 2 NUM cana-6326 67 55 πœ•Β² πœ•Β² PROPN cana-6326 67 56 πœ•π‘‘Β² πœ•π‘‘Β² PROPN cana-6326 67 57 ) ) PUNCT cana-6326 67 58 ( ( PUNCT cana-6326 67 59 𝛾1π‘‡π‘œ 𝛾1π‘‡π‘œ PROPN cana-6326 67 60 οΏ½ οΏ½ PROPN cana-6326 67 61 Μ‡ Μ‡ NOUN cana-6326 67 62 οΏ½ οΏ½ PROPN cana-6326 67 63 + + CCONJ cana-6326 67 64 𝑙1π‘‡π‘œ 𝑙1π‘‡π‘œ PROPN cana-6326 67 65 οΏ½ οΏ½ PROPN cana-6326 67 66 Μ‡ Μ‡ VERB cana-6326 67 67 οΏ½ οΏ½ PROPN cana-6326 67 68 + + CCONJ cana-6326 67 69 π‘‡π‘œ π‘‡π‘œ PROPN cana-6326 67 70 οΏ½ οΏ½ PROPN cana-6326 67 71 Μ‡ Μ‡ NOUN cana-6326 67 72 οΏ½ οΏ½ PROPN cana-6326 67 73 d d PROPN cana-6326 67 74 ) ) PUNCT cana-6326 68 1 = = SYM cana-6326 68 2 k(1 k(1 PROPN cana-6326 68 3 + + CCONJ cana-6326 68 4 πœπ‘‘ πœπ‘‘ PROPN cana-6326 68 5 πœ• πœ• PROPN cana-6326 68 6 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 68 7 ) ) PUNCT cana-6326 68 8 βˆ†t βˆ†t PROPN cana-6326 68 9 ( ( PUNCT cana-6326 68 10 3 3 NUM cana-6326 68 11 ) ) PUNCT cana-6326 68 12 ( ( PUNCT cana-6326 68 13 iv iv X cana-6326 68 14 ) ) PUNCT cana-6326 68 15 equation equation NOUN cana-6326 68 16 of of ADP cana-6326 68 17 mass mass ADJ cana-6326 68 18 diffusion diffusion NOUN cana-6326 68 19 ( ( PUNCT cana-6326 68 20 1 1 NUM cana-6326 68 21 Ο‚2βˆ† Ο‚2βˆ† NOUN cana-6326 68 22 + + NUM cana-6326 68 23 πœπ‘’ πœπ‘’ PRON cana-6326 68 24 πœ• πœ• PROPN cana-6326 68 25 πœ•π‘‘ πœ•π‘‘ NOUN cana-6326 68 26 + + NOUN cana-6326 68 27 1 1 NUM cana-6326 68 28 2 2 NUM cana-6326 68 29 πœπ‘’ πœπ‘’ ADP cana-6326 68 30 2 2 NUM cana-6326 68 31 πœ•Β² πœ•Β² PROPN cana-6326 68 32 πœ•π‘‘Β² πœ•π‘‘Β² PROPN cana-6326 68 33 ) ) PUNCT cana-6326 68 34 ( ( PUNCT cana-6326 68 35 𝛾2 𝛾2 PROPN cana-6326 68 36 οΏ½ οΏ½ PROPN cana-6326 68 37 Μ‡ Μ‡ NOUN cana-6326 68 38 οΏ½ οΏ½ PROPN cana-6326 68 39 + + CCONJ cana-6326 68 40 𝑑 𝑑 PROPN cana-6326 68 41 οΏ½ οΏ½ PROPN cana-6326 68 42 Μ‡ Μ‡ VERB cana-6326 68 43 οΏ½ οΏ½ PROPN cana-6326 68 44 + + CCONJ cana-6326 68 45 𝑛 𝑛 PROPN cana-6326 68 46 οΏ½ οΏ½ PROPN cana-6326 68 47 Μ‡ Μ‡ NOUN cana-6326 68 48 οΏ½ οΏ½ PROPN cana-6326 68 49 ) ) PUNCT cana-6326 69 1 = = PUNCT cana-6326 70 1 d(1+πœπ‘ d(1+πœπ‘ PROPN cana-6326 70 2 πœ• πœ• PROPN cana-6326 70 3 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 70 4 ) ) PUNCT cana-6326 70 5 βˆ†p βˆ†p PROPN cana-6326 70 6 ( ( PUNCT cana-6326 70 7 4 4 NUM cana-6326 70 8 ) ) PUNCT cana-6326 71 1 where where SCONJ cana-6326 71 2 : : PUNCT cana-6326 71 3 πœ†π‘œ= πœ†π‘œ= PROPN cana-6326 71 4 πœ† πœ† ADP cana-6326 71 5 𝛽2 𝛽2 PROPN cana-6326 71 6 2 2 NUM cana-6326 71 7 /b /b SYM cana-6326 71 8 , , PUNCT cana-6326 71 9 𝛾1 𝛾1 PROPN cana-6326 71 10 = = SYM cana-6326 71 11 𝛽1 𝛽1 PROPN cana-6326 71 12 + + CCONJ cana-6326 71 13 π‘Ž π‘Ž PROPN cana-6326 71 14 𝑏 𝑏 NOUN cana-6326 71 15 𝛽2 𝛽2 NOUN cana-6326 71 16 , , PUNCT cana-6326 71 17 𝛾2 𝛾2 NOUN cana-6326 71 18 = = SYM cana-6326 71 19 𝛽2 𝛽2 PROPN cana-6326 71 20 𝑏 𝑏 PROPN cana-6326 71 21 , , PUNCT cana-6326 71 22 𝑙1 𝑙1 PROPN cana-6326 71 23 = = PUNCT cana-6326 71 24 𝜌 𝜌 X cana-6326 71 25 𝐢𝑒/𝑇𝑂 𝐢𝑒/𝑇𝑂 PROPN cana-6326 71 26 + + CCONJ cana-6326 71 27 a2 a2 PROPN cana-6326 71 28 / / SYM cana-6326 71 29 b b PROPN cana-6326 71 30 , , PUNCT cana-6326 72 1 d d PROPN cana-6326 72 2 = = PUNCT cana-6326 72 3 π‘Ž π‘Ž PROPN cana-6326 72 4 𝑏 𝑏 NOUN cana-6326 72 5 , , PUNCT cana-6326 72 6 n n NOUN cana-6326 72 7 = = SYM cana-6326 72 8 1 1 NUM cana-6326 72 9 𝑏 𝑏 NOUN cana-6326 72 10 ( ( PUNCT cana-6326 72 11 5 5 NUM cana-6326 72 12 ) ) PUNCT cana-6326 72 13 where where SCONJ cana-6326 72 14 u u NOUN cana-6326 72 15 is be AUX cana-6326 72 16 the the DET cana-6326 72 17 displacement displacement ADJ cana-6326 72 18 vector vector NOUN cana-6326 72 19 , , PUNCT cana-6326 72 20 t t PROPN cana-6326 72 21 is be AUX cana-6326 72 22 the the DET cana-6326 72 23 temperature temperature NOUN cana-6326 72 24 , , PUNCT cana-6326 72 25 p p NOUN cana-6326 72 26 is be AUX cana-6326 72 27 the the DET cana-6326 72 28 chemical chemical ADJ cana-6326 72 29 potential potential NOUN cana-6326 72 30 , , PUNCT cana-6326 72 31 𝑒𝑖𝑗 𝑒𝑖𝑗 PROPN cana-6326 72 32 is be AUX cana-6326 72 33 the the DET cana-6326 72 34 strain strain NOUN cana-6326 72 35 tensor tensor NOUN cana-6326 72 36 , , PUNCT cana-6326 72 37 𝑑𝑖𝑗 𝑑𝑖𝑗 NOUN cana-6326 72 38 is be AUX cana-6326 72 39 the the DET cana-6326 72 40 stress stress NOUN cana-6326 72 41 tensor tensor NOUN cana-6326 72 42 , , PUNCT cana-6326 72 43 and and CCONJ cana-6326 72 44 πœ‡ πœ‡ X cana-6326 72 45 , , PUNCT cana-6326 72 46 πœ†0 πœ†0 NOUN cana-6326 72 47 , , PUNCT cana-6326 72 48 𝛾1 𝛾1 PROPN cana-6326 72 49 , , PUNCT cana-6326 72 50 , , PUNCT cana-6326 72 51 𝛾2 𝛾2 VERB cana-6326 72 52 , , PUNCT cana-6326 72 53 𝑙1 𝑙1 NOUN cana-6326 72 54 , , PUNCT cana-6326 72 55 d d PROPN cana-6326 72 56 , , PUNCT cana-6326 72 57 n n CCONJ cana-6326 72 58 , , PUNCT cana-6326 72 59 k k NOUN cana-6326 72 60 , , PUNCT cana-6326 72 61 d d PROPN cana-6326 72 62 , , PUNCT cana-6326 72 63 πœπ‘ž πœπ‘ž NOUN cana-6326 72 64 , , PUNCT cana-6326 72 65 πœπ‘‘ πœπ‘‘ PROPN cana-6326 72 66 , , PUNCT cana-6326 72 67 πœπ‘’ πœπ‘’ PROPN cana-6326 72 68 , , PUNCT cana-6326 72 69 πœπ‘ πœπ‘ NOUN cana-6326 72 70 , , PUNCT cana-6326 72 71 ΞΎ ΞΎ PROPN cana-6326 72 72 , , PUNCT cana-6326 72 73 ΞΆ ΞΆ NOUN cana-6326 72 74 , , PUNCT cana-6326 72 75 Ο‚ Ο‚ PROPN cana-6326 72 76 are be AUX cana-6326 72 77 material material NOUN cana-6326 72 78 and and CCONJ cana-6326 72 79 model model NOUN cana-6326 72 80 parameters parameter NOUN cana-6326 72 81 defined define VERB cana-6326 72 82 as as ADP cana-6326 72 83 per per ADP cana-6326 72 84 the the DET cana-6326 72 85 cited cite VERB cana-6326 72 86 references reference NOUN cana-6326 72 87 . . PUNCT cana-6326 73 1 πœ‰ πœ‰ X cana-6326 73 2 , , PUNCT cana-6326 73 3 𝜁 𝜁 PROPN cana-6326 73 4 , , PUNCT cana-6326 73 5 𝜍 𝜍 X cana-6326 73 6 -are -are ADJ cana-6326 73 7 non non ADJ cana-6326 73 8 - - ADJ cana-6326 73 9 local local ADJ cana-6326 73 10 parameters parameter NOUN cana-6326 73 11 in in ADP cana-6326 73 12 equations equation NOUN cana-6326 73 13 ( ( PUNCT cana-6326 73 14 1)-(4 1)-(4 NUM cana-6326 73 15 ) ) PUNCT cana-6326 73 16 . . PUNCT cana-6326 74 1 πœπ‘ž πœπ‘ž NOUN cana-6326 74 2 & & CCONJ cana-6326 74 3 πœπ‘‘ πœπ‘‘ PROPN cana-6326 74 4 are be AUX cana-6326 74 5 the the DET cana-6326 74 6 thermal thermal ADJ cana-6326 74 7 relaxation relaxation NOUN cana-6326 74 8 times time NOUN cana-6326 74 9 with with ADP cana-6326 74 10 πœπ‘ž πœπ‘ž NOUN cana-6326 74 11 , , PUNCT cana-6326 74 12 πœπ‘‘ πœπ‘‘ PROPN cana-6326 74 13 β‰₯ β‰₯ NOUN cana-6326 74 14 0 0 NUM cana-6326 74 15 and and CCONJ cana-6326 74 16 πœπ‘’ πœπ‘’ PRON cana-6326 74 17 & & CCONJ cana-6326 74 18 πœπ‘ πœπ‘ PROPN cana-6326 74 19 are be AUX cana-6326 74 20 the the DET cana-6326 74 21 diffusion diffusion NOUN cana-6326 74 22 relaxation relaxation NOUN cana-6326 74 23 times time NOUN cana-6326 74 24 with with ADP cana-6326 74 25 πœπ‘’ πœπ‘’ PRON cana-6326 74 26 , , PUNCT cana-6326 74 27 πœπ‘ πœπ‘ ADP cana-6326 74 28 β‰₯ β‰₯ NOUN cana-6326 74 29 0 0 NUM cana-6326 74 30 . . PUNCT cana-6326 75 1 𝛽1 𝛽1 NOUN cana-6326 75 2 = = SYM cana-6326 75 3 ( ( PUNCT cana-6326 75 4 3Ξ»+2Β΅)𝛼𝑑 3Ξ»+2Β΅)𝛼𝑑 NUM cana-6326 75 5 , , PUNCT cana-6326 75 6 𝛽2 𝛽2 PROPN cana-6326 75 7 = = SYM cana-6326 75 8 ( ( PUNCT cana-6326 75 9 3Ξ»+2Β΅)𝛼𝑐 3Ξ»+2Β΅)𝛼𝑐 NUM cana-6326 75 10 . . PUNCT cana-6326 76 1 in in ADP cana-6326 76 2 this this DET cana-6326 76 3 case case NOUN cana-6326 76 4 , , PUNCT cana-6326 76 5 𝛼𝑑 𝛼𝑑 X cana-6326 76 6 , , PUNCT cana-6326 76 7 𝛼𝑐 𝛼𝑐 NOUN cana-6326 76 8 are be AUX cana-6326 76 9 the the DET cana-6326 76 10 coefficient coefficient NOUN cana-6326 76 11 of of ADP cana-6326 76 12 linear linear ADJ cana-6326 76 13 thermal thermal ADJ cana-6326 76 14 expansion expansion NOUN cana-6326 76 15 and and CCONJ cana-6326 76 16 diffusion diffusion NOUN cana-6326 76 17 expansion expansion NOUN cana-6326 76 18 respectively respectively ADV cana-6326 76 19 . . PUNCT cana-6326 77 1 βˆ† βˆ† PROPN cana-6326 77 2 is be AUX cana-6326 77 3 the the DET cana-6326 77 4 laplacian laplacian ADJ cana-6326 77 5 operator operator NOUN cana-6326 77 6 , , PUNCT cana-6326 77 7 βˆ‡ βˆ‡ X cana-6326 77 8 is be AUX cana-6326 77 9 nabla nabla NOUN cana-6326 77 10 operator operator NOUN cana-6326 77 11 which which PRON cana-6326 77 12 is be AUX cana-6326 77 13 also also ADV cana-6326 77 14 known know VERB cana-6326 77 15 as as ADP cana-6326 77 16 the the DET cana-6326 77 17 laplacian laplacian ADJ cana-6326 77 18 operator operator NOUN cana-6326 77 19 . . PUNCT cana-6326 78 1 other other ADJ cana-6326 78 2 signs sign NOUN cana-6326 78 3 mean mean VERB cana-6326 78 4 what what PRON cana-6326 78 5 they they PRON cana-6326 78 6 normally normally ADV cana-6326 78 7 do do VERB cana-6326 78 8 . . PUNCT cana-6326 79 1 3 3 X cana-6326 79 2 . . X cana-6326 79 3 problem problem NOUN cana-6326 79 4 description description NOUN cana-6326 79 5 we we PRON cana-6326 79 6 look look VERB cana-6326 79 7 at at ADP cana-6326 79 8 a a DET cana-6326 79 9 half half ADJ cana-6326 79 10 - - PUNCT cana-6326 79 11 space space NOUN cana-6326 79 12 that that PRON cana-6326 79 13 is be AUX cana-6326 79 14 uniform uniform ADJ cana-6326 79 15 , , PUNCT cana-6326 79 16 isotropic isotropic NOUN cana-6326 79 17 , , PUNCT cana-6326 79 18 non non ADJ cana-6326 79 19 - - ADJ cana-6326 79 20 local local ADJ cana-6326 79 21 , , PUNCT cana-6326 79 22 thermoelastic thermoelastic ADJ cana-6326 79 23 , , PUNCT cana-6326 79 24 and and CCONJ cana-6326 79 25 diffusive diffusive ADJ cana-6326 79 26 . . PUNCT cana-6326 80 1 this this DET cana-6326 80 2 half half ADJ cana-6326 80 3 - - PUNCT cana-6326 80 4 space space NOUN cana-6326 80 5 has have VERB cana-6326 80 6 dual dual ADJ cana-6326 80 7 - - PUNCT cana-6326 80 8 phase phase NOUN cana-6326 80 9 - - PUNCT cana-6326 80 10 lag lag NOUN cana-6326 80 11 effects effect NOUN cana-6326 80 12 and and CCONJ cana-6326 80 13 is be AUX cana-6326 80 14 in in ADP cana-6326 80 15 the the DET cana-6326 80 16 region region NOUN cana-6326 80 17 π‘₯3 π‘₯3 NOUN cana-6326 80 18 β‰₯ β‰₯ NOUN cana-6326 80 19 0 0 NUM cana-6326 80 20 . . PUNCT cana-6326 81 1 a a DET cana-6326 81 2 rectangular rectangular ADJ cana-6326 81 3 set set NOUN cana-6326 81 4 of of ADP cana-6326 81 5 cartesian cartesian ADJ cana-6326 81 6 coordinate coordinate NOUN cana-6326 81 7 system system NOUN cana-6326 81 8 is be AUX cana-6326 81 9 chosen choose VERB cana-6326 81 10 with with ADP cana-6326 81 11 ( ( PUNCT cana-6326 81 12 π‘₯1 π‘₯1 NOUN cana-6326 81 13 , , PUNCT cana-6326 81 14 π‘₯2 π‘₯2 NOUN cana-6326 81 15 , , PUNCT cana-6326 81 16 π‘₯3 π‘₯3 NOUN cana-6326 81 17 ) ) PUNCT cana-6326 81 18 as as ADP cana-6326 81 19 its its PRON cana-6326 81 20 points point NOUN cana-6326 81 21 of of ADP cana-6326 81 22 reference reference NOUN cana-6326 81 23 . . PUNCT cana-6326 82 1 the the DET cana-6326 82 2 origin origin NOUN cana-6326 82 3 is be AUX cana-6326 82 4 placed place VERB cana-6326 82 5 on on ADP cana-6326 82 6 the the DET cana-6326 82 7 boundary boundary ADJ cana-6326 82 8 plane plane NOUN cana-6326 82 9 with with ADP cana-6326 82 10 π‘₯3 π‘₯3 NOUN cana-6326 82 11 = = SYM cana-6326 82 12 0 0 NUM cana-6326 82 13 . . PUNCT cana-6326 83 1 the the DET cana-6326 83 2 study study NOUN cana-6326 83 3 only only ADV cana-6326 83 4 looks look VERB cana-6326 83 5 at at ADP cana-6326 83 6 deformations deformation NOUN cana-6326 83 7 in in ADP cana-6326 83 8 a a DET cana-6326 83 9 plane plane NOUN cana-6326 83 10 , , PUNCT cana-6326 83 11 and and CCONJ cana-6326 83 12 all all DET cana-6326 83 13 the the DET cana-6326 83 14 field field NOUN cana-6326 83 15 variables variable NOUN cana-6326 83 16 are be AUX cana-6326 83 17 functions function NOUN cana-6326 83 18 of of ADP cana-6326 83 19 ( ( PUNCT cana-6326 83 20 π‘₯1 π‘₯1 NOUN cana-6326 83 21 , , PUNCT cana-6326 83 22 π‘₯3 π‘₯3 NOUN cana-6326 83 23 , , PUNCT cana-6326 83 24 𝑑 𝑑 PROPN cana-6326 83 25 ) ) PUNCT cana-6326 83 26 . . PUNCT cana-6326 84 1 the the DET cana-6326 84 2 half half ADJ cana-6326 84 3 - - PUNCT cana-6326 84 4 space space NOUN cana-6326 84 5 is be AUX cana-6326 84 6 loaded load VERB cana-6326 84 7 mechanically mechanically ADV cana-6326 84 8 with with ADP cana-6326 84 9 a a DET cana-6326 84 10 normal normal ADJ cana-6326 84 11 force force NOUN cana-6326 84 12 , , PUNCT cana-6326 84 13 communications communication NOUN cana-6326 84 14 on on ADP cana-6326 84 15 applied apply VERB cana-6326 84 16 nonlinear nonlinear ADJ cana-6326 84 17 analysis analysis NOUN cana-6326 84 18 issn issn NOUN cana-6326 84 19 : : PUNCT cana-6326 84 20 1074 1074 NUM cana-6326 84 21 - - PUNCT cana-6326 84 22 133x 133x NUM cana-6326 84 23 vol vol VERB cana-6326 84 24 32 32 NUM cana-6326 84 25 no no NOUN cana-6326 84 26 . . PUNCT cana-6326 85 1 10s 10 NOUN cana-6326 85 2 ( ( PUNCT cana-6326 85 3 2025 2025 NUM cana-6326 85 4 ) ) PUNCT cana-6326 85 5 3718 3718 NUM cana-6326 85 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 85 7 heated heat VERB cana-6326 85 8 up up ADP cana-6326 85 9 , , PUNCT cana-6326 85 10 and and CCONJ cana-6326 85 11 given give VERB cana-6326 85 12 a a DET cana-6326 85 13 chemical chemical ADJ cana-6326 85 14 potential potential ADJ cana-6326 85 15 source source NOUN cana-6326 85 16 at at ADP cana-6326 85 17 the the DET cana-6326 85 18 boundary boundary ADJ cana-6326 85 19 plane plane NOUN cana-6326 85 20 π‘₯3 π‘₯3 NOUN cana-6326 85 21 = = NOUN cana-6326 85 22 0 0 X cana-6326 85 23 . . PUNCT cana-6326 86 1 we we PRON cana-6326 86 2 assume assume VERB cana-6326 86 3 that that SCONJ cana-6326 86 4 the the DET cana-6326 86 5 variations variation NOUN cana-6326 86 6 are be AUX cana-6326 86 7 limited limit VERB cana-6326 86 8 to to ADP cana-6326 86 9 the the DET cana-6326 86 10 π‘₯1 π‘₯1 NOUN cana-6326 86 11 π‘₯3 π‘₯3 NOUN cana-6326 86 12 plane plane NOUN cana-6326 86 13 for for ADP cana-6326 86 14 two two NUM cana-6326 86 15 - - PUNCT cana-6326 86 16 dimensional dimensional ADJ cana-6326 86 17 modeling modeling NOUN cana-6326 86 18 . . PUNCT cana-6326 87 1 𝑒1(π‘₯1 𝑒1(π‘₯1 NOUN cana-6326 87 2 , , PUNCT cana-6326 87 3 π‘₯3 π‘₯3 NOUN cana-6326 87 4 , , PUNCT cana-6326 87 5 𝑑 𝑑 PROPN cana-6326 87 6 ) ) PUNCT cana-6326 87 7 and and CCONJ cana-6326 87 8 𝑒3(π‘₯1 𝑒3(π‘₯1 NOUN cana-6326 87 9 , , PUNCT cana-6326 87 10 π‘₯3 π‘₯3 NOUN cana-6326 87 11 , , PUNCT cana-6326 87 12 𝑑 𝑑 PROPN cana-6326 87 13 ) ) PUNCT cana-6326 87 14 can can AUX cana-6326 87 15 be be AUX cana-6326 87 16 written write VERB cana-6326 87 17 in in ADP cana-6326 87 18 terms term NOUN cana-6326 87 19 of of ADP cana-6326 87 20 πœ‘(π‘₯1 πœ‘(π‘₯1 ADJ cana-6326 87 21 , , PUNCT cana-6326 87 22 π‘₯3 π‘₯3 NOUN cana-6326 87 23 , , PUNCT cana-6326 87 24 𝑑 𝑑 PROPN cana-6326 87 25 ) ) PUNCT cana-6326 87 26 and and CCONJ cana-6326 87 27 ψ ψ X cana-6326 87 28 ( ( PUNCT cana-6326 87 29 π‘₯1 π‘₯1 NOUN cana-6326 87 30 , , PUNCT cana-6326 87 31 π‘₯3 π‘₯3 NOUN cana-6326 87 32 , , PUNCT cana-6326 87 33 𝑑 𝑑 PROPN cana-6326 87 34 ) ) PUNCT cana-6326 87 35 in in ADP cana-6326 87 36 a a DET cana-6326 87 37 form form NOUN cana-6326 87 38 that that PRON cana-6326 87 39 does do AUX cana-6326 87 40 n't not PART cana-6326 87 41 depend depend VERB cana-6326 87 42 on on ADP cana-6326 87 43 the the DET cana-6326 87 44 dimensions dimension NOUN cana-6326 87 45 . . PUNCT cana-6326 88 1 for for ADP cana-6326 88 2 two two NUM cana-6326 88 3 dimensional dimensional ADJ cana-6326 88 4 problems problem NOUN cana-6326 88 5 , , PUNCT cana-6326 88 6 we we PRON cana-6326 88 7 take take VERB cana-6326 88 8 : : PUNCT cana-6326 88 9 u u NOUN cana-6326 88 10 = = SYM cana-6326 88 11 ( ( PUNCT cana-6326 88 12 𝑒1(π‘₯1 𝑒1(π‘₯1 X cana-6326 88 13 , , PUNCT cana-6326 88 14 π‘₯3 π‘₯3 NOUN cana-6326 88 15 , , PUNCT cana-6326 88 16 𝑑 𝑑 PROPN cana-6326 88 17 ) ) PUNCT cana-6326 88 18 , , PUNCT cana-6326 88 19 0 0 NUM cana-6326 88 20 , , PUNCT cana-6326 88 21 𝑒3(π‘₯1 𝑒3(π‘₯1 NOUN cana-6326 88 22 , , PUNCT cana-6326 88 23 π‘₯3 π‘₯3 NOUN cana-6326 88 24 , , PUNCT cana-6326 88 25 𝑑 𝑑 NOUN cana-6326 88 26 ) ) PUNCT cana-6326 88 27 ) ) PUNCT cana-6326 88 28 , , PUNCT cana-6326 88 29 t t PROPN cana-6326 88 30 ( ( PUNCT cana-6326 88 31 π‘₯1 π‘₯1 PROPN cana-6326 88 32 , , PUNCT cana-6326 88 33 π‘₯3 π‘₯3 NOUN cana-6326 88 34 , , PUNCT cana-6326 88 35 𝑑 𝑑 PROPN cana-6326 88 36 ) ) PUNCT cana-6326 88 37 , , PUNCT cana-6326 88 38 p p X cana-6326 88 39 ( ( PUNCT cana-6326 88 40 π‘₯1 π‘₯1 NOUN cana-6326 88 41 , , PUNCT cana-6326 88 42 π‘₯3 π‘₯3 NOUN cana-6326 88 43 , , PUNCT cana-6326 88 44 𝑑 𝑑 PROPN cana-6326 88 45 ) ) PUNCT cana-6326 88 46 ( ( PUNCT cana-6326 88 47 6 6 X cana-6326 88 48 ) ) PUNCT cana-6326 88 49 the the DET cana-6326 88 50 following follow VERB cana-6326 88 51 dimensionless dimensionless NOUN cana-6326 88 52 quantities quantity NOUN cana-6326 88 53 are be AUX cana-6326 88 54 introduced introduce VERB cana-6326 88 55 for for ADP cana-6326 88 56 normalization normalization NOUN cana-6326 88 57 : : PUNCT cana-6326 88 58 ξˈ= ξˈ= PROPN cana-6326 88 59 πœ”βˆ— πœ”βˆ— PROPN cana-6326 88 60 𝑐₁ 𝑐₁ PROPN cana-6326 88 61 ΞΎ ΞΎ PROPN cana-6326 88 62 , , PUNCT cana-6326 88 63 ΢ˈ= ΢ˈ= VERB cana-6326 88 64 πœ”βˆ— πœ”βˆ— ADJ cana-6326 88 65 𝑐₁ 𝑐₁ PROPN cana-6326 88 66 ΞΆ ΞΆ NOUN cana-6326 88 67 , , PUNCT cana-6326 88 68 Ο‚Λˆ= Ο‚Λˆ= NOUN cana-6326 88 69 πœ”βˆ— πœ”βˆ— PROPN cana-6326 88 70 𝑐₁ 𝑐₁ PROPN cana-6326 88 71 Ο‚ Ο‚ PROPN cana-6326 88 72 , , PUNCT cana-6326 88 73 π‘₯π‘–Λˆ= π‘₯π‘–Λˆ= NUM cana-6326 88 74 πœ”βˆ— πœ”βˆ— ADJ cana-6326 88 75 𝑐₁ 𝑐₁ PROPN cana-6326 88 76 π‘₯𝑖 π‘₯𝑖 NOUN cana-6326 88 77 , , PUNCT cana-6326 88 78 π‘’π‘–Λˆ= π‘’π‘–Λˆ= PROPN cana-6326 88 79 πœ”βˆ— πœ”βˆ— VERB cana-6326 88 80 𝑐₁ 𝑐₁ ADJ cana-6326 88 81 𝑒𝑖 𝑒𝑖 NOUN cana-6326 88 82 , , PUNCT cana-6326 88 83 tˈ= tˈ= ADJ cana-6326 88 84 Ο‰*t Ο‰*t NOUN cana-6326 88 85 , , PUNCT cana-6326 88 86 πœπ‘‘Λˆ= πœπ‘‘Λˆ= PROPN cana-6326 88 87 Ο‰*πœπ‘‘ Ο‰*πœπ‘‘ ADJ cana-6326 88 88 , , PUNCT cana-6326 88 89 πœπ‘žΛˆ=Ο‰*πœπ‘ž πœπ‘žΛˆ=Ο‰*πœπ‘ž PROPN cana-6326 88 90 , , PUNCT cana-6326 88 91 πœπ‘’Λˆ πœπ‘’Λˆ ADJ cana-6326 88 92 = = SYM cana-6326 88 93 Ο‰*πœπ‘’ Ο‰*πœπ‘’ NOUN cana-6326 88 94 , , PUNCT cana-6326 88 95 πœπ‘Λˆ πœπ‘Λˆ NOUN cana-6326 88 96 = = SYM cana-6326 88 97 Ο‰*πœπ‘ Ο‰*πœπ‘ NOUN cana-6326 88 98 , , PUNCT cana-6326 88 99 π‘‘π‘–π‘—Λˆ π‘‘π‘–π‘—Λˆ NOUN cana-6326 88 100 = = SYM cana-6326 88 101 1 1 NUM cana-6326 88 102 𝛾₁𝑇₀ 𝛾₁𝑇₀ NOUN cana-6326 88 103 𝑑𝑖𝑗 𝑑𝑖𝑗 NOUN cana-6326 88 104 , , PUNCT cana-6326 88 105 π‘šπ‘–π‘—Λˆ π‘šπ‘–π‘—Λˆ NOUN cana-6326 88 106 = = SYM cana-6326 88 107 1 1 NUM cana-6326 88 108 𝛾₁𝑇₀ 𝛾₁𝑇₀ NUM cana-6326 88 109 πœ”βˆ— πœ”βˆ— PRON cana-6326 88 110 𝑐₁ 𝑐₁ ADJ cana-6326 88 111 π‘šπ‘–π‘— π‘šπ‘–π‘— NOUN cana-6326 88 112 , , PUNCT cana-6326 88 113 ( ( PUNCT cana-6326 88 114 7 7 X cana-6326 88 115 ) ) PUNCT cana-6326 88 116 tˈ= tˈ= ADJ cana-6326 88 117 𝛾₁ 𝛾₁ PROPN cana-6326 88 118 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 88 119 t t PROPN cana-6326 88 120 , , PUNCT cana-6326 88 121 pˈ= pˈ= NOUN cana-6326 88 122 1 1 NUM cana-6326 88 123 𝑏𝛾₂ 𝑏𝛾₂ NOUN cana-6326 88 124 p p NOUN cana-6326 88 125 where where SCONJ cana-6326 88 126 : : PUNCT cana-6326 88 127 Ο‰ Ο‰ X cana-6326 88 128 * * PUNCT cana-6326 88 129 = = SYM cana-6326 88 130 πœŒπΆπ‘’π‘1 πœŒπΆπ‘’π‘1 PROPN cana-6326 88 131 2 2 NUM cana-6326 88 132 𝐾 𝐾 NOUN cana-6326 88 133 , , PUNCT cana-6326 88 134 𝑐1 𝑐1 NOUN cana-6326 88 135 2 2 NUM cana-6326 88 136 = = SYM cana-6326 88 137 πœ†π‘œ+2Β΅ πœ†π‘œ+2Β΅ X cana-6326 88 138 𝜌 𝜌 X cana-6326 88 139 here here ADV cana-6326 88 140 Ο‰ Ο‰ PROPN cana-6326 88 141 * * PROPN cana-6326 88 142 denotes denote VERB cana-6326 88 143 the the DET cana-6326 88 144 characteristic characteristic ADJ cana-6326 88 145 frequency frequency NOUN cana-6326 88 146 and and CCONJ cana-6326 88 147 𝑐1 𝑐1 NOUN cana-6326 88 148 is be AUX cana-6326 88 149 the the DET cana-6326 88 150 longitudinal longitudinal ADJ cana-6326 88 151 wave wave NOUN cana-6326 88 152 velocity velocity NOUN cana-6326 88 153 in in ADP cana-6326 88 154 the the DET cana-6326 88 155 medium medium NOUN cana-6326 88 156 . . PUNCT cana-6326 89 1 using use VERB cana-6326 89 2 equations equation NOUN cana-6326 89 3 ( ( PUNCT cana-6326 89 4 2)-(4 2)-(4 NUM cana-6326 89 5 ) ) PUNCT cana-6326 89 6 along along ADP cana-6326 89 7 with with ADP cana-6326 89 8 ( ( PUNCT cana-6326 89 9 6)(7 6)(7 NUM cana-6326 89 10 ) ) PUNCT cana-6326 89 11 and and CCONJ cana-6326 89 12 suppressing suppress VERB cana-6326 89 13 the the DET cana-6326 89 14 primes prime NOUN cana-6326 89 15 , , PUNCT cana-6326 89 16 the the DET cana-6326 89 17 system system NOUN cana-6326 89 18 reduces reduce VERB cana-6326 89 19 to to ADP cana-6326 89 20 the the DET cana-6326 89 21 following follow VERB cana-6326 89 22 dimensionless dimensionless NOUN cana-6326 89 23 form form NOUN cana-6326 89 24 ( ( PUNCT cana-6326 89 25 πœ†π‘œ+ πœ†π‘œ+ NOUN cana-6326 89 26 Β΅ Β΅ X cana-6326 89 27 ) ) PUNCT cana-6326 89 28 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 89 29 πœ•π‘’ πœ•π‘’ ADJ cana-6326 89 30 πœ•π‘₯1 πœ•π‘₯1 NOUN cana-6326 89 31 + + NUM cana-6326 89 32 Β΅ Β΅ DET cana-6326 89 33 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 89 34 βˆ†π‘’1 βˆ†π‘’1 PROPN cana-6326 89 35 βˆ‚t βˆ‚t PROPN cana-6326 89 36 πœ•π‘₯1 πœ•π‘₯1 PROPN cana-6326 89 37 𝑏𝛾₂² 𝑏𝛾₂² PROPN cana-6326 89 38 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 89 39 βˆ‚p βˆ‚p PROPN cana-6326 89 40 βˆ‚π‘₯1 βˆ‚π‘₯1 NOUN cana-6326 90 1 = = PUNCT cana-6326 90 2 ( ( PUNCT cana-6326 90 3 1πœ‰2βˆ† 1πœ‰2βˆ† NUM cana-6326 90 4 ) ) PUNCT cana-6326 90 5 πœ•Β²π‘’β‚ πœ•Β²π‘’β‚ ADJ cana-6326 90 6 πœ•π‘‘Β² πœ•π‘‘Β² NOUN cana-6326 90 7 , , PUNCT cana-6326 90 8 ( ( PUNCT cana-6326 90 9 8) 8) NUM cana-6326 90 10 ( ( PUNCT cana-6326 90 11 πœ†π‘œ+ πœ†π‘œ+ NOUN cana-6326 90 12 Β΅ Β΅ X cana-6326 90 13 ) ) PUNCT cana-6326 90 14 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 90 15 πœ•π‘’ πœ•π‘’ ADJ cana-6326 90 16 πœ•π‘₯3 πœ•π‘₯3 NOUN cana-6326 90 17 + + NUM cana-6326 90 18 Β΅ Β΅ DET cana-6326 90 19 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 90 20 βˆ†π‘’3 βˆ†π‘’3 PROPN cana-6326 90 21 βˆ‚t βˆ‚t PROPN cana-6326 90 22 πœ•π‘₯3 πœ•π‘₯3 PROPN cana-6326 90 23 𝑏𝛾₂² 𝑏𝛾₂² PROPN cana-6326 90 24 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 90 25 βˆ‚p βˆ‚p PROPN cana-6326 90 26 βˆ‚π‘₯3 βˆ‚π‘₯3 PROPN cana-6326 90 27 = = PUNCT cana-6326 90 28 ( ( PUNCT cana-6326 90 29 1πœ‰2βˆ† 1πœ‰2βˆ† NUM cana-6326 90 30 ) ) PUNCT cana-6326 90 31 πœ•Β²π‘’β‚ƒ πœ•Β²π‘’β‚ƒ NOUN cana-6326 90 32 πœ•π‘‘Β² πœ•π‘‘Β² NOUN cana-6326 90 33 , , PUNCT cana-6326 90 34 ( ( PUNCT cana-6326 90 35 9 9 NUM cana-6326 90 36 ) ) PUNCT cana-6326 90 37 ( ( PUNCT cana-6326 90 38 1ΞΆ2βˆ† 1ΞΆ2βˆ† NUM cana-6326 90 39 + + CCONJ cana-6326 90 40 πœπ‘ž πœπ‘ž PROPN cana-6326 90 41 πœ• πœ• PROPN cana-6326 90 42 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 90 43 + + CCONJ cana-6326 90 44 1 1 NUM cana-6326 90 45 2 2 NUM cana-6326 90 46 πœπ‘ž πœπ‘ž NOUN cana-6326 90 47 2 2 NUM cana-6326 90 48 πœ•Β² πœ•Β² PROPN cana-6326 90 49 πœ•π‘‘Β² πœ•π‘‘Β² PROPN cana-6326 90 50 ) ) PUNCT cana-6326 90 51 ( ( PUNCT cana-6326 90 52 𝛾₁² 𝛾₁² PROPN cana-6326 90 53 πΎπœŒπœ”βˆ— πΎπœŒπœ”βˆ— PROPN cana-6326 90 54 π‘‡π‘œ π‘‡π‘œ PROPN cana-6326 90 55 οΏ½ οΏ½ PROPN cana-6326 90 56 Μ‡ Μ‡ VERB cana-6326 90 57 οΏ½ οΏ½ PROPN cana-6326 90 58 + + CCONJ cana-6326 90 59 𝑙₁𝑐₁² 𝑙₁𝑐₁² PROPN cana-6326 90 60 πΎπœ”βˆ— πΎπœ”βˆ— VERB cana-6326 90 61 π‘‡π‘œ π‘‡π‘œ PROPN cana-6326 90 62 οΏ½ οΏ½ PROPN cana-6326 90 63 Μ‡ Μ‡ VERB cana-6326 90 64 οΏ½ οΏ½ PROPN cana-6326 90 65 + + CCONJ cana-6326 90 66 𝑏𝛾₂𝛾₁ 𝑏𝛾₂𝛾₁ PROPN cana-6326 90 67 πΎπœŒπœ”βˆ— πΎπœŒπœ”βˆ— PROPN cana-6326 90 68 π‘‡π‘œ π‘‡π‘œ PROPN cana-6326 90 69 οΏ½ οΏ½ PROPN cana-6326 90 70 Μ‡ Μ‡ NOUN cana-6326 90 71 οΏ½ οΏ½ PROPN cana-6326 90 72 d d PROPN cana-6326 90 73 ) ) PUNCT cana-6326 90 74 = = SYM cana-6326 90 75 ( ( PUNCT cana-6326 90 76 1+πœπ‘‘ 1+πœπ‘‘ NUM cana-6326 90 77 πœ• πœ• PROPN cana-6326 90 78 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 90 79 ) ) PUNCT cana-6326 90 80 βˆ†t βˆ†t PROPN cana-6326 90 81 , , PUNCT cana-6326 90 82 ( ( PUNCT cana-6326 90 83 10 10 NUM cana-6326 90 84 ) ) PUNCT cana-6326 90 85 ( ( PUNCT cana-6326 90 86 1Ο‚2βˆ† 1Ο‚2βˆ† NUM cana-6326 90 87 + + PUNCT cana-6326 90 88 πœπ‘’ πœπ‘’ PRON cana-6326 90 89 πœ• πœ• PROPN cana-6326 90 90 πœ•π‘‘ πœ•π‘‘ NOUN cana-6326 90 91 + + NOUN cana-6326 90 92 1 1 NUM cana-6326 90 93 2 2 NUM cana-6326 90 94 πœπ‘’ πœπ‘’ ADP cana-6326 90 95 2 2 NUM cana-6326 90 96 πœ•Β² πœ•Β² PROPN cana-6326 90 97 πœ•π‘‘Β² πœ•π‘‘Β² PROPN cana-6326 90 98 ) ) PUNCT cana-6326 90 99 ( ( PUNCT cana-6326 90 100 𝑐₁² 𝑐₁² ADV cana-6326 90 101 π·π‘πœ”βˆ— π·π‘πœ”βˆ— PROPN cana-6326 90 102 οΏ½ οΏ½ PROPN cana-6326 90 103 Μ‡ Μ‡ PROPN cana-6326 90 104 οΏ½ οΏ½ PROPN cana-6326 90 105 + + CCONJ cana-6326 90 106 π‘β‚β΄π‘‘πœŒ π‘β‚β΄π‘‘πœŒ ADJ cana-6326 90 107 π·π‘πœ”βˆ—π›Ύβ‚π›Ύβ‚‚ π·π‘πœ”βˆ—π›Ύβ‚π›Ύβ‚‚ X cana-6326 90 108 οΏ½ οΏ½ PROPN cana-6326 90 109 Μ‡ Μ‡ PROPN cana-6326 90 110 οΏ½ οΏ½ PROPN cana-6326 90 111 + + CCONJ cana-6326 90 112 𝑛𝑐₁² 𝑛𝑐₁² PROPN cana-6326 90 113 π·πœ”βˆ— π·πœ”βˆ— NOUN cana-6326 90 114 οΏ½ οΏ½ PROPN cana-6326 90 115 Μ‡ Μ‡ PROPN cana-6326 90 116 οΏ½ οΏ½ PROPN cana-6326 90 117 ) ) PUNCT cana-6326 90 118 = = PUNCT cana-6326 90 119 ( ( PUNCT cana-6326 90 120 1+πœπ‘ 1+πœπ‘ NUM cana-6326 90 121 πœ• πœ• PROPN cana-6326 90 122 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 90 123 ) ) PUNCT cana-6326 90 124 βˆ†p βˆ†p PROPN cana-6326 90 125 ( ( PUNCT cana-6326 90 126 11 11 NUM cana-6326 90 127 ) ) PUNCT cana-6326 90 128 where where SCONJ cana-6326 90 129 : : PUNCT cana-6326 90 130 βˆ† βˆ† PROPN cana-6326 90 131 = = SYM cana-6326 90 132 πœ•Β² πœ•Β² PROPN cana-6326 90 133 πœ•π‘₯₁² πœ•π‘₯₁² NOUN cana-6326 90 134 + + X cana-6326 90 135 πœ•Β² πœ•Β² PROPN cana-6326 90 136 πœ•π‘₯₃² πœ•π‘₯₃² ADJ cana-6326 90 137 , , PUNCT cana-6326 90 138 e e X cana-6326 90 139 = = PUNCT cana-6326 90 140 πœ•π‘’β‚ πœ•π‘’β‚ PUNCT cana-6326 90 141 πœ•π‘₯₁ πœ•π‘₯₁ NOUN cana-6326 90 142 + + CCONJ cana-6326 90 143 πœ•π‘’β‚ƒ πœ•π‘’β‚ƒ NOUN cana-6326 90 144 πœ•π‘₯₃ πœ•π‘₯₃ NUM cana-6326 90 145 4 4 NUM cana-6326 90 146 . . PUNCT cana-6326 90 147 solution solution NOUN cana-6326 90 148 procedure procedure NOUN cana-6326 90 149 the the DET cana-6326 90 150 displacement displacement ADJ cana-6326 90 151 components component NOUN cana-6326 90 152 𝑒1(π‘₯1 𝑒1(π‘₯1 ADJ cana-6326 90 153 , , PUNCT cana-6326 90 154 π‘₯3 π‘₯3 NOUN cana-6326 90 155 , , PUNCT cana-6326 90 156 𝑑 𝑑 PROPN cana-6326 90 157 ) ) PUNCT cana-6326 90 158 and and CCONJ cana-6326 90 159 𝑒3 𝑒3 PROPN cana-6326 90 160 ( ( PUNCT cana-6326 90 161 π‘₯1 π‘₯1 NOUN cana-6326 90 162 , , PUNCT cana-6326 90 163 π‘₯3 π‘₯3 NOUN cana-6326 90 164 , , PUNCT cana-6326 90 165 𝑑 𝑑 PROPN cana-6326 90 166 ) ) PUNCT cana-6326 90 167 can can AUX cana-6326 90 168 be be AUX cana-6326 90 169 expressed express VERB cana-6326 90 170 in in ADP cana-6326 90 171 terms term NOUN cana-6326 90 172 of of ADP cana-6326 90 173 the the DET cana-6326 90 174 scalar scalar ADJ cana-6326 90 175 potentials potential NOUN cana-6326 90 176 πœ‘(π‘₯1 πœ‘(π‘₯1 ADJ cana-6326 90 177 , , PUNCT cana-6326 90 178 π‘₯3 π‘₯3 NOUN cana-6326 90 179 , , PUNCT cana-6326 90 180 𝑑 𝑑 PROPN cana-6326 90 181 ) ) PUNCT cana-6326 90 182 and and CCONJ cana-6326 90 183 ψ ψ X cana-6326 90 184 ( ( PUNCT cana-6326 90 185 π‘₯1 π‘₯1 NOUN cana-6326 90 186 , , PUNCT cana-6326 90 187 π‘₯3 π‘₯3 NOUN cana-6326 90 188 , , PUNCT cana-6326 90 189 𝑑 𝑑 PROPN cana-6326 90 190 ) ) PUNCT cana-6326 90 191 in in ADP cana-6326 90 192 dimensionless dimensionless NOUN cana-6326 90 193 form form NOUN cana-6326 90 194 as as ADP cana-6326 90 195 𝑒1 𝑒1 NOUN cana-6326 90 196 = = PROPN cana-6326 90 197 πœ•πœ‘ πœ•πœ‘ PROPN cana-6326 90 198 πœ•π‘₯₁ πœ•π‘₯₁ NOUN cana-6326 90 199 πœ•πœ“ πœ•πœ“ NOUN cana-6326 90 200 πœ•π‘₯₃ πœ•π‘₯₃ NOUN cana-6326 90 201 , , PUNCT cana-6326 90 202 𝑒3 𝑒3 PROPN cana-6326 90 203 = = PROPN cana-6326 90 204 πœ•πœ‘ πœ•πœ‘ NOUN cana-6326 90 205 πœ•π‘₯₃ πœ•π‘₯₃ NOUN cana-6326 90 206 + + NUM cana-6326 90 207 πœ•πœ“ πœ•πœ“ NOUN cana-6326 90 208 πœ•π‘₯₁ πœ•π‘₯₁ NOUN cana-6326 90 209 ( ( PUNCT cana-6326 90 210 12 12 NUM cana-6326 90 211 ) ) PUNCT cana-6326 90 212 communications communication NOUN cana-6326 90 213 on on ADP cana-6326 90 214 applied apply VERB cana-6326 90 215 nonlinear nonlinear ADJ cana-6326 90 216 analysis analysis NOUN cana-6326 90 217 issn issn NOUN cana-6326 90 218 : : PUNCT cana-6326 90 219 1074 1074 NUM cana-6326 90 220 - - PUNCT cana-6326 90 221 133x 133x NUM cana-6326 90 222 vol vol VERB cana-6326 90 223 32 32 NUM cana-6326 90 224 no no NOUN cana-6326 90 225 . . PUNCT cana-6326 91 1 10s 10 NOUN cana-6326 91 2 ( ( PUNCT cana-6326 91 3 2025 2025 NUM cana-6326 91 4 ) ) PUNCT cana-6326 91 5 3719 3719 NUM cana-6326 91 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 91 7 substituting substitute VERB cana-6326 91 8 ( ( PUNCT cana-6326 91 9 12 12 NUM cana-6326 91 10 ) ) PUNCT cana-6326 91 11 into into ADP cana-6326 91 12 equations equation NOUN cana-6326 91 13 ( ( PUNCT cana-6326 91 14 8)-(11 8)-(11 NUM cana-6326 91 15 ) ) PUNCT cana-6326 91 16 the the DET cana-6326 91 17 governing govern VERB cana-6326 91 18 system system NOUN cana-6326 91 19 leads lead VERB cana-6326 91 20 to to ADP cana-6326 91 21 the the DET cana-6326 91 22 following follow VERB cana-6326 91 23 set set NOUN cana-6326 91 24 of of ADP cana-6326 91 25 coupled couple VERB cana-6326 91 26 equations equation NOUN cana-6326 91 27 : : PUNCT cana-6326 91 28 ( ( PUNCT cana-6326 91 29 𝑏₁ 𝑏₁ PROPN cana-6326 91 30 + + NOUN cana-6326 91 31 𝑏₂ 𝑏₂ ADJ cana-6326 91 32 ) ) PUNCT cana-6326 91 33 βˆ†Ο† βˆ†Ο† PROPN cana-6326 91 34 – – PUNCT cana-6326 91 35 t t PROPN cana-6326 91 36 – – PUNCT cana-6326 91 37 𝑏₃p 𝑏₃p PROPN cana-6326 91 38 ( ( PUNCT cana-6326 91 39 1πœ‰2βˆ† 1πœ‰2βˆ† NUM cana-6326 91 40 ) ) PUNCT cana-6326 92 1 πœ•Β²πœ‘ πœ•Β²πœ‘ NOUN cana-6326 92 2 πœ•π‘‘Β² πœ•π‘‘Β² NOUN cana-6326 92 3 = = SYM cana-6326 92 4 0 0 NUM cana-6326 92 5 , , PUNCT cana-6326 92 6 ( ( PUNCT cana-6326 92 7 13 13 NUM cana-6326 92 8 ) ) PUNCT cana-6326 92 9 𝑏2βˆ†Οˆ 𝑏2βˆ†Οˆ NOUN cana-6326 92 10 ( ( PUNCT cana-6326 92 11 1πœ‰2βˆ† 1πœ‰2βˆ† NUM cana-6326 92 12 ) ) PUNCT cana-6326 92 13 πœ•Β²πœ“ πœ•Β²πœ“ PROPN cana-6326 92 14 πœ•π‘‘Β² πœ•π‘‘Β² NOUN cana-6326 92 15 = = SYM cana-6326 92 16 0 0 NUM cana-6326 92 17 , , PUNCT cana-6326 92 18 ( ( PUNCT cana-6326 92 19 14 14 NUM cana-6326 92 20 ) ) PUNCT cana-6326 92 21 ( ( PUNCT cana-6326 92 22 1ΞΆ2βˆ† 1ΞΆ2βˆ† NUM cana-6326 92 23 + + CCONJ cana-6326 93 1 πœπ‘ž πœπ‘ž PROPN cana-6326 93 2 πœ• πœ• PROPN cana-6326 93 3 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 93 4 + + CCONJ cana-6326 93 5 1 1 NUM cana-6326 93 6 2 2 NUM cana-6326 93 7 πœπ‘ž πœπ‘ž NOUN cana-6326 93 8 2 2 NUM cana-6326 93 9 πœ•Β² πœ•Β² PROPN cana-6326 93 10 πœ•π‘‘Β² πœ•π‘‘Β² PROPN cana-6326 93 11 ) ) PUNCT cana-6326 93 12 ( ( PUNCT cana-6326 93 13 π‘β‚„βˆ† π‘β‚„βˆ† PROPN cana-6326 93 14 οΏ½ οΏ½ PROPN cana-6326 93 15 Μ‡ Μ‡ PROPN cana-6326 93 16 οΏ½ οΏ½ PROPN cana-6326 93 17 + + PROPN cana-6326 93 18 𝑏₅ 𝑏₅ PROPN cana-6326 93 19 οΏ½ οΏ½ PROPN cana-6326 93 20 Μ‡ Μ‡ PROPN cana-6326 93 21 οΏ½ οΏ½ PROPN cana-6326 93 22 + + CCONJ cana-6326 93 23 𝑏₆ 𝑏₆ PROPN cana-6326 93 24 οΏ½ οΏ½ PROPN cana-6326 93 25 Μ‡ Μ‡ NOUN cana-6326 93 26 οΏ½ οΏ½ PROPN cana-6326 93 27 ) ) PUNCT cana-6326 93 28 = = PUNCT cana-6326 94 1 ( ( PUNCT cana-6326 94 2 1+πœπ‘‘ 1+πœπ‘‘ NUM cana-6326 94 3 πœ• πœ• PROPN cana-6326 94 4 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 94 5 ) ) PUNCT cana-6326 94 6 βˆ†t βˆ†t PROPN cana-6326 94 7 , , PUNCT cana-6326 94 8 ( ( PUNCT cana-6326 94 9 15 15 NUM cana-6326 94 10 ) ) PUNCT cana-6326 94 11 ( ( PUNCT cana-6326 94 12 1Ο‚2βˆ† 1Ο‚2βˆ† NUM cana-6326 94 13 + + PUNCT cana-6326 94 14 πœπ‘’ πœπ‘’ PRON cana-6326 94 15 πœ• πœ• PROPN cana-6326 94 16 πœ•π‘‘ πœ•π‘‘ NOUN cana-6326 94 17 + + NOUN cana-6326 94 18 1 1 NUM cana-6326 94 19 2 2 NUM cana-6326 94 20 πœπ‘’ πœπ‘’ ADP cana-6326 94 21 2 2 NUM cana-6326 94 22 πœ•Β² πœ•Β² PROPN cana-6326 94 23 πœ•π‘‘Β² πœ•π‘‘Β² NOUN cana-6326 94 24 ) ) PUNCT cana-6326 94 25 ( ( PUNCT cana-6326 94 26 π‘β‚‡βˆ† π‘β‚‡βˆ† PROPN cana-6326 94 27 οΏ½ οΏ½ SYM cana-6326 94 28 Μ‡ Μ‡ PROPN cana-6326 94 29 οΏ½ οΏ½ PROPN cana-6326 94 30 + + PROPN cana-6326 94 31 π‘β‚ˆ π‘β‚ˆ PROPN cana-6326 94 32 οΏ½ οΏ½ PROPN cana-6326 94 33 Μ‡ Μ‡ PROPN cana-6326 94 34 οΏ½ οΏ½ PROPN cana-6326 94 35 + + SYM cana-6326 94 36 𝑏₉ 𝑏₉ PROPN cana-6326 94 37 οΏ½ οΏ½ PROPN cana-6326 94 38 Μ‡ Μ‡ PROPN cana-6326 94 39 οΏ½ οΏ½ PROPN cana-6326 94 40 ) ) PUNCT cana-6326 94 41 = = PUNCT cana-6326 94 42 ( ( PUNCT cana-6326 94 43 1+πœπ‘ 1+πœπ‘ NUM cana-6326 94 44 πœ• πœ• PROPN cana-6326 94 45 πœ•π‘‘ πœ•π‘‘ PROPN cana-6326 94 46 ) ) PUNCT cana-6326 94 47 βˆ†p βˆ†p PROPN cana-6326 94 48 ( ( PUNCT cana-6326 94 49 16 16 NUM cana-6326 94 50 ) ) PUNCT cana-6326 94 51 where where SCONJ cana-6326 94 52 : : PUNCT cana-6326 94 53 𝑏₁ 𝑏₁ PROPN cana-6326 94 54 = = SYM cana-6326 94 55 ( ( PUNCT cana-6326 94 56 πœ†π‘œ+ πœ†π‘œ+ NOUN cana-6326 94 57 Β΅ Β΅ X cana-6326 94 58 ) ) PUNCT cana-6326 94 59 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 94 60 , , PUNCT cana-6326 94 61 𝑏₂ 𝑏₂ PROPN cana-6326 94 62 = = SYM cana-6326 94 63 Β΅ Β΅ DET cana-6326 94 64 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 94 65 𝑏₃ 𝑏₃ NOUN cana-6326 94 66 = = SYM cana-6326 94 67 𝑏𝛾₂² 𝑏𝛾₂² PROPN cana-6326 94 68 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 94 69 , , PUNCT cana-6326 94 70 𝑏₄ 𝑏₄ NOUN cana-6326 94 71 = = PUNCT cana-6326 94 72 𝛾₁² 𝛾₁² NOUN cana-6326 94 73 πΎπœŒπœ”βˆ— πΎπœŒπœ”βˆ— PROPN cana-6326 94 74 π‘‡π‘œ π‘‡π‘œ PROPN cana-6326 94 75 , , PUNCT cana-6326 94 76 𝑏₅ 𝑏₅ NOUN cana-6326 94 77 = = PUNCT cana-6326 94 78 𝑙₁𝑐₁² 𝑙₁𝑐₁² PROPN cana-6326 94 79 πΎπœ”βˆ— πΎπœ”βˆ— NOUN cana-6326 94 80 π‘‡π‘œ π‘‡π‘œ NOUN cana-6326 94 81 , , PUNCT cana-6326 94 82 𝑏₆ 𝑏₆ NOUN cana-6326 94 83 = = PUNCT cana-6326 94 84 𝑏𝛾₂𝛾₁ 𝑏𝛾₂𝛾₁ PROPN cana-6326 94 85 πΎπœŒπœ”βˆ— πΎπœŒπœ”βˆ— PROPN cana-6326 94 86 π‘‡π‘œπ‘‘ π‘‡π‘œπ‘‘ PROPN cana-6326 94 87 , , PUNCT cana-6326 94 88 𝑏₇ 𝑏₇ NOUN cana-6326 94 89 = = PUNCT cana-6326 94 90 𝑐₁² 𝑐₁² ADV cana-6326 94 91 π·π‘πœ”βˆ— π·π‘πœ”βˆ— NOUN cana-6326 94 92 , , PUNCT cana-6326 94 93 π‘β‚ˆ π‘β‚ˆ PROPN cana-6326 94 94 = = PUNCT cana-6326 94 95 π‘β‚β΄π‘‘πœŒ π‘β‚β΄π‘‘πœŒ ADJ cana-6326 94 96 π·π‘πœ”βˆ—π›Ύβ‚π›Ύβ‚‚ π·π‘πœ”βˆ—π›Ύβ‚π›Ύβ‚‚ X cana-6326 94 97 , , PUNCT cana-6326 94 98 𝑏₉ 𝑏₉ NOUN cana-6326 94 99 = = PUNCT cana-6326 94 100 𝑛𝑐₁² 𝑛𝑐₁² PROPN cana-6326 94 101 π·πœ”βˆ— π·πœ”βˆ— NOUN cana-6326 94 102 ( ( PUNCT cana-6326 94 103 17 17 NUM cana-6326 94 104 ) ) PUNCT cana-6326 94 105 we we PRON cana-6326 94 106 assume assume VERB cana-6326 94 107 ( ( PUNCT cana-6326 94 108 οΏ½ οΏ½ NOUN cana-6326 94 109 Μ… Μ… NOUN cana-6326 94 110 οΏ½ οΏ½ PROPN cana-6326 94 111 , , PUNCT cana-6326 94 112 οΏ½ οΏ½ PROPN cana-6326 94 113 Μ… Μ… NOUN cana-6326 94 114 οΏ½ οΏ½ PROPN cana-6326 94 115 , , PUNCT cana-6326 94 116 οΏ½ οΏ½ PROPN cana-6326 94 117 Μ… Μ… NOUN cana-6326 94 118 οΏ½ οΏ½ PROPN cana-6326 94 119 , , PUNCT cana-6326 94 120 οΏ½ οΏ½ PROPN cana-6326 94 121 Μ… Μ… NOUN cana-6326 94 122 οΏ½ οΏ½ NOUN cana-6326 94 123 ) ) PUNCT cana-6326 94 124 = = PUNCT cana-6326 94 125 ( ( PUNCT cana-6326 94 126 Ο† Ο† PROPN cana-6326 94 127 , , PUNCT cana-6326 94 128 ψ ψ PROPN cana-6326 94 129 , , PUNCT cana-6326 94 130 t t PROPN cana-6326 94 131 , , PUNCT cana-6326 94 132 p)π‘’π‘–πœ”π‘‘ p)π‘’π‘–πœ”π‘‘ PROPN cana-6326 94 133 ( ( PUNCT cana-6326 94 134 18 18 NUM cana-6326 94 135 ) ) PUNCT cana-6326 94 136 we we PRON cana-6326 94 137 define define VERB cana-6326 94 138 fourier fourier NOUN cana-6326 94 139 transform transform NOUN cana-6326 94 140 as as ADP cana-6326 94 141 : : PUNCT cana-6326 94 142 𝑓 𝑓 PROPN cana-6326 94 143 ( ( PUNCT cana-6326 94 144 πœ‰1 πœ‰1 PROPN cana-6326 94 145 , , PUNCT cana-6326 94 146 π‘₯3 π‘₯3 NOUN cana-6326 94 147 , , PUNCT cana-6326 94 148 πœ” πœ” ADJ cana-6326 94 149 ) ) PUNCT cana-6326 94 150 = = NOUN cana-6326 94 151 ∫ ∫ PROPN cana-6326 94 152 𝑓(Μ…π‘₯1 𝑓(Μ…π‘₯1 PROPN cana-6326 94 153 , , PUNCT cana-6326 94 154 π‘₯3 π‘₯3 NOUN cana-6326 94 155 , , PUNCT cana-6326 94 156 πœ” πœ” ADP cana-6326 94 157 ∞ ∞ PROPN cana-6326 94 158 βˆ’βˆž βˆ’βˆž NOUN cana-6326 94 159 ) ) PUNCT cana-6326 94 160 π‘’π‘–πœ‰β‚π‘₯₁ π‘’π‘–πœ‰β‚π‘₯₁ NOUN cana-6326 94 161 dπ‘₯1 dπ‘₯1 NOUN cana-6326 94 162 ( ( PUNCT cana-6326 94 163 19 19 NUM cana-6326 94 164 ) ) PUNCT cana-6326 94 165 by by ADP cana-6326 94 166 substituting substitute VERB cana-6326 94 167 equations equation NOUN cana-6326 94 168 ( ( PUNCT cana-6326 94 169 18 18 NUM cana-6326 94 170 ) ) PUNCT cana-6326 94 171 and and CCONJ cana-6326 94 172 ( ( PUNCT cana-6326 94 173 19 19 NUM cana-6326 94 174 ) ) PUNCT cana-6326 94 175 into into ADP cana-6326 94 176 ( ( PUNCT cana-6326 94 177 13)-(16 13)-(16 NOUN cana-6326 94 178 ) ) PUNCT cana-6326 94 179 and and CCONJ cana-6326 94 180 simplifying simplifying NOUN cana-6326 94 181 , , PUNCT cana-6326 94 182 the the DET cana-6326 94 183 system system NOUN cana-6326 94 184 reduces reduce VERB cana-6326 94 185 to to ADP cana-6326 94 186 ( ( PUNCT cana-6326 94 187 𝐾₁𝐷1 𝐾₁𝐷1 X cana-6326 94 188 6 6 NUM cana-6326 94 189 + + NOUN cana-6326 94 190 𝐾₂𝐷1 𝐾₂𝐷1 ADP cana-6326 94 191 4 4 NUM cana-6326 94 192 + + CCONJ cana-6326 94 193 𝐾₃𝐷1 𝐾₃𝐷1 PROPN cana-6326 94 194 2 2 NUM cana-6326 94 195 + + NOUN cana-6326 94 196 𝐾₄)(πœ‘ 𝐾₄)(πœ‘ NOUN cana-6326 94 197 Μ‚ Μ‚ NUM cana-6326 94 198 , , PUNCT cana-6326 94 199 𝑇,Μ‚ 𝑇,Μ‚ PROPN cana-6326 94 200 οΏ½ οΏ½ PROPN cana-6326 94 201 Μ‚ Μ‚ NUM cana-6326 94 202 οΏ½ οΏ½ PROPN cana-6326 94 203 ) ) PUNCT cana-6326 94 204 = = SYM cana-6326 94 205 0 0 NUM cana-6326 95 1 ( ( PUNCT cana-6326 95 2 20 20 NUM cana-6326 95 3 ) ) PUNCT cana-6326 95 4 ( ( PUNCT cana-6326 95 5 𝐷1 𝐷1 NOUN cana-6326 95 6 2 2 NUM cana-6326 95 7 π‘š4 π‘š4 NOUN cana-6326 95 8 2 2 NUM cana-6326 95 9 ) ) PUNCT cana-6326 95 10 οΏ½ οΏ½ PROPN cana-6326 95 11 Μ‚ Μ‚ VERB cana-6326 95 12 οΏ½ οΏ½ NOUN cana-6326 95 13 = = SYM cana-6326 95 14 0 0 NUM cana-6326 95 15 ( ( PUNCT cana-6326 95 16 21 21 NUM cana-6326 95 17 ) ) PUNCT cana-6326 96 1 where where SCONJ cana-6326 96 2 : : PUNCT cana-6326 96 3 𝐾₁ 𝐾₁ PROPN cana-6326 96 4 = = PROPN cana-6326 96 5 𝐾₁₁𝐾₁₃𝐾₁₅ 𝐾₁₁𝐾₁₃𝐾₁₅ PROPN cana-6326 96 6 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœ2𝜍2𝐾₁₁ πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœ2𝜍2𝐾₁₁ PROPN cana-6326 97 1 + + NUM cana-6326 97 2 πΎβ‚ƒβ‚πœ2𝐾₁₅ πΎβ‚ƒβ‚πœ2𝐾₁₅ ADJ cana-6326 97 3 βˆ’ βˆ’ NOUN cana-6326 97 4 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚„πœ2𝜍2 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚„πœ2𝜍2 ADP cana-6326 97 5 βˆ’ βˆ’ PROPN cana-6326 97 6 πΎβ‚ƒβ‚πΎβ‚ƒβ‚…πœ2𝜍2𝑏₄ πΎβ‚ƒβ‚πΎβ‚ƒβ‚…πœ2𝜍2𝑏₄ PROPN cana-6326 97 7 + + CCONJ cana-6326 97 8 πΎβ‚ƒβ‚„π‘β‚„πΎβ‚β‚ƒπœ2 πΎβ‚ƒβ‚„π‘β‚„πΎβ‚β‚ƒπœ2 ADJ cana-6326 97 9 , , PUNCT cana-6326 97 10 𝐾₂ 𝐾₂ PROPN cana-6326 98 1 = = SYM cana-6326 98 2 𝐾₀₁ 𝐾₀₁ PROPN cana-6326 99 1 βˆ’ βˆ’ NOUN cana-6326 99 2 3πœ‰β‚Β²πΎβ‚ 3πœ‰β‚Β²πΎβ‚ NUM cana-6326 99 3 , , PUNCT cana-6326 99 4 𝐾₃ 𝐾₃ ADV cana-6326 99 5 = = SYM cana-6326 99 6 3πœ‰β‚β΄πΎβ‚ 3πœ‰β‚β΄πΎβ‚ NUM cana-6326 99 7 βˆ’ βˆ’ ADP cana-6326 99 8 2πœ‰β‚Β²πΎβ‚€β‚ 2πœ‰β‚Β²πΎβ‚€β‚ PRON cana-6326 100 1 + + CCONJ cana-6326 100 2 𝐾₀₂ 𝐾₀₂ PROPN cana-6326 100 3 , , PUNCT cana-6326 100 4 𝐾₄ 𝐾₄ X cana-6326 100 5 = = NOUN cana-6326 100 6 πΎβ‚€β‚πœ‰β‚β΄ πΎβ‚€β‚πœ‰β‚β΄ NOUN cana-6326 100 7 βˆ’ βˆ’ PROPN cana-6326 100 8 πœ‰β‚βΆπΎβ‚ πœ‰β‚βΆπΎβ‚ PROPN cana-6326 100 9 βˆ’ βˆ’ NOUN cana-6326 100 10 πœ‰β‚Β²πΎβ‚€β‚‚ πœ‰β‚Β²πΎβ‚€β‚‚ NOUN cana-6326 100 11 βˆ’ βˆ’ PROPN cana-6326 100 12 𝐾₀₃ 𝐾₀₃ PROPN cana-6326 100 13 , , PUNCT cana-6326 100 14 π‘š4 π‘š4 PROPN cana-6326 100 15 2 2 NUM cana-6326 100 16 = = SYM cana-6326 100 17 πœ‰1 πœ‰1 NOUN cana-6326 100 18 2 2 NUM cana-6326 100 19 βˆ’ βˆ’ NOUN cana-6326 100 20 πœ”2 πœ”2 PROPN cana-6326 100 21 𝑏2βˆ’πœ‰ 𝑏2βˆ’πœ‰ PROPN cana-6326 100 22 2πœ”2 2πœ”2 NUM cana-6326 100 23 𝐷1 𝐷1 NOUN cana-6326 101 1 = = PUNCT cana-6326 101 2 𝑑 𝑑 NOUN cana-6326 101 3 𝑑π‘₯3 𝑑π‘₯3 NOUN cana-6326 101 4 and and CCONJ cana-6326 101 5 𝐾01=βˆ’πΎβ‚β‚πΎβ‚‚β‚‚πΎβ‚β‚… 𝐾01=βˆ’πΎβ‚β‚πΎβ‚‚β‚‚πΎβ‚β‚… PROPN cana-6326 101 6 βˆ’ βˆ’ PROPN cana-6326 101 7 𝐾₁₁𝐾₁₃𝐾₂₆ 𝐾₁₁𝐾₁₃𝐾₂₆ PROPN cana-6326 101 8 + + NUM cana-6326 101 9 πΎβ‚β‚ƒπΎβ‚β‚…πœ”2 πΎβ‚β‚ƒπΎβ‚β‚…πœ”2 PROPN cana-6326 101 10 + + CCONJ cana-6326 101 11 πΎβ‚ƒβ‚ƒπΎβ‚β‚πœ2𝐾₂₅ πΎβ‚ƒβ‚ƒπΎβ‚β‚πœ2𝐾₂₅ X cana-6326 102 1 + + NOUN cana-6326 102 2 πΎβ‚ƒβ‚…πœ2𝐾₂₃𝐾₁₁ πΎβ‚ƒβ‚…πœ2𝐾₂₃𝐾₁₁ PRON cana-6326 102 3 βˆ’ βˆ’ X cana-6326 103 1 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœ2𝜍2πœ”2 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœ2𝜍2πœ”2 PROPN cana-6326 103 2 βˆ’ βˆ’ X cana-6326 103 3 πΎβ‚ƒβ‚πœ2𝐾₂₆ πΎβ‚ƒβ‚πœ2𝐾₂₆ INTJ cana-6326 104 1 βˆ’ βˆ’ PROPN cana-6326 104 2 𝐾₂₁𝐾₁₅ 𝐾₂₁𝐾₁₅ VERB cana-6326 104 3 + + NUM cana-6326 104 4 πΎβ‚ƒβ‚ƒπœ2𝐾₂₄ πΎβ‚ƒβ‚ƒπœ2𝐾₂₄ NUM cana-6326 104 5 + + NUM cana-6326 104 6 πΎβ‚ƒβ‚„πœ2𝐾₂₃ πΎβ‚ƒβ‚„πœ2𝐾₂₃ NOUN cana-6326 105 1 + + CCONJ cana-6326 105 2 πΎβ‚ƒβ‚πœ2𝐾₂₄𝑏₃ πΎβ‚ƒβ‚πœ2𝐾₂₄𝑏₃ ADJ cana-6326 105 3 + + CCONJ cana-6326 105 4 πΎβ‚ƒβ‚…πœ2𝐾₂₁𝑏₃ πΎβ‚ƒβ‚…πœ2𝐾₂₁𝑏₃ NOUN cana-6326 105 5 βˆ’ βˆ’ PROPN cana-6326 105 6 𝐾₁₃𝐾₂₄𝑏₃ 𝐾₁₃𝐾₂₄𝑏₃ PUNCT cana-6326 105 7 βˆ’ βˆ’ PROPN cana-6326 105 8 π‘β‚ƒπΎβ‚ƒβ‚„πœΒ²πΎβ‚‚β‚‚ π‘β‚ƒπΎβ‚ƒβ‚„πœΒ²πΎβ‚‚β‚‚ PROPN cana-6326 105 9 , , PUNCT cana-6326 105 10 communications communication NOUN cana-6326 105 11 on on ADP cana-6326 105 12 applied apply VERB cana-6326 105 13 nonlinear nonlinear ADJ cana-6326 105 14 analysis analysis NOUN cana-6326 105 15 issn issn NOUN cana-6326 105 16 : : PUNCT cana-6326 105 17 1074 1074 NUM cana-6326 105 18 - - PUNCT cana-6326 105 19 133x 133x NUM cana-6326 105 20 vol vol VERB cana-6326 105 21 32 32 NUM cana-6326 105 22 no no NOUN cana-6326 105 23 . . PUNCT cana-6326 106 1 10s 10 NOUN cana-6326 106 2 ( ( PUNCT cana-6326 106 3 2025 2025 NUM cana-6326 106 4 ) ) PUNCT cana-6326 106 5 3720 3720 NUM cana-6326 106 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 107 1 𝐾₀₂ 𝐾₀₂ PROPN cana-6326 107 2 = = PUNCT cana-6326 108 1 𝐾₁₁𝐾₂₂𝐾₂₆ 𝐾₁₁𝐾₂₂𝐾₂₆ ADJ cana-6326 108 2 βˆ’ βˆ’ PROPN cana-6326 108 3 πΎβ‚β‚ƒπΎβ‚‚β‚†πœ”2 πΎβ‚β‚ƒπΎβ‚‚β‚†πœ”2 NUM cana-6326 108 4 βˆ’ βˆ’ PROPN cana-6326 108 5 πΎβ‚‚β‚‚πΎβ‚β‚…πœ”Β² πΎβ‚‚β‚‚πΎβ‚β‚…πœ”Β² NOUN cana-6326 108 6 βˆ’ βˆ’ NOUN cana-6326 108 7 𝐾₁₁𝐾₂₃𝐾₂₅ 𝐾₁₁𝐾₂₃𝐾₂₅ NOUN cana-6326 108 8 + + CCONJ cana-6326 108 9 πΎβ‚ƒβ‚ƒπœΒ²πΎβ‚‚β‚…πœ”Β² πΎβ‚ƒβ‚ƒπœΒ²πΎβ‚‚β‚…πœ”Β² ADJ cana-6326 108 10 + + CCONJ cana-6326 108 11 πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ƒπœ”Β² πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ƒπœ”Β² PROPN cana-6326 108 12 + + CCONJ cana-6326 108 13 𝐾₂₁𝐾₂₆ 𝐾₂₁𝐾₂₆ ADJ cana-6326 108 14 βˆ’ βˆ’ PROPN cana-6326 108 15 𝐾₂₃𝐾₂₄ 𝐾₂₃𝐾₂₄ NOUN cana-6326 108 16 βˆ’ βˆ’ NOUN cana-6326 108 17 𝑏₃𝐾₂₁𝐾₂₅ 𝑏₃𝐾₂₁𝐾₂₅ NOUN cana-6326 108 18 + + CCONJ cana-6326 108 19 𝑏₃𝐾₂₂𝐾₂₄ 𝑏₃𝐾₂₂𝐾₂₄ NOUN cana-6326 108 20 , , PUNCT cana-6326 108 21 𝐾₀₃ 𝐾₀₃ PRON cana-6326 108 22 = = PUNCT cana-6326 108 23 πœ”2𝐾₂₆𝐾₂₂ πœ”2𝐾₂₆𝐾₂₂ NOUN cana-6326 108 24 βˆ’ βˆ’ NOUN cana-6326 108 25 πœ”Β²πΎβ‚‚β‚ƒπΎβ‚‚β‚… πœ”Β²πΎβ‚‚β‚ƒπΎβ‚‚β‚… NOUN cana-6326 108 26 , , PUNCT cana-6326 108 27 𝐾₁₁ 𝐾₁₁ PROPN cana-6326 108 28 = = SYM cana-6326 108 29 𝑏₁ 𝑏₁ PROPN cana-6326 108 30 + + CCONJ cana-6326 108 31 𝑏₂ 𝑏₂ ADV cana-6326 108 32 βˆ’ βˆ’ PROPN cana-6326 108 33 πœ‰2πœ”2 πœ‰2πœ”2 PUNCT cana-6326 108 34 , , PUNCT cana-6326 108 35 𝐾₁₂ 𝐾₁₂ PROPN cana-6326 108 36 = = SYM cana-6326 108 37 1 1 NUM cana-6326 108 38 + + CCONJ cana-6326 108 39 π‘–πœ”πœπ‘ž π‘–πœ”πœπ‘ž ADJ cana-6326 108 40 βˆ’ βˆ’ PROPN cana-6326 108 41 πœ”Β² πœ”Β² NOUN cana-6326 108 42 2 2 NUM cana-6326 108 43 πœπ‘ž πœπ‘ž ADP cana-6326 108 44 2 2 NUM cana-6326 108 45 , , PUNCT cana-6326 108 46 𝐾₁₃ 𝐾₁₃ PROPN cana-6326 108 47 = = SYM cana-6326 108 48 π‘β‚…π‘–πœ”πœΒ² π‘β‚…π‘–πœ”πœΒ² NOUN cana-6326 108 49 + + X cana-6326 108 50 1 1 NUM cana-6326 108 51 + + CCONJ cana-6326 108 52 π‘–πœ”πœπ‘‘ π‘–πœ”πœπ‘‘ NOUN cana-6326 108 53 , , PUNCT cana-6326 108 54 𝐾₁₄ 𝐾₁₄ PROPN cana-6326 108 55 = = SYM cana-6326 109 1 1 1 NUM cana-6326 109 2 + + CCONJ cana-6326 109 3 π‘–πœ”πœπ‘’ π‘–πœ”πœπ‘’ ADJ cana-6326 109 4 βˆ’ βˆ’ PROPN cana-6326 109 5 πœ”Β² πœ”Β² NOUN cana-6326 109 6 2 2 NUM cana-6326 109 7 πœπ‘’ πœπ‘’ ADP cana-6326 109 8 2 2 NUM cana-6326 109 9 , , PUNCT cana-6326 109 10 𝐾₁₅ 𝐾₁₅ PROPN cana-6326 109 11 = = PRON cana-6326 109 12 1+π‘–πœ”πœπ‘ 1+π‘–πœ”πœπ‘ NUM cana-6326 110 1 + + CCONJ cana-6326 110 2 π‘–πœ”πœΒ²π‘β‚‰ π‘–πœ”πœΒ²π‘β‚‰ ADV cana-6326 110 3 , , PUNCT cana-6326 110 4 𝐾₂₁ 𝐾₂₁ PROPN cana-6326 110 5 = = SYM cana-6326 110 6 𝐾₃₁𝐾₁₂ 𝐾₃₁𝐾₁₂ PROPN cana-6326 110 7 , , PUNCT cana-6326 110 8 𝐾22= 𝐾22= NUM cana-6326 110 9 𝐾₃₂𝐾₁₂ 𝐾₃₂𝐾₁₂ NOUN cana-6326 110 10 , , PUNCT cana-6326 110 11 𝐾₂₃ 𝐾₂₃ PROPN cana-6326 110 12 = = SYM cana-6326 110 13 𝐾₃₃𝐾₁₂ 𝐾₃₃𝐾₁₂ ADJ cana-6326 110 14 , , PUNCT cana-6326 110 15 𝐾₂₄ 𝐾₂₄ NOUN cana-6326 110 16 = = PUNCT cana-6326 110 17 𝐾₃₄𝐾₁₄ 𝐾₃₄𝐾₁₄ PROPN cana-6326 110 18 , , PUNCT cana-6326 110 19 𝐾₂₅ 𝐾₂₅ PUNCT cana-6326 110 20 = = PUNCT cana-6326 111 1 𝐾₃₅𝐾₁₄ 𝐾₃₅𝐾₁₄ ADV cana-6326 111 2 , , PUNCT cana-6326 111 3 𝐾₂₆ 𝐾₂₆ PROPN cana-6326 111 4 = = PUNCT cana-6326 111 5 𝐾₃₆𝐾₁₄ 𝐾₃₆𝐾₁₄ NOUN cana-6326 111 6 , , PUNCT cana-6326 111 7 𝐾₃₁ 𝐾₃₁ PROPN cana-6326 111 8 = = SYM cana-6326 111 9 π‘β‚„π‘–πœ” π‘β‚„π‘–πœ” X cana-6326 111 10 , , PUNCT cana-6326 111 11 𝐾₃₂ 𝐾₃₂ X cana-6326 112 1 = = NOUN cana-6326 112 2 π‘β‚…π‘–πœ” π‘β‚…π‘–πœ” NUM cana-6326 112 3 , , PUNCT cana-6326 112 4 𝐾₃₃ 𝐾₃₃ PROPN cana-6326 112 5 = = SYM cana-6326 112 6 π‘β‚†π‘–πœ” π‘β‚†π‘–πœ” PROPN cana-6326 112 7 , , PUNCT cana-6326 112 8 𝐾₃₄ 𝐾₃₄ PROPN cana-6326 112 9 = = PUNCT cana-6326 112 10 π‘β‚‡π‘–πœ” π‘β‚‡π‘–πœ” PUNCT cana-6326 112 11 , , PUNCT cana-6326 112 12 𝐾₃₅ 𝐾₃₅ PROPN cana-6326 112 13 = = SYM cana-6326 112 14 π‘β‚ˆπ‘–πœ” π‘β‚ˆπ‘–πœ” X cana-6326 112 15 , , PUNCT cana-6326 112 16 𝐾₃₆ 𝐾₃₆ PROPN cana-6326 112 17 = = PUNCT cana-6326 112 18 π‘β‚‰π‘–πœ” π‘β‚‰π‘–πœ” VERB cana-6326 112 19 to to PART cana-6326 112 20 solve solve VERB cana-6326 112 21 equations equation NOUN cana-6326 112 22 ( ( PUNCT cana-6326 112 23 20 20 NUM cana-6326 112 24 ) ) PUNCT cana-6326 112 25 and and CCONJ cana-6326 112 26 ( ( PUNCT cana-6326 112 27 21 21 NUM cana-6326 112 28 ) ) PUNCT cana-6326 112 29 with with ADP cana-6326 112 30 οΏ½ οΏ½ PROPN cana-6326 112 31 Μ‚ Μ‚ SYM cana-6326 112 32 οΏ½ οΏ½ PROPN cana-6326 112 33 , , PUNCT cana-6326 112 34 ΟˆΜ‚ ΟˆΜ‚ PRON cana-6326 112 35 , , PUNCT cana-6326 112 36 tΜ‚ tΜ‚ NUM cana-6326 112 37 and and CCONJ cana-6326 112 38 οΏ½ οΏ½ PROPN cana-6326 112 39 Μ‚ Μ‚ VERB cana-6326 112 40 οΏ½ οΏ½ NOUN cana-6326 112 41 disappear disappear VERB cana-6326 112 42 as as SCONJ cana-6326 112 43 π‘₯₃ π‘₯₃ ADJ cana-6326 112 44 approaches approach NOUN cana-6326 112 45 infinity infinity NOUN cana-6326 112 46 , , PUNCT cana-6326 112 47 we we PRON cana-6326 112 48 write write VERB cana-6326 112 49 ( ( PUNCT cana-6326 112 50 οΏ½ οΏ½ PROPN cana-6326 112 51 Μ‚ Μ‚ VERB cana-6326 112 52 οΏ½ οΏ½ PROPN cana-6326 112 53 , , PUNCT cana-6326 112 54 tΜ‚ tΜ‚ NUM cana-6326 112 55 , , PUNCT cana-6326 112 56 pΜ‚ pΜ‚ X cana-6326 112 57 ) ) PUNCT cana-6326 112 58 ( ( PUNCT cana-6326 112 59 π‘₯₃ π‘₯₃ PROPN cana-6326 112 60 , , PUNCT cana-6326 112 61 πœ‰1 πœ‰1 PROPN cana-6326 112 62 , , PUNCT cana-6326 112 63 𝑠 𝑠 PROPN cana-6326 112 64 ) ) PUNCT cana-6326 112 65 = = SYM cana-6326 112 66 βˆ‘ βˆ‘ PUNCT cana-6326 112 67 ( ( PUNCT cana-6326 112 68 1 1 NUM cana-6326 112 69 , , PUNCT cana-6326 112 70 𝑅𝑖 𝑅𝑖 PROPN cana-6326 112 71 βˆ— βˆ— NOUN cana-6326 112 72 , , PUNCT cana-6326 112 73 𝑆𝑖 𝑆𝑖 PROPN cana-6326 112 74 βˆ—)3 βˆ—)3 PUNCT cana-6326 112 75 𝑖=1 𝑖=1 PROPN cana-6326 112 76 𝐴𝑖𝑒 𝐴𝑖𝑒 PROPN cana-6326 112 77 βˆ’π‘šα΅’π‘₯₃ βˆ’π‘šα΅’π‘₯₃ PROPN cana-6326 112 78 ( ( PUNCT cana-6326 112 79 22 22 NUM cana-6326 112 80 ) ) PUNCT cana-6326 112 81 οΏ½ οΏ½ PROPN cana-6326 112 82 Μ‚ Μ‚ SYM cana-6326 112 83 οΏ½ οΏ½ PROPN cana-6326 112 84 ( ( PUNCT cana-6326 112 85 π‘₯₃ π‘₯₃ PROPN cana-6326 112 86 , , PUNCT cana-6326 112 87 πœ‰1 πœ‰1 PROPN cana-6326 112 88 , , PUNCT cana-6326 112 89 𝑠 𝑠 PROPN cana-6326 112 90 ) ) PUNCT cana-6326 112 91 = = VERB cana-6326 113 1 π΄β‚„π‘’βˆ’π‘šβ‚„π‘₯₃ π΄β‚„π‘’βˆ’π‘šβ‚„π‘₯₃ VERB cana-6326 113 2 ( ( PUNCT cana-6326 113 3 23 23 NUM cana-6326 113 4 ) ) PUNCT cana-6326 113 5 the the DET cana-6326 113 6 roots root NOUN cana-6326 113 7 of of ADP cana-6326 113 8 the the DET cana-6326 113 9 characteristic characteristic ADJ cana-6326 113 10 equations equation NOUN cana-6326 113 11 ( ( PUNCT cana-6326 113 12 20 20 NUM cana-6326 113 13 ) ) PUNCT cana-6326 113 14 , , PUNCT cana-6326 113 15 ( ( PUNCT cana-6326 113 16 21 21 NUM cana-6326 113 17 ) ) PUNCT cana-6326 113 18 are be AUX cana-6326 113 19 mα΅’ mα΅’ X cana-6326 113 20 ( ( PUNCT cana-6326 113 21 i=1,2,3,4 i=1,2,3,4 ADJ cana-6326 113 22 ) ) PUNCT cana-6326 113 23 and and CCONJ cana-6326 113 24 𝐴𝑖(i=1,2,3,4 𝐴𝑖(i=1,2,3,4 ADJ cana-6326 113 25 ) ) PUNCT cana-6326 113 26 are be AUX cana-6326 113 27 the the DET cana-6326 113 28 corresponding corresponding ADJ cana-6326 113 29 amplitude amplitude NOUN cana-6326 113 30 coefficients coefficient NOUN cana-6326 113 31 determined determine VERB cana-6326 113 32 from from ADP cana-6326 113 33 boundary boundary ADJ cana-6326 113 34 conditions condition NOUN cana-6326 113 35 and and CCONJ cana-6326 113 36 𝑅𝑖 𝑅𝑖 PROPN cana-6326 113 37 βˆ— βˆ— NOUN cana-6326 113 38 and and CCONJ cana-6326 113 39 𝑆𝑖 𝑆𝑖 PROPN cana-6326 113 40 βˆ— βˆ— NOUN cana-6326 113 41 are be AUX cana-6326 113 42 derived derive VERB cana-6326 113 43 as as SCONJ cana-6326 113 44 follows follow VERB cana-6326 113 45 : : PUNCT cana-6326 113 46 𝑅𝑖 𝑅𝑖 PROPN cana-6326 113 47 βˆ— βˆ— NOUN cana-6326 113 48 = = PUNCT cana-6326 113 49 ( ( PUNCT cana-6326 113 50 π‘šα΅’2 π‘šα΅’2 PROPN cana-6326 113 51 βˆ’ βˆ’ ADP cana-6326 113 52 πœ‰β‚Β²)Β³(πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚„πœΒ²πœΒ² πœ‰β‚Β²)Β³(πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚„πœΒ²πœΒ² PROPN cana-6326 113 53 βˆ’ βˆ’ PROPN cana-6326 113 54 πΎβ‚ƒβ‚πœΒ²πΎβ‚β‚… πΎβ‚ƒβ‚πœΒ²πΎβ‚β‚… NUM cana-6326 113 55 ) ) PUNCT cana-6326 113 56 + + CCONJ cana-6326 113 57 ( ( PUNCT cana-6326 113 58 π‘šα΅’2 π‘šα΅’2 X cana-6326 113 59 βˆ’ βˆ’ NOUN cana-6326 113 60 πœ‰β‚Β²)Β²(πΎβ‚ƒβ‚πœ2𝐾₂₆ πœ‰β‚Β²)Β²(πΎβ‚ƒβ‚πœ2𝐾₂₆ ADJ cana-6326 113 61 + + CCONJ cana-6326 113 62 𝐾₂₁𝐾₁₅ 𝐾₂₁𝐾₁₅ ADJ cana-6326 113 63 βˆ’πΎβ‚ƒβ‚ƒπœ2𝐾₂₄ βˆ’πΎβ‚ƒβ‚ƒπœ2𝐾₂₄ NOUN cana-6326 113 64 βˆ’ βˆ’ NOUN cana-6326 113 65 πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ NOUN cana-6326 113 66 ) ) PUNCT cana-6326 113 67 + + CCONJ cana-6326 113 68 ( ( PUNCT cana-6326 113 69 π‘šα΅’2 π‘šα΅’2 PROPN cana-6326 113 70 βˆ’ βˆ’ PROPN cana-6326 113 71 πœ‰β‚Β²)(𝐾₂₁𝐾₂₆ πœ‰β‚Β²)(𝐾₂₁𝐾₂₆ VERB cana-6326 113 72 βˆ’ βˆ’ ADP cana-6326 113 73 𝐾₂₃𝐾₂₄ 𝐾₂₃𝐾₂₄ NUM cana-6326 113 74 ) ) PUNCT cana-6326 113 75 ( ( PUNCT cana-6326 113 76 π‘šα΅’2 π‘šα΅’2 NOUN cana-6326 113 77 βˆ’ βˆ’ PROPN cana-6326 113 78 πœ‰β‚Β²)Β² πœ‰β‚Β²)Β² NOUN cana-6326 113 79 ( ( PUNCT cana-6326 113 80 𝐾₁₃𝐾₁₅ 𝐾₁₃𝐾₁₅ VERB cana-6326 113 81 βˆ’ βˆ’ NOUN cana-6326 113 82 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœΒ²πœΒ² πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœΒ²πœΒ² NUM cana-6326 113 83 ) ) PUNCT cana-6326 114 1 + + CCONJ cana-6326 114 2 ( ( PUNCT cana-6326 114 3 π‘šα΅’2 π‘šα΅’2 X cana-6326 114 4 βˆ’ βˆ’ PROPN cana-6326 114 5 πœ‰β‚Β²)(βˆ’πΎβ‚‚β‚‚πΎβ‚β‚… πœ‰β‚Β²)(βˆ’πΎβ‚‚β‚‚πΎβ‚β‚… NOUN cana-6326 114 6 βˆ’ βˆ’ PROPN cana-6326 114 7 𝐾₁₃𝐾₂₆ 𝐾₁₃𝐾₂₆ ADJ cana-6326 114 8 + + NUM cana-6326 114 9 πΎβ‚ƒβ‚ƒπœΒ²πΎβ‚‚β‚… πΎβ‚ƒβ‚ƒπœΒ²πΎβ‚‚β‚… NOUN cana-6326 114 10 + + SYM cana-6326 114 11 πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ƒ πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ƒ PROPN cana-6326 114 12 ) ) PUNCT cana-6326 114 13 + + CCONJ cana-6326 114 14 ( ( PUNCT cana-6326 114 15 𝐾₂₂𝐾₂₆ 𝐾₂₂𝐾₂₆ ADJ cana-6326 114 16 βˆ’ βˆ’ ADP cana-6326 114 17 𝐾₂₃𝐾₂₅ 𝐾₂₃𝐾₂₅ NOUN cana-6326 114 18 ) ) PUNCT cana-6326 114 19 𝑆𝑖 𝑆𝑖 PROPN cana-6326 114 20 βˆ— βˆ— NOUN cana-6326 114 21 = = PUNCT cana-6326 114 22 ( ( PUNCT cana-6326 114 23 π‘šα΅’2 π‘šα΅’2 NOUN cana-6326 114 24 βˆ’ βˆ’ VERB cana-6326 114 25 πœ‰β‚Β²)Β³(πΎβ‚ƒβ‚πΎβ‚ƒβ‚…πœΒ²πœΒ² πœ‰β‚Β²)Β³(πΎβ‚ƒβ‚πΎβ‚ƒβ‚…πœΒ²πœΒ² PROPN cana-6326 114 26 βˆ’ βˆ’ PROPN cana-6326 114 27 πΎβ‚ƒβ‚„πΎβ‚β‚ƒπœΒ² πΎβ‚ƒβ‚„πΎβ‚β‚ƒπœΒ² PROPN cana-6326 114 28 ) ) PUNCT cana-6326 115 1 + + CCONJ cana-6326 115 2 ( ( PUNCT cana-6326 115 3 π‘šα΅’2 π‘šα΅’2 PROPN cana-6326 115 4 βˆ’ βˆ’ PROPN cana-6326 115 5 πœ‰β‚Β²)Β²(𝐾₁₃𝐾₂₄ πœ‰β‚Β²)Β²(𝐾₁₃𝐾₂₄ NOUN cana-6326 116 1 + + CCONJ cana-6326 116 2 πΎβ‚ƒβ‚„πœΒ²πΎβ‚‚β‚‚ πΎβ‚ƒβ‚„πœΒ²πΎβ‚‚β‚‚ X cana-6326 117 1 βˆ’ βˆ’ NOUN cana-6326 117 2 πΎβ‚ƒβ‚πœΒ²πΎβ‚‚β‚… πΎβ‚ƒβ‚πœΒ²πΎβ‚‚β‚… NOUN cana-6326 117 3 βˆ’πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ βˆ’πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ NOUN cana-6326 117 4 ) ) PUNCT cana-6326 118 1 + + CCONJ cana-6326 118 2 ( ( PUNCT cana-6326 118 3 π‘šα΅’2 π‘šα΅’2 NOUN cana-6326 118 4 βˆ’ βˆ’ PROPN cana-6326 118 5 πœ‰β‚Β²)(𝐾₂₁𝐾₂₅ πœ‰β‚Β²)(𝐾₂₁𝐾₂₅ NOUN cana-6326 118 6 βˆ’ βˆ’ ADP cana-6326 118 7 𝐾₂₂𝐾₂₄ 𝐾₂₂𝐾₂₄ NOUN cana-6326 118 8 ) ) PUNCT cana-6326 118 9 ( ( PUNCT cana-6326 118 10 π‘šα΅’2 π‘šα΅’2 NOUN cana-6326 118 11 βˆ’ βˆ’ PROPN cana-6326 118 12 πœ‰β‚Β²)Β² πœ‰β‚Β²)Β² NOUN cana-6326 118 13 ( ( PUNCT cana-6326 118 14 𝐾₁₃𝐾₁₅ 𝐾₁₃𝐾₁₅ VERB cana-6326 118 15 βˆ’ βˆ’ NOUN cana-6326 118 16 πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœΒ²πœΒ² πΎβ‚ƒβ‚ƒπΎβ‚ƒβ‚…πœΒ²πœΒ² NUM cana-6326 118 17 ) ) PUNCT cana-6326 118 18 + + CCONJ cana-6326 118 19 ( ( PUNCT cana-6326 118 20 π‘šα΅’2 π‘šα΅’2 X cana-6326 118 21 βˆ’ βˆ’ PROPN cana-6326 118 22 πœ‰β‚Β²)(βˆ’πΎβ‚‚β‚‚πΎβ‚β‚… πœ‰β‚Β²)(βˆ’πΎβ‚‚β‚‚πΎβ‚β‚… NOUN cana-6326 118 23 βˆ’ βˆ’ PROPN cana-6326 118 24 𝐾₁₃𝐾₂₆ 𝐾₁₃𝐾₂₆ ADJ cana-6326 118 25 + + NUM cana-6326 118 26 πΎβ‚ƒβ‚ƒπœΒ²πΎβ‚‚β‚… πΎβ‚ƒβ‚ƒπœΒ²πΎβ‚‚β‚… NOUN cana-6326 118 27 + + SYM cana-6326 118 28 πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ƒ πΎβ‚ƒβ‚…πœΒ²πΎβ‚‚β‚ƒ PROPN cana-6326 118 29 ) ) PUNCT cana-6326 118 30 + + CCONJ cana-6326 118 31 ( ( PUNCT cana-6326 118 32 𝐾₂₂𝐾₂₆ 𝐾₂₂𝐾₂₆ ADJ cana-6326 118 33 βˆ’ βˆ’ ADP cana-6326 118 34 𝐾₂₃𝐾₂₅ 𝐾₂₃𝐾₂₅ NOUN cana-6326 118 35 ) ) PUNCT cana-6326 118 36 i=1,2,3 i=1,2,3 VERB cana-6326 118 37 5 5 NUM cana-6326 118 38 . . PUNCT cana-6326 118 39 boundary boundary ADJ cana-6326 118 40 conditions condition NOUN cana-6326 118 41 at at ADP cana-6326 118 42 the the DET cana-6326 118 43 point point NOUN cana-6326 118 44 where where SCONJ cana-6326 118 45 π‘₯3 π‘₯3 NOUN cana-6326 118 46 = = SYM cana-6326 118 47 0 0 NUM cana-6326 118 48 , , PUNCT cana-6326 118 49 on on ADP cana-6326 118 50 the the DET cana-6326 118 51 plane plane NOUN cana-6326 118 52 boundary boundary NOUN cana-6326 118 53 , , PUNCT cana-6326 118 54 the the DET cana-6326 118 55 half half ADJ cana-6326 118 56 - - PUNCT cana-6326 118 57 space space NOUN cana-6326 118 58 is be AUX cana-6326 118 59 excited excite VERB cana-6326 118 60 from from ADP cana-6326 118 61 the the DET cana-6326 118 62 outside outside NOUN cana-6326 118 63 by by ADP cana-6326 118 64 a a DET cana-6326 118 65 normal normal ADJ cana-6326 118 66 mechanical mechanical ADJ cana-6326 118 67 load load NOUN cana-6326 118 68 , , PUNCT cana-6326 118 69 a a DET cana-6326 118 70 thermal thermal ADJ cana-6326 118 71 input input NOUN cana-6326 118 72 , , PUNCT cana-6326 118 73 and and CCONJ cana-6326 118 74 a a DET cana-6326 118 75 chemical chemical ADJ cana-6326 118 76 potential potential ADJ cana-6326 118 77 source source NOUN cana-6326 118 78 . . PUNCT cana-6326 119 1 so so ADV cana-6326 119 2 , , PUNCT cana-6326 119 3 the the DET cana-6326 119 4 boundary boundary ADJ cana-6326 119 5 conditions condition NOUN cana-6326 119 6 at at ADP cana-6326 119 7 π‘₯3 π‘₯3 NOUN cana-6326 119 8 = = SYM cana-6326 119 9 0 0 NUM cana-6326 119 10 are be AUX cana-6326 119 11 set set VERB cana-6326 119 12 up up ADP cana-6326 119 13 to to PART cana-6326 119 14 show show VERB cana-6326 119 15 these these DET cana-6326 119 16 three three NUM cana-6326 119 17 types type NOUN cana-6326 119 18 of of ADP cana-6326 119 19 applied apply VERB cana-6326 119 20 fields field NOUN cana-6326 119 21 . . PUNCT cana-6326 120 1 𝑑33 𝑑33 VERB cana-6326 120 2 = = SYM cana-6326 120 3 βˆ’πΉ1(π‘₯1)𝑒 βˆ’πΉ1(π‘₯1)𝑒 PROPN cana-6326 120 4 π‘–πœ”π‘‘ π‘–πœ”π‘‘ NOUN cana-6326 120 5 , , PUNCT cana-6326 120 6 𝑑31 𝑑31 NOUN cana-6326 120 7 = = SYM cana-6326 120 8 0 0 NUM cana-6326 120 9 , , PUNCT cana-6326 120 10 𝑇 𝑇 PROPN cana-6326 120 11 = = SYM cana-6326 120 12 𝐹2(π‘₯1)𝑒 𝐹2(π‘₯1)𝑒 PROPN cana-6326 120 13 π‘–πœ”π‘‘ π‘–πœ”π‘‘ NOUN cana-6326 120 14 , , PUNCT cana-6326 120 15 𝑃 𝑃 PROPN cana-6326 120 16 = = SYM cana-6326 120 17 𝐹3(π‘₯1)𝑒 𝐹3(π‘₯1)𝑒 NUM cana-6326 120 18 π‘–πœ”π‘‘ π‘–πœ”π‘‘ NOUN cana-6326 120 19 ( ( PUNCT cana-6326 120 20 24 24 NUM cana-6326 120 21 ) ) PUNCT cana-6326 120 22 the the DET cana-6326 120 23 non non ADJ cana-6326 120 24 dimensional dimensional ADJ cana-6326 120 25 stress stress NOUN cana-6326 120 26 components component NOUN cana-6326 120 27 are be AUX cana-6326 120 28 expressed express VERB cana-6326 120 29 by by ADP cana-6326 120 30 communications communication NOUN cana-6326 120 31 on on ADP cana-6326 120 32 applied apply VERB cana-6326 120 33 nonlinear nonlinear ADJ cana-6326 120 34 analysis analysis NOUN cana-6326 120 35 issn issn NOUN cana-6326 120 36 : : PUNCT cana-6326 120 37 1074 1074 NUM cana-6326 120 38 - - PUNCT cana-6326 120 39 133x 133x NUM cana-6326 120 40 vol vol VERB cana-6326 120 41 32 32 NUM cana-6326 120 42 no no NOUN cana-6326 120 43 . . PUNCT cana-6326 121 1 10s 10 NOUN cana-6326 121 2 ( ( PUNCT cana-6326 121 3 2025 2025 NUM cana-6326 121 4 ) ) PUNCT cana-6326 121 5 3721 3721 NUM cana-6326 121 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 121 7 𝑑33 𝑑33 NOUN cana-6326 121 8 = = SYM cana-6326 121 9 2πœ‡ 2πœ‡ NUM cana-6326 121 10 𝛾₁𝑇₀ 𝛾₁𝑇₀ PUNCT cana-6326 122 1 ( ( PUNCT cana-6326 122 2 πœ•π‘’β‚ƒ πœ•π‘’β‚ƒ NOUN cana-6326 122 3 πœ•π‘₯₃ πœ•π‘₯₃ X cana-6326 122 4 ) ) PUNCT cana-6326 123 1 + + CCONJ cana-6326 123 2 πœ†β‚€ πœ†β‚€ NOUN cana-6326 123 3 𝛾₁𝑇₀ 𝛾₁𝑇₀ X cana-6326 123 4 ( ( PUNCT cana-6326 123 5 πœ•π‘’β‚ πœ•π‘’β‚ PUNCT cana-6326 123 6 πœ•π‘₯₃ πœ•π‘₯₃ ADJ cana-6326 123 7 + + NUM cana-6326 123 8 πœ•π‘’β‚ƒ πœ•π‘’β‚ƒ NOUN cana-6326 123 9 πœ•π‘₯₁ πœ•π‘₯₁ PROPN cana-6326 123 10 ) ) PUNCT cana-6326 123 11 βˆ’ βˆ’ PROPN cana-6326 124 1 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 124 2 𝛾₁𝑇₀ 𝛾₁𝑇₀ PUNCT cana-6326 124 3 𝑇 𝑇 PROPN cana-6326 124 4 βˆ’ βˆ’ PROPN cana-6326 124 5 𝛾₂²𝑏 𝛾₂²𝑏 PUNCT cana-6326 124 6 𝛾₁𝑇₀ 𝛾₁𝑇₀ PUNCT cana-6326 125 1 p p X cana-6326 125 2 ( ( PUNCT cana-6326 125 3 25 25 NUM cana-6326 125 4 ) ) PUNCT cana-6326 125 5 𝑑₃₁ 𝑑₃₁ NOUN cana-6326 125 6 = = SYM cana-6326 125 7 πœ‡ πœ‡ ADP cana-6326 125 8 𝛾₁𝑇₀ 𝛾₁𝑇₀ PROPN cana-6326 125 9 ( ( PUNCT cana-6326 125 10 πœ•π‘’β‚ πœ•π‘’β‚ PUNCT cana-6326 125 11 πœ•π‘₯₁ πœ•π‘₯₁ NOUN cana-6326 125 12 + + CCONJ cana-6326 125 13 πœ•π‘’β‚ƒ πœ•π‘’β‚ƒ NOUN cana-6326 125 14 πœ•π‘₯₃ πœ•π‘₯₃ NUM cana-6326 125 15 ) ) PUNCT cana-6326 125 16 ( ( PUNCT cana-6326 125 17 26 26 NUM cana-6326 125 18 ) ) PUNCT cana-6326 125 19 applying apply VERB cana-6326 125 20 fourier fourier NOUN cana-6326 125 21 transform transform NOUN cana-6326 125 22 on on ADP cana-6326 125 23 ( ( PUNCT cana-6326 125 24 25 25 NUM cana-6326 125 25 ) ) PUNCT cana-6326 125 26 and and CCONJ cana-6326 125 27 ( ( PUNCT cana-6326 125 28 26),we 26),we NUM cana-6326 125 29 get get VERB cana-6326 125 30 𝑑 𝑑 PRON cana-6326 125 31 33= 33= NUM cana-6326 125 32 βˆ’ βˆ’ PROPN cana-6326 125 33 οΏ½ οΏ½ PROPN cana-6326 125 34 Μ‚ Μ‚ NOUN cana-6326 125 35 οΏ½ οΏ½ NOUN cana-6326 125 36 1 1 NUM cana-6326 125 37 ( ( PUNCT cana-6326 125 38 πœ‰β‚)π‘’π‘–πœ”π‘‘ πœ‰β‚)π‘’π‘–πœ”π‘‘ NOUN cana-6326 125 39 , , PUNCT cana-6326 125 40 𝑑 𝑑 X cana-6326 125 41 31 31 NUM cana-6326 125 42 = = SYM cana-6326 125 43 0 0 NUM cana-6326 125 44 , , PUNCT cana-6326 125 45 tΜ‚ tΜ‚ NUM cana-6326 125 46 = = SYM cana-6326 125 47 οΏ½ οΏ½ PROPN cana-6326 125 48 Μ‚ Μ‚ NOUN cana-6326 125 49 οΏ½ οΏ½ NOUN cana-6326 125 50 2 2 NUM cana-6326 125 51 ( ( PUNCT cana-6326 125 52 πœ‰β‚)π‘’π‘–πœ”π‘‘ πœ‰β‚)π‘’π‘–πœ”π‘‘ NOUN cana-6326 125 53 , , PUNCT cana-6326 125 54 pΜ‚ pΜ‚ X cana-6326 125 55 = = SYM cana-6326 125 56 οΏ½ οΏ½ PROPN cana-6326 125 57 Μ‚ Μ‚ PROPN cana-6326 125 58 οΏ½ οΏ½ NOUN cana-6326 125 59 3(πœ‰β‚ 3(πœ‰β‚ NUM cana-6326 125 60 ) ) PUNCT cana-6326 125 61 π‘’π‘–πœ”π‘‘ π‘’π‘–πœ”π‘‘ NOUN cana-6326 125 62 ( ( PUNCT cana-6326 125 63 27 27 NUM cana-6326 125 64 ) ) PUNCT cana-6326 125 65 displacement displacement NOUN cana-6326 125 66 , , PUNCT cana-6326 125 67 stress stress NOUN cana-6326 125 68 , , PUNCT cana-6326 125 69 temperature temperature NOUN cana-6326 125 70 variation variation NOUN cana-6326 125 71 , , PUNCT cana-6326 125 72 and and CCONJ cana-6326 125 73 chemical chemical NOUN cana-6326 125 74 potential potential NOUN cana-6326 125 75 are be AUX cana-6326 125 76 determined determine VERB cana-6326 125 77 by by ADP cana-6326 125 78 applying apply VERB cana-6326 125 79 equations equation NOUN cana-6326 125 80 ( ( PUNCT cana-6326 125 81 22 22 NUM cana-6326 125 82 ) ) PUNCT cana-6326 125 83 and and CCONJ cana-6326 125 84 ( ( PUNCT cana-6326 125 85 23 23 NUM cana-6326 125 86 ) ) PUNCT cana-6326 125 87 to to ADP cana-6326 125 88 the the DET cana-6326 125 89 boundary boundary ADJ cana-6326 125 90 conditions condition NOUN cana-6326 125 91 ( ( PUNCT cana-6326 125 92 27 27 NUM cana-6326 125 93 ) ) PUNCT cana-6326 125 94 , , PUNCT cana-6326 125 95 taking take VERB cana-6326 125 96 into into ADP cana-6326 125 97 account account NOUN cana-6326 125 98 equations equation NOUN cana-6326 125 99 ( ( PUNCT cana-6326 125 100 12 12 NUM cana-6326 125 101 ) ) PUNCT cana-6326 125 102 , , PUNCT cana-6326 125 103 ( ( PUNCT cana-6326 125 104 22 22 NUM cana-6326 125 105 ) ) PUNCT cana-6326 125 106 and and CCONJ cana-6326 125 107 ( ( PUNCT cana-6326 125 108 23 23 NUM cana-6326 125 109 ) ) PUNCT cana-6326 125 110 , , PUNCT cana-6326 125 111 as as SCONJ cana-6326 125 112 follows follow VERB cana-6326 125 113 : : PUNCT cana-6326 125 114 𝑒 𝑒 NOUN cana-6326 125 115 ₁ ₁ NUM cana-6326 125 116 = = SYM cana-6326 125 117 βˆ’ βˆ’ PROPN cana-6326 125 118 π‘–πœ‰β‚ π‘–πœ‰β‚ ADV cana-6326 125 119 βˆ† βˆ† PROPN cana-6326 125 120 βˆ‘ βˆ‘ PUNCT cana-6326 126 1 βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃3 βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃3 PROPN cana-6326 126 2 𝑖=1 𝑖=1 PUNCT cana-6326 127 1 + + CCONJ cana-6326 127 2 βˆ†β‚„π‘šβ‚„π‘’ βˆ†β‚„π‘šβ‚„π‘’ PROPN cana-6326 127 3 βˆ’π‘šβ‚„π‘₯₃ βˆ’π‘šβ‚„π‘₯₃ PROPN cana-6326 127 4 βˆ† βˆ† X cana-6326 127 5 ( ( PUNCT cana-6326 127 6 28 28 NUM cana-6326 127 7 ) ) PUNCT cana-6326 127 8 𝑒 𝑒 PROPN cana-6326 127 9 ₃ ₃ NOUN cana-6326 127 10 = = SYM cana-6326 127 11 βˆ’ βˆ’ PROPN cana-6326 127 12 1 1 NUM cana-6326 127 13 βˆ† βˆ† PROPN cana-6326 127 14 βˆ‘ βˆ‘ PUNCT cana-6326 127 15 π‘š3 π‘š3 PROPN cana-6326 127 16 𝑖=1 𝑖=1 PROPN cana-6326 127 17 α΅’βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ α΅’βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ NOUN cana-6326 127 18 βˆ’ βˆ’ PROPN cana-6326 127 19 π‘–πœ‰β‚βˆ†β‚„π‘’βˆ’π‘šβ‚„π‘₯₃ π‘–πœ‰β‚βˆ†β‚„π‘’βˆ’π‘šβ‚„π‘₯₃ NUM cana-6326 127 20 βˆ† βˆ† PROPN cana-6326 127 21 ( ( PUNCT cana-6326 127 22 29 29 NUM cana-6326 127 23 ) ) PUNCT cana-6326 127 24 𝑑 𝑑 VERB cana-6326 127 25 33= 33= NUM cana-6326 127 26 1 1 NUM cana-6326 127 27 βˆ† βˆ† PROPN cana-6326 127 28 βˆ‘ βˆ‘ PUNCT cana-6326 127 29 𝑏1𝑖 𝑏1𝑖 PROPN cana-6326 127 30 3 3 NUM cana-6326 127 31 𝑖=1 𝑖=1 PUNCT cana-6326 127 32 βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ PROPN cana-6326 127 33 + + CCONJ cana-6326 127 34 βˆ†β‚„π‘14𝑒 βˆ†β‚„π‘14𝑒 ADJ cana-6326 127 35 βˆ’π‘šβ‚„π‘₯₃ βˆ’π‘šβ‚„π‘₯₃ PROPN cana-6326 127 36 βˆ† βˆ† PROPN cana-6326 127 37 ( ( PUNCT cana-6326 127 38 30 30 NUM cana-6326 127 39 ) ) PUNCT cana-6326 127 40 𝑑 𝑑 PROPN cana-6326 127 41 31 31 NUM cana-6326 127 42 = = SYM cana-6326 127 43 1 1 NUM cana-6326 127 44 βˆ† βˆ† X cana-6326 127 45 βˆ‘ βˆ‘ PROPN cana-6326 127 46 𝑏2𝑖 𝑏2𝑖 PROPN cana-6326 127 47 3 3 NUM cana-6326 127 48 𝑖=1 𝑖=1 PROPN cana-6326 127 49 βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ PROPN cana-6326 127 50 + + CCONJ cana-6326 127 51 βˆ†β‚„π‘24𝑒 βˆ†β‚„π‘24𝑒 PROPN cana-6326 127 52 βˆ’π‘šβ‚„π‘₯₃ βˆ’π‘šβ‚„π‘₯₃ PROPN cana-6326 127 53 βˆ† βˆ† PROPN cana-6326 127 54 ( ( PUNCT cana-6326 127 55 31 31 NUM cana-6326 127 56 ) ) PUNCT cana-6326 127 57 tΜ‚ tΜ‚ PUNCT cana-6326 128 1 = = SYM cana-6326 128 2 1 1 NUM cana-6326 128 3 βˆ† βˆ† X cana-6326 128 4 βˆ‘ βˆ‘ PUNCT cana-6326 128 5 𝑅𝑖 𝑅𝑖 PROPN cana-6326 128 6 βˆ—3 βˆ—3 PRON cana-6326 128 7 𝑖=1 𝑖=1 PUNCT cana-6326 128 8 βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ NOUN cana-6326 128 9 ( ( PUNCT cana-6326 128 10 32 32 NUM cana-6326 128 11 ) ) PUNCT cana-6326 128 12 pΜ‚ pΜ‚ X cana-6326 129 1 = = SYM cana-6326 129 2 1 1 NUM cana-6326 129 3 βˆ† βˆ† X cana-6326 129 4 βˆ‘ βˆ‘ PUNCT cana-6326 129 5 𝑆𝑖 𝑆𝑖 PROPN cana-6326 129 6 βˆ—3 βˆ—3 INTJ cana-6326 129 7 𝑖=1 𝑖=1 PROPN cana-6326 129 8 βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ βˆ†α΅’π‘’βˆ’π‘šα΅’π‘₯₃ PROPN cana-6326 129 9 ( ( PUNCT cana-6326 129 10 33 33 NUM cana-6326 129 11 ) ) PUNCT cana-6326 129 12 here here ADV cana-6326 129 13 βˆ†= βˆ†= VERB cana-6326 129 14 ( ( PUNCT cana-6326 129 15 𝑆2 𝑆2 PROPN cana-6326 129 16 βˆ—π‘…1 βˆ—π‘…1 PROPN cana-6326 129 17 βˆ— βˆ— NOUN cana-6326 129 18 βˆ’ βˆ’ PROPN cana-6326 129 19 𝑆1 𝑆1 NOUN cana-6326 129 20 βˆ—π‘…2 βˆ—π‘…2 PROPN cana-6326 129 21 βˆ—)𝑛1 βˆ—)𝑛1 PROPN cana-6326 129 22 + + CCONJ cana-6326 129 23 ( ( PUNCT cana-6326 129 24 𝑆1 𝑆1 NOUN cana-6326 129 25 βˆ—π‘…3 βˆ—π‘…3 NOUN cana-6326 129 26 βˆ— βˆ— NOUN cana-6326 129 27 βˆ’ βˆ’ NOUN cana-6326 130 1 𝑆3 𝑆3 PROPN cana-6326 130 2 βˆ—π‘…1 βˆ—π‘…1 PROPN cana-6326 130 3 βˆ—)𝑛2+(𝑆3 βˆ—)𝑛2+(𝑆3 PROPN cana-6326 130 4 βˆ—π‘…2 βˆ—π‘…2 PROPN cana-6326 130 5 βˆ— βˆ— VERB cana-6326 130 6 βˆ’ βˆ’ PROPN cana-6326 130 7 𝑆2 𝑆2 PROPN cana-6326 131 1 βˆ—π‘…3 βˆ—π‘…3 PROPN cana-6326 131 2 βˆ—)𝑛3 βˆ—)𝑛3 PROPN cana-6326 131 3 , , PUNCT cana-6326 131 4 𝑛1 𝑛1 ADJ cana-6326 131 5 = = PROPN cana-6326 131 6 𝑏₁₃𝑏₂₄ 𝑏₁₃𝑏₂₄ PROPN cana-6326 131 7 βˆ’ βˆ’ PROPN cana-6326 131 8 𝑏₁₄𝑏₂₃ 𝑏₁₄𝑏₂₃ PROPN cana-6326 131 9 , , PUNCT cana-6326 131 10 𝑛2 𝑛2 NOUN cana-6326 131 11 = = PROPN cana-6326 131 12 𝑏₁₂𝑏₂₄ 𝑏₁₂𝑏₂₄ PROPN cana-6326 131 13 βˆ’ βˆ’ PROPN cana-6326 131 14 𝑏₁₄𝑏₂₂ 𝑏₁₄𝑏₂₂ PROPN cana-6326 131 15 , , PUNCT cana-6326 131 16 𝑛3 𝑛3 NOUN cana-6326 131 17 = = SYM cana-6326 131 18 𝑏₁₁𝑏₂₄ 𝑏₁₁𝑏₂₄ ADJ cana-6326 131 19 βˆ’ βˆ’ PROPN cana-6326 131 20 𝑏₁₄𝑏₂₁ 𝑏₁₄𝑏₂₁ NOUN cana-6326 131 21 , , PUNCT cana-6326 131 22 and and CCONJ cana-6326 131 23 𝑏1𝑖 𝑏1𝑖 PROPN cana-6326 131 24 = = SYM cana-6326 131 25 ( ( PUNCT cana-6326 131 26 2π‘Ÿβ‚ 2π‘Ÿβ‚ NUM cana-6326 131 27 + + ADP cana-6326 131 28 π‘Ÿβ‚‚)π‘šπ‘–Β² π‘Ÿβ‚‚)π‘šπ‘–Β² ADP cana-6326 131 29 βˆ’ βˆ’ PROPN cana-6326 131 30 πœ‰β‚Β²π‘Ÿβ‚‚ πœ‰β‚Β²π‘Ÿβ‚‚ PROPN cana-6326 131 31 βˆ’ βˆ’ PROPN cana-6326 131 32 π‘Ÿβ‚ƒπ‘…π‘– π‘Ÿβ‚ƒπ‘…π‘– ADJ cana-6326 131 33 βˆ— βˆ— NOUN cana-6326 131 34 βˆ’ βˆ’ PROPN cana-6326 131 35 π‘Ÿβ‚„π‘†π‘– π‘Ÿβ‚„π‘†π‘– X cana-6326 131 36 βˆ— βˆ— NOUN cana-6326 131 37 , , PUNCT cana-6326 131 38 𝑏14 𝑏14 NOUN cana-6326 131 39 = = SYM cana-6326 131 40 2π‘–πœ‰β‚π‘Ÿβ‚π‘š4 2π‘–πœ‰β‚π‘Ÿβ‚π‘š4 NUM cana-6326 131 41 , , PUNCT cana-6326 131 42 𝑏2𝑖 𝑏2𝑖 PROPN cana-6326 131 43 = = SYM cana-6326 131 44 2π‘–πœ‰β‚π‘Ÿβ‚π‘šπ‘– 2π‘–πœ‰β‚π‘Ÿβ‚π‘šπ‘– NUM cana-6326 131 45 , , PUNCT cana-6326 131 46 𝑏24 𝑏24 NOUN cana-6326 131 47 = = SYM cana-6326 131 48 βˆ’π‘Ÿβ‚(π‘š4 βˆ’π‘Ÿβ‚(π‘š4 NOUN cana-6326 131 49 2 2 NUM cana-6326 131 50 + + CCONJ cana-6326 131 51 πœ‰β‚Β² πœ‰β‚Β² PROPN cana-6326 131 52 ) ) PUNCT cana-6326 131 53 , , PUNCT cana-6326 131 54 π‘Ÿβ‚ π‘Ÿβ‚ NOUN cana-6326 131 55 = = SYM cana-6326 131 56 πœ‡ πœ‡ ADP cana-6326 131 57 𝛾₁𝑇₀ 𝛾₁𝑇₀ PROPN cana-6326 131 58 , , PUNCT cana-6326 131 59 π‘Ÿβ‚‚ π‘Ÿβ‚‚ NOUN cana-6326 131 60 = = SYM cana-6326 131 61 πœ†β‚€ πœ†β‚€ NOUN cana-6326 131 62 𝛾₁𝑇₀ 𝛾₁𝑇₀ PROPN cana-6326 131 63 , , PUNCT cana-6326 131 64 π‘Ÿβ‚ƒ π‘Ÿβ‚ƒ PROPN cana-6326 131 65 = = SYM cana-6326 131 66 πœŒπ‘β‚Β² πœŒπ‘β‚Β² PROPN cana-6326 131 67 𝛾₁𝑇₀ 𝛾₁𝑇₀ PUNCT cana-6326 131 68 , , PUNCT cana-6326 131 69 π‘Ÿβ‚„ π‘Ÿβ‚„ PROPN cana-6326 131 70 = = SYM cana-6326 131 71 𝛾₂²𝑏 𝛾₂²𝑏 PROPN cana-6326 131 72 𝛾₁𝑇₀ 𝛾₁𝑇₀ X cana-6326 131 73 , , PUNCT cana-6326 131 74 i=1 i=1 PROPN cana-6326 131 75 , , PUNCT cana-6326 131 76 2 2 NUM cana-6326 131 77 , , PUNCT cana-6326 131 78 3 3 NUM cana-6326 131 79 βˆ†α΅’ βˆ†α΅’ NOUN cana-6326 131 80 (= (= NOUN cana-6326 131 81 1,2,3,4 1,2,3,4 NUM cana-6326 131 82 ) ) PUNCT cana-6326 131 83 are be AUX cana-6326 131 84 determined determine VERB cana-6326 131 85 by by ADP cana-6326 131 86 changing change VERB cana-6326 131 87 the the DET cana-6326 131 88 first first ADJ cana-6326 131 89 , , PUNCT cana-6326 131 90 second second ADJ cana-6326 131 91 , , PUNCT cana-6326 131 92 third third ADJ cana-6326 131 93 , , PUNCT cana-6326 131 94 and and CCONJ cana-6326 131 95 fourth fourth ADJ cana-6326 131 96 columns column NOUN cana-6326 131 97 of of ADP cana-6326 131 98 βˆ† βˆ† PROPN cana-6326 131 99 to to ADP cana-6326 131 100 [ [ X cana-6326 131 101 - - PUNCT cana-6326 131 102 οΏ½ οΏ½ NOUN cana-6326 131 103 Μ‚ Μ‚ NOUN cana-6326 131 104 οΏ½ οΏ½ NOUN cana-6326 131 105 1(πœ‰β‚)π‘’π‘–πœ”π‘‘,0 1(πœ‰β‚)π‘’π‘–πœ”π‘‘,0 NUM cana-6326 131 106 , , PUNCT cana-6326 131 107 οΏ½ οΏ½ PROPN cana-6326 131 108 Μ‚ Μ‚ PROPN cana-6326 131 109 οΏ½ οΏ½ NOUN cana-6326 131 110 2(πœ‰β‚)π‘’π‘–πœ”π‘‘ 2(πœ‰β‚)π‘’π‘–πœ”π‘‘ NUM cana-6326 131 111 , , PUNCT cana-6326 131 112 οΏ½ οΏ½ PROPN cana-6326 131 113 Μ‚ Μ‚ NOUN cana-6326 131 114 οΏ½ οΏ½ NOUN cana-6326 131 115 3(πœ‰β‚ 3(πœ‰β‚ NUM cana-6326 131 116 ) ) PUNCT cana-6326 131 117 π‘’π‘–πœ”π‘‘]tr π‘’π‘–πœ”π‘‘]tr PROPN cana-6326 131 118 communications communication NOUN cana-6326 131 119 on on ADP cana-6326 131 120 applied apply VERB cana-6326 131 121 nonlinear nonlinear ADJ cana-6326 131 122 analysis analysis NOUN cana-6326 131 123 issn issn NOUN cana-6326 131 124 : : PUNCT cana-6326 131 125 1074 1074 NUM cana-6326 131 126 - - PUNCT cana-6326 131 127 133x 133x NUM cana-6326 131 128 vol vol VERB cana-6326 131 129 32 32 NUM cana-6326 131 130 no no NOUN cana-6326 131 131 . . PUNCT cana-6326 132 1 10s 10 NOUN cana-6326 132 2 ( ( PUNCT cana-6326 132 3 2025 2025 NUM cana-6326 132 4 ) ) PUNCT cana-6326 132 5 3722 3722 NUM cana-6326 132 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 132 7 6 6 NUM cana-6326 132 8 . . PUNCT cana-6326 132 9 applications application NOUN cana-6326 132 10 linearly linearly ADV cana-6326 132 11 distributed distribute VERB cana-6326 132 12 source source NOUN cana-6326 132 13 the the DET cana-6326 132 14 linearly linearly ADV cana-6326 132 15 varying vary VERB cana-6326 132 16 source source NOUN cana-6326 132 17 is be AUX cana-6326 132 18 defined define VERB cana-6326 132 19 as as ADP cana-6326 132 20 : : PUNCT cana-6326 132 21 [ [ X cana-6326 132 22 𝐹1(π‘₯1 𝐹1(π‘₯1 X cana-6326 132 23 ) ) PUNCT cana-6326 132 24 , , PUNCT cana-6326 132 25 𝐹2(π‘₯1 𝐹2(π‘₯1 NUM cana-6326 132 26 ) ) PUNCT cana-6326 132 27 , , PUNCT cana-6326 132 28 𝐹3(π‘₯1 𝐹3(π‘₯1 NOUN cana-6326 132 29 ) ) PUNCT cana-6326 132 30 ] ] PUNCT cana-6326 133 1 = = PUNCT cana-6326 133 2 { { PUNCT cana-6326 133 3 1 1 NUM cana-6326 133 4 βˆ’ βˆ’ NOUN cana-6326 133 5 |π‘₯1| |π‘₯1| ADV cana-6326 133 6 π‘Žβ‚€ π‘Žβ‚€ ADV cana-6326 133 7 𝑖𝑓 𝑖𝑓 ADP cana-6326 133 8 |π‘₯1| |π‘₯1| PRON cana-6326 133 9 ≀ ≀ NUM cana-6326 133 10 π‘Žβ‚€ π‘Žβ‚€ ADV cana-6326 133 11 0 0 NUM cana-6326 133 12 𝑖𝑓 𝑖𝑓 ADP cana-6326 133 13 |π‘₯1| |π‘₯1| X cana-6326 133 14 > > X cana-6326 133 15 π‘Žβ‚€ π‘Žβ‚€ PROPN cana-6326 133 16 applying apply VERB cana-6326 133 17 the the DET cana-6326 133 18 fourier fourier NOUN cana-6326 133 19 transform transform NOUN cana-6326 133 20 at at ADP cana-6326 133 21 the the DET cana-6326 133 22 plane plane NOUN cana-6326 133 23 boundary boundary NOUN cana-6326 133 24 π‘₯₃ π‘₯₃ NOUN cana-6326 133 25 = = NOUN cana-6326 133 26 0 0 NUM cana-6326 133 27 in in ADP cana-6326 133 28 dimensionless dimensionless NOUN cana-6326 133 29 form form NOUN cana-6326 133 30 gives give VERB cana-6326 133 31 [ [ PUNCT cana-6326 133 32 οΏ½ οΏ½ PROPN cana-6326 133 33 Μ‚ Μ‚ NOUN cana-6326 133 34 οΏ½ οΏ½ NOUN cana-6326 133 35 1(πœ‰β‚ 1(πœ‰β‚ NUM cana-6326 133 36 ) ) PUNCT cana-6326 133 37 , , PUNCT cana-6326 133 38 οΏ½ οΏ½ PROPN cana-6326 133 39 Μ‚ Μ‚ NOUN cana-6326 133 40 οΏ½ οΏ½ NOUN cana-6326 133 41 2(πœ‰β‚ 2(πœ‰β‚ NUM cana-6326 133 42 ) ) PUNCT cana-6326 133 43 , , PUNCT cana-6326 133 44 οΏ½ οΏ½ PROPN cana-6326 133 45 Μ‚ Μ‚ PROPN cana-6326 133 46 οΏ½ οΏ½ NOUN cana-6326 133 47 3(πœ‰β‚ 3(πœ‰β‚ NUM cana-6326 133 48 ) ) PUNCT cana-6326 133 49 ] ] PUNCT cana-6326 134 1 = = PUNCT cana-6326 134 2 2[1βˆ’cos(πœ‰β‚π‘Žβ‚€ 2[1βˆ’cos(πœ‰β‚π‘Žβ‚€ NUM cana-6326 134 3 ) ) PUNCT cana-6326 134 4 ] ] PUNCT cana-6326 135 1 πœ‰β‚Β²π‘Žβ‚€ πœ‰β‚Β²π‘Žβ‚€ PROPN cana-6326 135 2 ( ( PUNCT cana-6326 135 3 34 34 NUM cana-6326 135 4 ) ) PUNCT cana-6326 135 5 here here ADV cana-6326 135 6 , , PUNCT cana-6326 135 7 π‘Žβ‚€ π‘Žβ‚€ PRON cana-6326 135 8 represents represent VERB cana-6326 135 9 the the DET cana-6326 135 10 dimensionless dimensionless ADJ cana-6326 135 11 width width NOUN cana-6326 135 12 of of ADP cana-6326 135 13 the the DET cana-6326 135 14 source source NOUN cana-6326 135 15 strip strip NOUN cana-6326 135 16 . . PUNCT cana-6326 136 1 substituting substitute VERB cana-6326 136 2 these these DET cana-6326 136 3 expressions expression NOUN cana-6326 136 4 into into ADP cana-6326 136 5 equations equation NOUN cana-6326 136 6 ( ( PUNCT cana-6326 136 7 28)-(33 28)-(33 NUM cana-6326 136 8 ) ) PUNCT cana-6326 136 9 yields yield VERB cana-6326 136 10 the the DET cana-6326 136 11 corresponding correspond VERB cana-6326 136 12 solutions solution NOUN cana-6326 136 13 for for ADP cana-6326 136 14 the the DET cana-6326 136 15 field field NOUN cana-6326 136 16 variables variable NOUN cana-6326 136 17 . . PUNCT cana-6326 137 1 7 7 X cana-6326 137 2 . . X cana-6326 137 3 validation validation NOUN cana-6326 137 4 setting set VERB cana-6326 137 5 𝐹2 𝐹2 NOUN cana-6326 137 6 = = PUNCT cana-6326 137 7 𝐹3 𝐹3 PROPN cana-6326 138 1 = = PUNCT cana-6326 138 2 0 0 NUM cana-6326 138 3 in in ADP cana-6326 138 4 equations equation NOUN cana-6326 138 5 ( ( PUNCT cana-6326 138 6 28)-(33 28)-(33 NUM cana-6326 138 7 ) ) PUNCT cana-6326 138 8 yields yield VERB cana-6326 138 9 the the DET cana-6326 138 10 field field NOUN cana-6326 138 11 quantities quantity NOUN cana-6326 138 12 corresponding correspond VERB cana-6326 138 13 to to ADP cana-6326 138 14 a a DET cana-6326 138 15 normal normal ADJ cana-6326 138 16 force force NOUN cana-6326 138 17 . . PUNCT cana-6326 139 1 special special ADJ cana-6326 139 2 cases case NOUN cana-6326 139 3 β€’ β€’ ADV cana-6326 139 4 setting set VERB cana-6326 139 5 ΞΎ ΞΎ NOUN cana-6326 139 6 = = SYM cana-6326 139 7 ΞΆ ΞΆ NOUN cana-6326 139 8 = = SYM cana-6326 139 9 Ο‚ Ο‚ PROPN cana-6326 139 10 = = SYM cana-6326 139 11 0 0 NUM cana-6326 139 12 in in ADP cana-6326 139 13 equations equation NOUN cana-6326 139 14 ( ( PUNCT cana-6326 139 15 28)-(33 28)-(33 NUM cana-6326 139 16 ) ) PUNCT cana-6326 139 17 invoke invoke VERB cana-6326 139 18 the the DET cana-6326 139 19 case case NOUN cana-6326 139 20 of of ADP cana-6326 139 21 thermoelastic thermoelastic ADJ cana-6326 139 22 diffusion diffusion NOUN cana-6326 139 23 described describe VERB cana-6326 139 24 by by ADP cana-6326 139 25 the the DET cana-6326 139 26 dual dual ADJ cana-6326 139 27 - - PUNCT cana-6326 139 28 phase phase NOUN cana-6326 139 29 - - PUNCT cana-6326 139 30 lag lag NOUN cana-6326 139 31 model model NOUN cana-6326 139 32 . . PUNCT cana-6326 140 1 β€’ β€’ NOUN cana-6326 140 2 setting set VERB cana-6326 140 3 πœπ‘‘ πœπ‘‘ PROPN cana-6326 140 4 = = PUNCT cana-6326 140 5 πœπ‘ž πœπ‘ž NOUN cana-6326 140 6 = = ADJ cana-6326 140 7 πœπ‘’ πœπ‘’ NOUN cana-6326 140 8 = = PUNCT cana-6326 140 9 πœπ‘ πœπ‘ NOUN cana-6326 140 10 = = NOUN cana-6326 140 11 0 0 NUM cana-6326 140 12 in in ADP cana-6326 140 13 equations equation NOUN cana-6326 140 14 ( ( PUNCT cana-6326 140 15 28)-(33 28)-(33 NUM cana-6326 140 16 ) ) PUNCT cana-6326 140 17 invoke invoke VERB cana-6326 140 18 the the DET cana-6326 140 19 case case NOUN cana-6326 140 20 of of ADP cana-6326 140 21 non non ADJ cana-6326 140 22 - - ADJ cana-6326 140 23 local local ADJ cana-6326 140 24 thermoelastic thermoelastic ADJ cana-6326 140 25 diffusion diffusion NOUN cana-6326 140 26 . . PUNCT cana-6326 141 1 8 8 X cana-6326 141 2 . . X cana-6326 141 3 inversion inversion NOUN cana-6326 141 4 of of ADP cana-6326 141 5 the the DET cana-6326 141 6 transformation transformation NOUN cana-6326 141 7 the the PRON cana-6326 141 8 transforms transform VERB cana-6326 141 9 in in ADP cana-6326 141 10 equations equation NOUN cana-6326 141 11 ( ( PUNCT cana-6326 141 12 28)-(33 28)-(33 NUM cana-6326 141 13 ) ) PUNCT cana-6326 141 14 are be AUX cana-6326 141 15 inverted invert VERB cana-6326 141 16 following follow VERB cana-6326 141 17 the the DET cana-6326 141 18 procedure procedure NOUN cana-6326 141 19 outlined outline VERB cana-6326 141 20 in in ADP cana-6326 141 21 [ [ X cana-6326 141 22 29 29 NUM cana-6326 141 23 ] ] PUNCT cana-6326 141 24 . . PUNCT cana-6326 142 1 9 9 X cana-6326 142 2 . . X cana-6326 142 3 numerical numerical ADJ cana-6326 142 4 implementation implementation NOUN cana-6326 142 5 and and CCONJ cana-6326 142 6 explanation explanation NOUN cana-6326 142 7 in in ADP cana-6326 142 8 the the DET cana-6326 142 9 numerical numerical ADJ cana-6326 142 10 analysis analysis NOUN cana-6326 142 11 , , PUNCT cana-6326 142 12 copper copper NOUN cana-6326 142 13 is be AUX cana-6326 142 14 employed employ VERB cana-6326 142 15 as as ADP cana-6326 142 16 the the DET cana-6326 142 17 representative representative ADJ cana-6326 142 18 thermoelastic thermoelastic ADJ cana-6326 142 19 diffusion diffusion NOUN cana-6326 142 20 material material NOUN cana-6326 142 21 , , PUNCT cana-6326 142 22 in in ADP cana-6326 142 23 line line NOUN cana-6326 142 24 with with ADP cana-6326 142 25 the the DET cana-6326 142 26 procedure procedure NOUN cana-6326 142 27 outlined outline VERB cana-6326 142 28 in in ADP cana-6326 142 29 [ [ X cana-6326 142 30 19 19 NUM cana-6326 142 31 ] ] PUNCT cana-6326 142 32 . . PUNCT cana-6326 143 1 Ξ» Ξ» X cana-6326 143 2 = = SYM cana-6326 143 3 7.76Γ— 7.76Γ— NUM cana-6326 143 4 1010kgπ‘šβˆ’1π‘ βˆ’2 1010kgπ‘šβˆ’1π‘ βˆ’2 NUM cana-6326 143 5 , , PUNCT cana-6326 143 6 πœ‡ πœ‡ X cana-6326 143 7 = = PROPN cana-6326 143 8 3.86 3.86 NUM cana-6326 143 9 Γ— Γ— NOUN cana-6326 143 10 1010 1010 NUM cana-6326 143 11 kgπ‘šβˆ’1π‘ βˆ’2 kgπ‘šβˆ’1π‘ βˆ’2 PROPN cana-6326 143 12 , , PUNCT cana-6326 143 13 𝑇0= 𝑇0= VERB cana-6326 143 14 0.293Γ— 0.293Γ— PROPN cana-6326 144 1 103𝐾 103𝐾 NUM cana-6326 144 2 , , PUNCT cana-6326 145 1 𝐢𝑒 𝐢𝑒 PROPN cana-6326 145 2 = = PROPN cana-6326 145 3 0.3891Γ— 0.3891Γ— NOUN cana-6326 145 4 103 103 NUM cana-6326 145 5 jπΎπ‘”βˆ’1πΎβˆ’1 jπΎπ‘”βˆ’1πΎβˆ’1 PROPN cana-6326 145 6 , , PUNCT cana-6326 145 7 𝛼𝑑= 𝛼𝑑= PROPN cana-6326 145 8 1.78Γ— 1.78Γ— NUM cana-6326 145 9 10βˆ’5πΎβˆ’1 10βˆ’5πΎβˆ’1 PROPN cana-6326 145 10 , , PUNCT cana-6326 145 11 𝛼𝑐= 𝛼𝑐= VERB cana-6326 145 12 1.98Γ— 1.98Γ— NUM cana-6326 145 13 10βˆ’4π‘š3πΎπ‘”βˆ’1 10βˆ’4π‘š3πΎπ‘”βˆ’1 NUM cana-6326 145 14 , , PUNCT cana-6326 145 15 π‘Ž π‘Ž PROPN cana-6326 145 16 = = SYM cana-6326 145 17 1.02 1.02 NUM cana-6326 145 18 Γ— Γ— NOUN cana-6326 145 19 104π‘š2π‘ βˆ’2πΎβˆ’1 104π‘š2π‘ βˆ’2πΎβˆ’1 NUM cana-6326 145 20 , , PUNCT cana-6326 145 21 𝑏 𝑏 NOUN cana-6326 145 22 = = SYM cana-6326 145 23 9 9 NUM cana-6326 145 24 Γ— Γ— NOUN cana-6326 145 25 105πΎπ‘”βˆ’1π‘š5π‘ βˆ’2 105πΎπ‘”βˆ’1π‘š5π‘ βˆ’2 NUM cana-6326 145 26 , , PUNCT cana-6326 145 27 𝐷 𝐷 NOUN cana-6326 145 28 = = SYM cana-6326 145 29 0.85 0.85 NUM cana-6326 145 30 Γ— Γ— NOUN cana-6326 145 31 10βˆ’8kgsπ‘šβˆ’3 10βˆ’8kgsπ‘šβˆ’3 NOUN cana-6326 145 32 , , PUNCT cana-6326 145 33 𝜌 𝜌 X cana-6326 145 34 = = SYM cana-6326 145 35 8.954 8.954 NUM cana-6326 145 36 Γ— Γ— NOUN cana-6326 145 37 103πΎπ‘”π‘šβˆ’3 103πΎπ‘”π‘šβˆ’3 NUM cana-6326 145 38 , , PUNCT cana-6326 145 39 k= k= X cana-6326 146 1 0.386Γ— 0.386Γ— PUNCT cana-6326 147 1 103π‘Šπ‘šβˆ’1πΎβˆ’1 103π‘Šπ‘šβˆ’1πΎβˆ’1 NUM cana-6326 147 2 , , PUNCT cana-6326 147 3 𝑑 𝑑 PROPN cana-6326 147 4 = = SYM cana-6326 147 5 0.01𝑠 0.01𝑠 PROPN cana-6326 147 6 , , PUNCT cana-6326 147 7 𝑑0= 𝑑0= PROPN cana-6326 147 8 0.2s 0.2s NUM cana-6326 147 9 , , PUNCT cana-6326 147 10 πœπ‘‘ πœπ‘‘ PROPN cana-6326 147 11 = = PUNCT cana-6326 147 12 0.6𝑠 0.6𝑠 PROPN cana-6326 147 13 , , PUNCT cana-6326 147 14 πœπ‘ž= πœπ‘ž= ADJ cana-6326 147 15 0.7s 0.7s NUM cana-6326 147 16 , , PUNCT cana-6326 147 17 πœπ‘ πœπ‘ ADP cana-6326 147 18 = = SYM cana-6326 147 19 0.8𝑠 0.8𝑠 PROPN cana-6326 147 20 , , PUNCT cana-6326 147 21 πœπ‘’=0.9s πœπ‘’=0.9s NOUN cana-6326 147 22 , , PUNCT cana-6326 147 23 πœ‰ πœ‰ NOUN cana-6326 147 24 = = NOUN cana-6326 147 25 0.395 0.395 NUM cana-6326 147 26 Γ— Γ— NOUN cana-6326 147 27 10βˆ’9 10βˆ’9 NUM cana-6326 147 28 m m NOUN cana-6326 147 29 , , PUNCT cana-6326 147 30 𝜁 𝜁 PROPN cana-6326 147 31 = = SYM cana-6326 147 32 0.2 0.2 NUM cana-6326 147 33 Γ— Γ— NOUN cana-6326 147 34 10βˆ’9π‘š 10βˆ’9π‘š NUM cana-6326 147 35 , , PUNCT cana-6326 147 36 𝜍 𝜍 X cana-6326 147 37 = = SYM cana-6326 147 38 0.15 0.15 NUM cana-6326 147 39 Γ— Γ— NOUN cana-6326 147 40 10βˆ’9 10βˆ’9 NUM cana-6326 147 41 m m NOUN cana-6326 147 42 we we PRON cana-6326 147 43 use use VERB cana-6326 147 44 matlab matlab PROPN cana-6326 147 45 ( ( PUNCT cana-6326 147 46 r2016a r2016a NOUN cana-6326 147 47 ) ) PUNCT cana-6326 147 48 to to PART cana-6326 147 49 carry carry VERB cana-6326 147 50 out out ADP cana-6326 147 51 numerical numerical ADJ cana-6326 147 52 simulations simulation NOUN cana-6326 147 53 that that PRON cana-6326 147 54 evaluate evaluate VERB cana-6326 147 55 normal normal ADJ cana-6326 147 56 stress stress NOUN cana-6326 147 57 , , PUNCT cana-6326 147 58 tangential tangential ADJ cana-6326 147 59 stress stress NOUN cana-6326 147 60 , , PUNCT cana-6326 147 61 tangential tangential ADJ cana-6326 147 62 couple couple NOUN cana-6326 147 63 stress stress NOUN cana-6326 147 64 , , PUNCT cana-6326 147 65 temperature temperature NOUN cana-6326 147 66 changes change NOUN cana-6326 147 67 , , PUNCT cana-6326 147 68 and and CCONJ cana-6326 147 69 chemical chemical NOUN cana-6326 147 70 potential potential NOUN cana-6326 147 71 under under ADP cana-6326 147 72 the the DET cana-6326 147 73 following following ADJ cana-6326 147 74 conditions condition NOUN cana-6326 147 75 : : PUNCT cana-6326 147 76 1 1 X cana-6326 147 77 . . X cana-6326 147 78 thermoelastic thermoelastic ADJ cana-6326 147 79 diffusion diffusion NOUN cana-6326 147 80 incorporating incorporate VERB cana-6326 147 81 both both CCONJ cana-6326 147 82 non non ADJ cana-6326 147 83 - - ADJ cana-6326 147 84 local local ADJ cana-6326 147 85 effects effect NOUN cana-6326 147 86 and and CCONJ cana-6326 147 87 dual dual ADJ cana-6326 147 88 - - PUNCT cana-6326 147 89 phase phase NOUN cana-6326 147 90 - - PUNCT cana-6326 147 91 lag lag NOUN cana-6326 147 92 . . PUNCT cana-6326 148 1 communications communication NOUN cana-6326 148 2 on on ADP cana-6326 148 3 applied apply VERB cana-6326 148 4 nonlinear nonlinear ADJ cana-6326 148 5 analysis analysis NOUN cana-6326 148 6 issn issn NOUN cana-6326 148 7 : : PUNCT cana-6326 148 8 1074 1074 NUM cana-6326 148 9 - - PUNCT cana-6326 148 10 133x 133x NUM cana-6326 148 11 vol vol VERB cana-6326 148 12 32 32 NUM cana-6326 148 13 no no NOUN cana-6326 148 14 . . PUNCT cana-6326 149 1 10s 10 NOUN cana-6326 149 2 ( ( PUNCT cana-6326 149 3 2025 2025 NUM cana-6326 149 4 ) ) PUNCT cana-6326 149 5 3723 3723 NUM cana-6326 149 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 149 7 2 2 NUM cana-6326 149 8 . . PUNCT cana-6326 149 9 dual dual ADJ cana-6326 149 10 - - PUNCT cana-6326 149 11 phase phase NOUN cana-6326 149 12 - - PUNCT cana-6326 149 13 lag lag NOUN cana-6326 149 14 thermoelastic thermoelastic ADJ cana-6326 149 15 diffusion diffusion NOUN cana-6326 149 16 without without ADP cana-6326 149 17 non non ADJ cana-6326 149 18 - - ADJ cana-6326 149 19 local local ADJ cana-6326 149 20 effects effect NOUN cana-6326 149 21 . . PUNCT cana-6326 150 1 3 3 X cana-6326 150 2 . . X cana-6326 150 3 non non ADJ cana-6326 150 4 - - ADJ cana-6326 150 5 local local ADJ cana-6326 150 6 thermoelastic thermoelastic ADJ cana-6326 150 7 diffusion diffusion NOUN cana-6326 150 8 without without ADP cana-6326 150 9 diffusion diffusion NOUN cana-6326 150 10 phase phase NOUN cana-6326 150 11 - - PUNCT cana-6326 150 12 lags lag NOUN cana-6326 150 13 . . PUNCT cana-6326 151 1 4 4 X cana-6326 151 2 . . X cana-6326 151 3 non non ADJ cana-6326 151 4 - - ADJ cana-6326 151 5 local local ADJ cana-6326 151 6 thermoelastic thermoelastic ADJ cana-6326 151 7 diffusion diffusion NOUN cana-6326 151 8 without without ADP cana-6326 151 9 thermal thermal ADJ cana-6326 151 10 phase phase NOUN cana-6326 151 11 - - PUNCT cana-6326 151 12 lags lag NOUN cana-6326 151 13 . . PUNCT cana-6326 152 1 5 5 X cana-6326 152 2 . . X cana-6326 152 3 non non ADJ cana-6326 152 4 - - ADJ cana-6326 152 5 local local ADJ cana-6326 152 6 thermoelastic thermoelastic ADJ cana-6326 152 7 diffusion diffusion NOUN cana-6326 152 8 with with ADP cana-6326 152 9 no no DET cana-6326 152 10 phase phase NOUN cana-6326 152 11 - - PUNCT cana-6326 152 12 lags lag NOUN cana-6326 152 13 . . PUNCT cana-6326 153 1 in in ADP cana-6326 153 2 all all DET cana-6326 153 3 figures figure NOUN cana-6326 153 4 : : PUNCT cana-6326 153 5 β€’ β€’ NUM cana-6326 153 6 solid solid ADJ cana-6326 153 7 line line NOUN cana-6326 153 8 ( ( PUNCT cana-6326 153 9 ─ ─ X cana-6326 153 10 ─ ─ X cana-6326 153 11 ) ) PUNCT cana-6326 153 12 represents represent VERB cana-6326 153 13 thermoelastic thermoelastic ADJ cana-6326 153 14 diffusion diffusion NOUN cana-6326 153 15 with with ADP cana-6326 153 16 non non ADJ cana-6326 153 17 - - ADJ cana-6326 153 18 local local ADJ cana-6326 153 19 effects effect NOUN cana-6326 153 20 and and CCONJ cana-6326 153 21 dual dual ADJ cana-6326 153 22 - - PUNCT cana-6326 153 23 phaselag phaselag NOUN cana-6326 153 24 ( ( PUNCT cana-6326 153 25 tnp tnp PROPN cana-6326 153 26 ) ) PUNCT cana-6326 153 27 . . PUNCT cana-6326 154 1 β€’ β€’ NUM cana-6326 154 2 small small ADJ cana-6326 154 3 dashed dash VERB cana-6326 154 4 line line NOUN cana-6326 154 5 ( ( PUNCT cana-6326 154 6 - - PUNCT cana-6326 154 7 ) ) PUNCT cana-6326 154 8 denotes denote VERB cana-6326 154 9 thermoelastic thermoelastic ADJ cana-6326 154 10 diffusion diffusion NOUN cana-6326 154 11 with with ADP cana-6326 154 12 dual dual ADJ cana-6326 154 13 - - PUNCT cana-6326 154 14 phase phase NOUN cana-6326 154 15 - - PUNCT cana-6326 154 16 lag lag NOUN cana-6326 154 17 but but CCONJ cana-6326 154 18 without without ADP cana-6326 154 19 non non ADJ cana-6326 154 20 - - ADJ cana-6326 154 21 local local ADJ cana-6326 154 22 effects effect NOUN cana-6326 154 23 ( ( PUNCT cana-6326 154 24 wntp wntp NOUN cana-6326 154 25 ) ) PUNCT cana-6326 154 26 . . PUNCT cana-6326 155 1 β€’ β€’ NUM cana-6326 155 2 large large ADJ cana-6326 155 3 dashed dash VERB cana-6326 155 4 line line NOUN cana-6326 155 5 ( ( PUNCT cana-6326 155 6 ─ ─ X cana-6326 155 7 ─ ─ X cana-6326 155 8 ) ) PUNCT cana-6326 155 9 corresponds correspond VERB cana-6326 155 10 to to ADP cana-6326 155 11 non non ADJ cana-6326 155 12 - - ADJ cana-6326 155 13 local local ADJ cana-6326 155 14 thermoelastic thermoelastic ADJ cana-6326 155 15 diffusion diffusion NOUN cana-6326 155 16 without without ADP cana-6326 155 17 diffusion diffusion NOUN cana-6326 155 18 phase phase NOUN cana-6326 155 19 - - PUNCT cana-6326 155 20 lag lag NOUN cana-6326 155 21 ( ( PUNCT cana-6326 155 22 tnwdp tnwdp NOUN cana-6326 155 23 ) ) PUNCT cana-6326 155 24 . . PUNCT cana-6326 156 1 β€’ β€’ NUM cana-6326 156 2 solid solid ADJ cana-6326 156 3 line line NOUN cana-6326 156 4 with with ADP cana-6326 156 5 central central ADJ cana-6326 156 6 marker marker NOUN cana-6326 156 7 ( ( PUNCT cana-6326 156 8 ─ ─ ADJ cana-6326 156 9 * * PUNCT cana-6326 156 10 ─ ─ X cana-6326 156 11 ) ) PUNCT cana-6326 156 12 indicates indicate VERB cana-6326 156 13 non non ADJ cana-6326 156 14 - - ADJ cana-6326 156 15 local local ADJ cana-6326 156 16 thermoelastic thermoelastic ADJ cana-6326 156 17 diffusion diffusion NOUN cana-6326 156 18 without without ADP cana-6326 156 19 thermal thermal ADJ cana-6326 156 20 phase phase NOUN cana-6326 156 21 - - PUNCT cana-6326 156 22 lag lag NOUN cana-6326 156 23 ( ( PUNCT cana-6326 156 24 tnwtp tnwtp PROPN cana-6326 156 25 ) ) PUNCT cana-6326 156 26 . . PUNCT cana-6326 157 1 β€’ β€’ NUM cana-6326 157 2 large large ADJ cana-6326 157 3 dashed dash VERB cana-6326 157 4 line line NOUN cana-6326 157 5 with with ADP cana-6326 157 6 central central ADJ cana-6326 157 7 marker marker NOUN cana-6326 157 8 ( ( PUNCT cana-6326 157 9 ─ ─ NOUN cana-6326 157 10 β‚€ β‚€ NUM cana-6326 157 11 ─ ─ X cana-6326 157 12 ) ) PUNCT cana-6326 157 13 represents represent VERB cana-6326 157 14 non non ADJ cana-6326 157 15 - - ADJ cana-6326 157 16 local local ADJ cana-6326 157 17 thermoelastic thermoelastic ADJ cana-6326 157 18 diffusion diffusion NOUN cana-6326 157 19 without without ADP cana-6326 157 20 any any DET cana-6326 157 21 phase phase NOUN cana-6326 157 22 - - PUNCT cana-6326 157 23 lags lag NOUN cana-6326 157 24 ( ( PUNCT cana-6326 157 25 tn tn NOUN cana-6326 157 26 ) ) PUNCT cana-6326 157 27 . . PUNCT cana-6326 158 1 figure figure NOUN cana-6326 158 2 1 1 NUM cana-6326 158 3 displays display VERB cana-6326 158 4 the the DET cana-6326 158 5 distribution distribution NOUN cana-6326 158 6 of of ADP cana-6326 158 7 𝑑33 𝑑33 NOUN cana-6326 158 8 when when SCONJ cana-6326 158 9 the the DET cana-6326 158 10 boundary boundary NOUN cana-6326 158 11 is be AUX cana-6326 158 12 subjected subject VERB cana-6326 158 13 to to ADP cana-6326 158 14 a a DET cana-6326 158 15 normal normal ADJ cana-6326 158 16 load load NOUN cana-6326 158 17 . . PUNCT cana-6326 159 1 near near ADP cana-6326 159 2 the the DET cana-6326 159 3 loading loading NOUN cana-6326 159 4 zone zone NOUN cana-6326 159 5 , , PUNCT cana-6326 159 6 𝑑33 𝑑33 VERB cana-6326 159 7 decreases decrease NOUN cana-6326 159 8 in in ADP cana-6326 159 9 magnitude magnitude NOUN cana-6326 159 10 , , PUNCT cana-6326 159 11 reflecting reflect VERB cana-6326 159 12 stress stress NOUN cana-6326 159 13 release release NOUN cana-6326 159 14 in in ADP cana-6326 159 15 the the DET cana-6326 159 16 immediate immediate ADJ cana-6326 159 17 vicinity vicinity NOUN cana-6326 159 18 of of ADP cana-6326 159 19 the the DET cana-6326 159 20 applied apply VERB cana-6326 159 21 force force NOUN cana-6326 159 22 . . PUNCT cana-6326 160 1 beyond beyond ADP cana-6326 160 2 this this DET cana-6326 160 3 region region NOUN cana-6326 160 4 , , PUNCT cana-6326 160 5 the the DET cana-6326 160 6 stress stress NOUN cana-6326 160 7 response response NOUN cana-6326 160 8 becomes become VERB cana-6326 160 9 oscillatory oscillatory ADJ cana-6326 160 10 for for ADP cana-6326 160 11 all all DET cana-6326 160 12 the the DET cana-6326 160 13 cases case NOUN cana-6326 160 14 considered consider VERB cana-6326 160 15 . . PUNCT cana-6326 161 1 interestingly interestingly ADV cana-6326 161 2 , , PUNCT cana-6326 161 3 the the DET cana-6326 161 4 oscillation oscillation NOUN cana-6326 161 5 patterns pattern NOUN cana-6326 161 6 are be AUX cana-6326 161 7 nearly nearly ADV cana-6326 161 8 identical identical ADJ cana-6326 161 9 in in ADP cana-6326 161 10 amplitude amplitude NOUN cana-6326 161 11 and and CCONJ cana-6326 161 12 frequency frequency NOUN cana-6326 161 13 across across ADP cana-6326 161 14 all all DET cana-6326 161 15 cases case NOUN cana-6326 161 16 . . PUNCT cana-6326 162 1 this this PRON cana-6326 162 2 indicates indicate VERB cana-6326 162 3 a a DET cana-6326 162 4 strong strong ADJ cana-6326 162 5 dominance dominance NOUN cana-6326 162 6 of of ADP cana-6326 162 7 the the DET cana-6326 162 8 applied apply VERB cana-6326 162 9 mechanical mechanical ADJ cana-6326 162 10 source source NOUN cana-6326 162 11 over over ADP cana-6326 162 12 modelspecific modelspecific ADJ cana-6326 162 13 parameters parameter NOUN cana-6326 162 14 . . PUNCT cana-6326 163 1 the the DET cana-6326 163 2 variation variation NOUN cana-6326 163 3 of of ADP cana-6326 163 4 shear shear NOUN cana-6326 163 5 stress stress NOUN cana-6326 163 6 𝑑31 𝑑31 NOUN cana-6326 163 7 , , PUNCT cana-6326 163 8 illustrated illustrate VERB cana-6326 163 9 in in ADP cana-6326 163 10 figure figure NOUN cana-6326 163 11 2 2 NUM cana-6326 163 12 , , PUNCT cana-6326 163 13 exhibits exhibit VERB cana-6326 163 14 alternating alternate VERB cana-6326 163 15 increasing increase VERB cana-6326 163 16 and and CCONJ cana-6326 163 17 decreasing decrease VERB cana-6326 163 18 trends trend NOUN cana-6326 163 19 within within ADP cana-6326 163 20 the the DET cana-6326 163 21 bounded bounded ADJ cana-6326 163 22 region region NOUN cana-6326 163 23 close close ADJ cana-6326 163 24 to to ADP cana-6326 163 25 the the DET cana-6326 163 26 source source NOUN cana-6326 163 27 . . PUNCT cana-6326 164 1 this this PRON cana-6326 164 2 indicates indicate VERB cana-6326 164 3 that that SCONJ cana-6326 164 4 the the DET cana-6326 164 5 shear shear NOUN cana-6326 164 6 response response NOUN cana-6326 164 7 induced induce VERB cana-6326 164 8 by by ADP cana-6326 164 9 normal normal ADJ cana-6326 164 10 loading loading NOUN cana-6326 164 11 oscillates oscillate NOUN cana-6326 164 12 locally locally ADV cana-6326 164 13 before before ADP cana-6326 164 14 gradually gradually ADV cana-6326 164 15 stabilizing stabilize VERB cana-6326 164 16 further far ADV cana-6326 164 17 from from ADP cana-6326 164 18 the the DET cana-6326 164 19 boundary boundary NOUN cana-6326 164 20 . . PUNCT cana-6326 165 1 the the DET cana-6326 165 2 similarity similarity NOUN cana-6326 165 3 of of ADP cana-6326 165 4 𝑑31 𝑑31 NOUN cana-6326 165 5 across across ADP cana-6326 165 6 all all DET cana-6326 165 7 cases case NOUN cana-6326 165 8 shows show VERB cana-6326 165 9 that that SCONJ cana-6326 165 10 , , PUNCT cana-6326 165 11 like like ADP cana-6326 165 12 the the DET cana-6326 165 13 normal normal ADJ cana-6326 165 14 stress stress NOUN cana-6326 165 15 response response NOUN cana-6326 165 16 , , PUNCT cana-6326 165 17 shear shear NOUN cana-6326 165 18 stress stress NOUN cana-6326 165 19 is be AUX cana-6326 165 20 primarily primarily ADV cana-6326 165 21 governed govern VERB cana-6326 165 22 by by ADP cana-6326 165 23 the the DET cana-6326 165 24 direct direct ADJ cana-6326 165 25 mechanical mechanical ADJ cana-6326 165 26 loading loading NOUN cana-6326 165 27 and and CCONJ cana-6326 165 28 is be AUX cana-6326 165 29 less less ADV cana-6326 165 30 sensitive sensitive ADJ cana-6326 165 31 to to ADP cana-6326 165 32 the the DET cana-6326 165 33 differences difference NOUN cana-6326 165 34 in in ADP cana-6326 165 35 non non ADJ cana-6326 165 36 - - ADJ cana-6326 165 37 locality locality ADJ cana-6326 165 38 or or CCONJ cana-6326 165 39 phase phase NOUN cana-6326 165 40 - - PUNCT cana-6326 165 41 lag lag NOUN cana-6326 165 42 formulations formulation NOUN cana-6326 165 43 . . PUNCT cana-6326 166 1 figure figure VERB cana-6326 166 2 3 3 NUM cana-6326 166 3 describe describe VERB cana-6326 166 4 t t PROPN cana-6326 166 5 with with ADP cana-6326 166 6 π‘₯1 π‘₯1 PROPN cana-6326 166 7 . . PROPN cana-6326 167 1 for for ADP cana-6326 167 2 all all DET cana-6326 167 3 the the DET cana-6326 167 4 considered consider VERB cana-6326 167 5 cases case NOUN cana-6326 167 6 , , PUNCT cana-6326 167 7 the the DET cana-6326 167 8 temperature temperature NOUN cana-6326 167 9 decreases decrease VERB cana-6326 167 10 monotonically monotonically ADV cana-6326 167 11 with with ADP cana-6326 167 12 distance distance NOUN cana-6326 167 13 from from ADP cana-6326 167 14 the the DET cana-6326 167 15 boundary boundary NOUN cana-6326 167 16 , , PUNCT cana-6326 167 17 showing show VERB cana-6326 167 18 a a DET cana-6326 167 19 consistent consistent ADJ cana-6326 167 20 thermal thermal ADJ cana-6326 167 21 diffusion diffusion NOUN cana-6326 167 22 process process NOUN cana-6326 167 23 . . PUNCT cana-6326 168 1 the the DET cana-6326 168 2 rate rate NOUN cana-6326 168 3 of of ADP cana-6326 168 4 decrease decrease NOUN cana-6326 168 5 is be AUX cana-6326 168 6 almost almost ADV cana-6326 168 7 identical identical ADJ cana-6326 168 8 across across ADP cana-6326 168 9 all all DET cana-6326 168 10 models model NOUN cana-6326 168 11 , , PUNCT cana-6326 168 12 suggesting suggest VERB cana-6326 168 13 that that SCONJ cana-6326 168 14 under under ADP cana-6326 168 15 normal normal ADJ cana-6326 168 16 loading loading NOUN cana-6326 168 17 , , PUNCT cana-6326 168 18 the the DET cana-6326 168 19 thermal thermal ADJ cana-6326 168 20 response response NOUN cana-6326 168 21 is be AUX cana-6326 168 22 influenced influence VERB cana-6326 168 23 by by ADP cana-6326 168 24 the the DET cana-6326 168 25 presence presence NOUN cana-6326 168 26 or or CCONJ cana-6326 168 27 absence absence NOUN cana-6326 168 28 of of ADP cana-6326 168 29 non non ADJ cana-6326 168 30 - - ADJ cana-6326 168 31 local local ADJ cana-6326 168 32 or or CCONJ cana-6326 168 33 phase phase NOUN cana-6326 168 34 - - PUNCT cana-6326 168 35 lag lag NOUN cana-6326 168 36 effects effect NOUN cana-6326 168 37 . . PUNCT cana-6326 169 1 the the DET cana-6326 169 2 chemical chemical ADJ cana-6326 169 3 potential potential NOUN cana-6326 169 4 p p NOUN cana-6326 169 5 , , PUNCT cana-6326 169 6 shown show VERB cana-6326 169 7 in in ADP cana-6326 169 8 figure figure NOUN cana-6326 169 9 4 4 NUM cana-6326 169 10 , , PUNCT cana-6326 169 11 also also ADV cana-6326 169 12 decreases decrease VERB cana-6326 169 13 steadily steadily ADV cana-6326 169 14 with with ADP cana-6326 169 15 increasing increase VERB cana-6326 169 16 π‘₯1 π‘₯1 NOUN cana-6326 169 17 for for ADP cana-6326 169 18 all all DET cana-6326 169 19 cases case NOUN cana-6326 169 20 . . PUNCT cana-6326 170 1 the the DET cana-6326 170 2 trend trend NOUN cana-6326 170 3 is be AUX cana-6326 170 4 smooth smooth ADJ cana-6326 170 5 and and CCONJ cana-6326 170 6 nearly nearly ADV cana-6326 170 7 identical identical ADJ cana-6326 170 8 in in ADP cana-6326 170 9 each each DET cana-6326 170 10 case case NOUN cana-6326 170 11 , , PUNCT cana-6326 170 12 reflecting reflect VERB cana-6326 170 13 uniform uniform ADJ cana-6326 170 14 diffusion diffusion NOUN cana-6326 170 15 of of ADP cana-6326 170 16 chemical chemical NOUN cana-6326 170 17 potential potential NOUN cana-6326 170 18 away away ADV cana-6326 170 19 from from ADP cana-6326 170 20 the the DET cana-6326 170 21 loaded load VERB cana-6326 170 22 boundary boundary NOUN cana-6326 170 23 . . PUNCT cana-6326 171 1 the the DET cana-6326 171 2 fact fact NOUN cana-6326 171 3 that that SCONJ cana-6326 171 4 the the DET cana-6326 171 5 decrement decrement NOUN cana-6326 171 6 is be AUX cana-6326 171 7 the the DET cana-6326 171 8 same same ADJ cana-6326 171 9 across across ADP cana-6326 171 10 all all DET cana-6326 171 11 models model NOUN cana-6326 171 12 indicates indicate VERB cana-6326 171 13 that that SCONJ cana-6326 171 14 , , PUNCT cana-6326 171 15 similar similar ADJ cana-6326 171 16 to to ADP cana-6326 171 17 the the DET cana-6326 171 18 thermal thermal ADJ cana-6326 171 19 field field NOUN cana-6326 171 20 , , PUNCT cana-6326 171 21 chemical chemical ADJ cana-6326 171 22 potential potential ADJ cana-6326 171 23 diffusion diffusion NOUN cana-6326 171 24 under under ADP cana-6326 171 25 normal normal ADJ cana-6326 171 26 loading loading NOUN cana-6326 171 27 is be AUX cana-6326 171 28 affected affect VERB cana-6326 171 29 by by ADP cana-6326 171 30 variations variation NOUN cana-6326 171 31 in in ADP cana-6326 171 32 non non ADJ cana-6326 171 33 - - ADJ cana-6326 171 34 local local ADJ cana-6326 171 35 elasticity elasticity NOUN cana-6326 171 36 and and CCONJ cana-6326 171 37 phase phase NOUN cana-6326 171 38 - - PUNCT cana-6326 171 39 lag lag NOUN cana-6326 171 40 formulations formulation NOUN cana-6326 171 41 . . PUNCT cana-6326 172 1 communications communication NOUN cana-6326 172 2 on on ADP cana-6326 172 3 applied apply VERB cana-6326 172 4 nonlinear nonlinear ADJ cana-6326 172 5 analysis analysis NOUN cana-6326 172 6 issn issn NOUN cana-6326 172 7 : : PUNCT cana-6326 172 8 1074 1074 NUM cana-6326 172 9 - - PUNCT cana-6326 172 10 133x 133x NUM cana-6326 172 11 vol vol VERB cana-6326 172 12 32 32 NUM cana-6326 172 13 no no NOUN cana-6326 172 14 . . PUNCT cana-6326 173 1 10s 10 NOUN cana-6326 173 2 ( ( PUNCT cana-6326 173 3 2025 2025 NUM cana-6326 173 4 ) ) PUNCT cana-6326 173 5 3724 3724 NUM cana-6326 173 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 174 1 fig.1 fig.1 ADJ cana-6326 174 2 : : PUNCT cana-6326 174 3 distance distance NOUN cana-6326 174 4 - - PUNCT cana-6326 174 5 dependent dependent ADJ cana-6326 174 6 normal normal ADJ cana-6326 174 7 stress stress NOUN cana-6326 174 8 distribution distribution NOUN cana-6326 174 9 . . PUNCT cana-6326 175 1 fig fig NOUN cana-6326 175 2 . . PUNCT cana-6326 176 1 2 2 NUM cana-6326 176 2 : : PUNCT cana-6326 176 3 distance distance NOUN cana-6326 176 4 - - PUNCT cana-6326 176 5 dependent dependent ADJ cana-6326 176 6 tangential tangential ADJ cana-6326 176 7 stress stress NOUN cana-6326 176 8 distribution distribution NOUN cana-6326 176 9 . . PUNCT cana-6326 177 1 fig.3 fig.3 ADJ cana-6326 177 2 : : PUNCT cana-6326 177 3 distance distance NOUN cana-6326 177 4 - - PUNCT cana-6326 177 5 dependent dependent ADJ cana-6326 177 6 temperature temperature NOUN cana-6326 177 7 change change NOUN cana-6326 177 8 distribution distribution NOUN cana-6326 177 9 . . PUNCT cana-6326 178 1 communications communication NOUN cana-6326 178 2 on on ADP cana-6326 178 3 applied apply VERB cana-6326 178 4 nonlinear nonlinear ADJ cana-6326 178 5 analysis analysis NOUN cana-6326 178 6 issn issn NOUN cana-6326 178 7 : : PUNCT cana-6326 178 8 1074 1074 NUM cana-6326 178 9 - - PUNCT cana-6326 178 10 133x 133x NUM cana-6326 178 11 vol vol VERB cana-6326 178 12 32 32 NUM cana-6326 178 13 no no NOUN cana-6326 178 14 . . PUNCT cana-6326 179 1 10s 10 NOUN cana-6326 179 2 ( ( PUNCT cana-6326 179 3 2025 2025 NUM cana-6326 179 4 ) ) PUNCT cana-6326 179 5 3725 3725 NUM cana-6326 179 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 179 7 fig4 fig4 PROPN cana-6326 179 8 : : PUNCT cana-6326 179 9 distance distance NOUN cana-6326 179 10 - - PUNCT cana-6326 179 11 dependent dependent ADJ cana-6326 179 12 chemical chemical NOUN cana-6326 179 13 potential potential ADJ cana-6326 179 14 distribution distribution NOUN cana-6326 179 15 . . PUNCT cana-6326 180 1 10.conclusion 10.conclusion NUM cana-6326 180 2 this this DET cana-6326 180 3 study study NOUN cana-6326 180 4 investigates investigate VERB cana-6326 180 5 the the DET cana-6326 180 6 combined combine VERB cana-6326 180 7 effects effect NOUN cana-6326 180 8 of of ADP cana-6326 180 9 non non ADJ cana-6326 180 10 - - ADJ cana-6326 180 11 locality locality ADJ cana-6326 180 12 and and CCONJ cana-6326 180 13 phase phase NOUN cana-6326 180 14 - - PUNCT cana-6326 180 15 lag lag NOUN cana-6326 180 16 phenomena phenomenon NOUN cana-6326 180 17 in in ADP cana-6326 180 18 a a DET cana-6326 180 19 modified modify VERB cana-6326 180 20 couple couple NOUN cana-6326 180 21 stress stress NOUN cana-6326 180 22 thermoelastic thermoelastic ADJ cana-6326 180 23 half half ADJ cana-6326 180 24 - - PUNCT cana-6326 180 25 space space NOUN cana-6326 180 26 exposed expose VERB cana-6326 180 27 to to ADP cana-6326 180 28 mechanical mechanical ADJ cana-6326 180 29 loading loading NOUN cana-6326 180 30 . . PUNCT cana-6326 181 1 the the DET cana-6326 181 2 mathematical mathematical ADJ cana-6326 181 3 model model NOUN cana-6326 181 4 was be AUX cana-6326 181 5 developed develop VERB cana-6326 181 6 and and CCONJ cana-6326 181 7 solved solve VERB cana-6326 181 8 using use VERB cana-6326 181 9 integral integral ADJ cana-6326 181 10 transform transform NOUN cana-6326 181 11 methods method NOUN cana-6326 181 12 . . PUNCT cana-6326 182 1 for for ADP cana-6326 182 2 linearly linearly ADV cana-6326 182 3 distributed distribute VERB cana-6326 182 4 normal normal ADJ cana-6326 182 5 loading loading NOUN cana-6326 182 6 , , PUNCT cana-6326 182 7 the the DET cana-6326 182 8 normal normal ADJ cana-6326 182 9 stress stress NOUN cana-6326 182 10 and and CCONJ cana-6326 182 11 chemical chemical NOUN cana-6326 182 12 potential potential NOUN cana-6326 182 13 decreased decrease VERB cana-6326 182 14 in in ADP cana-6326 182 15 magnitude magnitude NOUN cana-6326 182 16 , , PUNCT cana-6326 182 17 while while SCONJ cana-6326 182 18 other other ADJ cana-6326 182 19 stress stress NOUN cana-6326 182 20 components component NOUN cana-6326 182 21 and and CCONJ cana-6326 182 22 the the DET cana-6326 182 23 temperature temperature NOUN cana-6326 182 24 field field NOUN cana-6326 182 25 displayed display VERB cana-6326 182 26 oscillatory oscillatory ADJ cana-6326 182 27 fluctuations fluctuation NOUN cana-6326 182 28 . . PUNCT cana-6326 183 1 the the DET cana-6326 183 2 problem problem NOUN cana-6326 183 3 find find VERB cana-6326 183 4 application application NOUN cana-6326 183 5 in in ADP cana-6326 183 6 semiconductor semiconductor NOUN cana-6326 183 7 technologies technology NOUN cana-6326 183 8 , , PUNCT cana-6326 183 9 thermal thermal ADJ cana-6326 183 10 barrier barrier NOUN cana-6326 183 11 coatings coating NOUN cana-6326 183 12 , , PUNCT cana-6326 183 13 and and CCONJ cana-6326 183 14 composite composite ADJ cana-6326 183 15 materials material NOUN cana-6326 183 16 , , PUNCT cana-6326 183 17 due due ADJ cana-6326 183 18 to to ADP cana-6326 183 19 coupled couple VERB cana-6326 183 20 thermo thermo NOUN cana-6326 183 21 - - PUNCT cana-6326 183 22 diffusive diffusive ADJ cana-6326 183 23 loading loading NOUN cana-6326 183 24 . . PUNCT cana-6326 184 1 furthermore furthermore ADV cana-6326 184 2 , , PUNCT cana-6326 184 3 the the DET cana-6326 184 4 results result NOUN cana-6326 184 5 are be AUX cana-6326 184 6 useful useful ADJ cana-6326 184 7 in in ADP cana-6326 184 8 biomechanics biomechanic NOUN cana-6326 184 9 and and CCONJ cana-6326 184 10 nanotechnology nanotechnology NOUN cana-6326 184 11 . . PUNCT cana-6326 185 1 there there PRON cana-6326 185 2 is be VERB cana-6326 185 3 no no DET cana-6326 185 4 conflict conflict NOUN cana-6326 185 5 of of ADP cana-6326 185 6 interest interest NOUN cana-6326 185 7 involved involve VERB cana-6326 185 8 in in ADP cana-6326 185 9 this this DET cana-6326 185 10 study study NOUN cana-6326 185 11 . . PUNCT cana-6326 186 1 references reference NOUN cana-6326 186 2 [ [ X cana-6326 186 3 1 1 NUM cana-6326 186 4 ] ] SYM cana-6326 186 5 edelen edelen NOUN cana-6326 186 6 , , PUNCT cana-6326 186 7 d. d. PROPN cana-6326 186 8 g. g. PROPN cana-6326 186 9 b. b. PROPN cana-6326 186 10 and and CCONJ cana-6326 186 11 laws law NOUN cana-6326 186 12 , , PUNCT cana-6326 186 13 n. n. NOUN cana-6326 186 14 : : PUNCT cana-6326 186 15 on on ADP cana-6326 186 16 the the DET cana-6326 186 17 thermodynamics thermodynamic NOUN cana-6326 186 18 of of ADP cana-6326 186 19 systems system NOUN cana-6326 186 20 with with ADP cana-6326 186 21 nonlocality nonlocality NOUN cana-6326 186 22 , , PUNCT cana-6326 186 23 archive archive NOUN cana-6326 186 24 for for ADP cana-6326 186 25 rational rational ADJ cana-6326 186 26 mechanics mechanic NOUN cana-6326 186 27 and and CCONJ cana-6326 186 28 analysis analysis NOUN cana-6326 186 29 . . PUNCT cana-6326 187 1 43(1 43(1 X cana-6326 187 2 ) ) PUNCT cana-6326 187 3 ( ( PUNCT cana-6326 187 4 1971 1971 NUM cana-6326 187 5 ) ) PUNCT cana-6326 187 6 ; ; PUNCT cana-6326 187 7 24 24 NUM cana-6326 187 8 - - SYM cana-6326 187 9 35 35 NUM cana-6326 187 10 . . PUNCT cana-6326 187 11 https://doi.org/10.1007/bf00251543 https://doi.org/10.1007/bf00251543 PART cana-6326 188 1 [ [ X cana-6326 188 2 2 2 NUM cana-6326 188 3 ] ] X cana-6326 188 4 eringen eringen PROPN cana-6326 188 5 , , PUNCT cana-6326 188 6 a.c a.c PROPN cana-6326 188 7 . . PROPN cana-6326 188 8 and and CCONJ cana-6326 188 9 edelen edelen PROPN cana-6326 188 10 , , PUNCT cana-6326 188 11 d. d. PROPN cana-6326 188 12 g. g. PROPN cana-6326 188 13 b. b. PROPN cana-6326 188 14 : : PUNCT cana-6326 188 15 on on ADP cana-6326 188 16 nonlocal nonlocal ADJ cana-6326 188 17 elasticity elasticity NOUN cana-6326 188 18 , , PUNCT cana-6326 188 19 international international ADJ cana-6326 188 20 journal journal NOUN cana-6326 188 21 of of ADP cana-6326 188 22 engineering engineering NOUN cana-6326 188 23 science science NOUN cana-6326 188 24 , , PUNCT cana-6326 188 25 10 10 NUM cana-6326 188 26 ( ( PUNCT cana-6326 188 27 1972 1972 NUM cana-6326 188 28 ) ) PUNCT cana-6326 188 29 ; ; PUNCT cana-6326 188 30 233-24.http://dx.doi.org/10.1016/0020-7225(72)90039-0 233-24.http://dx.doi.org/10.1016/0020-7225(72)90039-0 NUM cana-6326 189 1 [ [ X cana-6326 189 2 3 3 NUM cana-6326 189 3 ] ] X cana-6326 189 4 eringen eringen PROPN cana-6326 189 5 , , PUNCT cana-6326 189 6 a.c a.c PROPN cana-6326 189 7 . . PROPN cana-6326 189 8 : : PUNCT cana-6326 189 9 on on ADP cana-6326 189 10 nonlocal nonlocal ADJ cana-6326 189 11 fluid fluid ADJ cana-6326 189 12 mechanics mechanic NOUN cana-6326 189 13 , , PUNCT cana-6326 189 14 international international ADJ cana-6326 189 15 journal journal NOUN cana-6326 189 16 of of ADP cana-6326 189 17 engineering engineering NOUN cana-6326 189 18 science science NOUN cana-6326 189 19 , , PUNCT cana-6326 189 20 10 10 NUM cana-6326 189 21 ( ( PUNCT cana-6326 189 22 6 6 NUM cana-6326 189 23 ) ) PUNCT cana-6326 189 24 ( ( PUNCT cana-6326 189 25 1972 1972 NUM cana-6326 189 26 ) ) PUNCT cana-6326 189 27 561 561 NUM cana-6326 189 28 - - SYM cana-6326 189 29 575 575 NUM cana-6326 189 30 . . PUNCT cana-6326 190 1 https://doi.org/10.1016/0020-7225(72)90098-5 https://doi.org/10.1016/0020-7225(72)90098-5 PROPN cana-6326 190 2 [ [ X cana-6326 190 3 4 4 NUM cana-6326 190 4 ] ] X cana-6326 190 5 eringen eringen PROPN cana-6326 190 6 , , PUNCT cana-6326 190 7 a.c a.c PROPN cana-6326 190 8 . . PROPN cana-6326 190 9 : : PUNCT cana-6326 190 10 nonlocal nonlocal ADJ cana-6326 190 11 polar polar ADJ cana-6326 190 12 elastic elastic ADJ cana-6326 190 13 continua continuum NOUN cana-6326 190 14 , , PUNCT cana-6326 190 15 international international ADJ cana-6326 190 16 journal journal NOUN cana-6326 190 17 of of ADP cana-6326 190 18 engineering engineering NOUN cana-6326 190 19 science science NOUN cana-6326 190 20 , , PUNCT cana-6326 190 21 10(1 10(1 NUM cana-6326 190 22 ) ) PUNCT cana-6326 190 23 ( ( PUNCT cana-6326 190 24 1972 1972 NUM cana-6326 190 25 ) ) PUNCT cana-6326 190 26 ; ; PUNCT cana-6326 190 27 1 1 NUM cana-6326 190 28 - - SYM cana-6326 190 29 16 16 NUM cana-6326 190 30 . . PUNCT cana-6326 191 1 https://doi.org/10.1016/0020-7225(72)90070-5 https://doi.org/10.1016/0020-7225(72)90070-5 PUNCT cana-6326 192 1 [ [ X cana-6326 192 2 5 5 NUM cana-6326 192 3 ] ] X cana-6326 192 4 eringen eringen PROPN cana-6326 192 5 , , PUNCT cana-6326 192 6 a.c a.c PROPN cana-6326 192 7 . . PROPN cana-6326 192 8 : : PUNCT cana-6326 192 9 nonlocal nonlocal ADJ cana-6326 192 10 continuum continuum ADJ cana-6326 192 11 theory theory NOUN cana-6326 192 12 of of ADP cana-6326 192 13 liquid liquid ADJ cana-6326 192 14 crystals crystal NOUN cana-6326 192 15 , , PUNCT cana-6326 192 16 molecular molecular ADJ cana-6326 192 17 crystals crystal NOUN cana-6326 192 18 and and CCONJ cana-6326 192 19 liquid liquid ADJ cana-6326 192 20 crystals crystal NOUN cana-6326 192 21 . . PUNCT cana-6326 193 1 75(1 75(1 X cana-6326 193 2 ) ) PUNCT cana-6326 193 3 ( ( PUNCT cana-6326 193 4 1981 1981 NUM cana-6326 193 5 ) ) PUNCT cana-6326 193 6 ; ; PUNCT cana-6326 193 7 321 321 NUM cana-6326 193 8 - - SYM cana-6326 193 9 343 343 NUM cana-6326 193 10 . . PUNCT cana-6326 194 1 https://doi.org/10.1080/00268948108073623 https://doi.org/10.1080/00268948108073623 NOUN cana-6326 195 1 [ [ X cana-6326 195 2 6 6 NUM cana-6326 195 3 ] ] X cana-6326 195 4 eringen eringen PROPN cana-6326 195 5 , , PUNCT cana-6326 195 6 a.c a.c PROPN cana-6326 195 7 . . PROPN cana-6326 195 8 : : PUNCT cana-6326 196 1 nonlocal nonlocal ADJ cana-6326 196 2 inviscid inviscid ADJ cana-6326 196 3 magneto magneto NOUN cana-6326 196 4 - - PUNCT cana-6326 196 5 hydrodynamics hydrodynamic NOUN cana-6326 196 6 and and CCONJ cana-6326 196 7 dispersion dispersion NOUN cana-6326 196 8 of of ADP cana-6326 196 9 alfven alfven NOUN cana-6326 196 10 waves wave NOUN cana-6326 196 11 , , PUNCT cana-6326 196 12 bull bull NOUN cana-6326 196 13 . . PUNCT cana-6326 197 1 tech tech NOUN cana-6326 197 2 . . PUNCT cana-6326 198 1 univ univ PROPN cana-6326 198 2 . . PUNCT cana-6326 198 3 istanbul istanbul PROPN cana-6326 198 4 . . PUNCT cana-6326 199 1 39 39 NUM cana-6326 199 2 ( ( PUNCT cana-6326 199 3 1986 1986 NUM cana-6326 199 4 ) ) PUNCT cana-6326 199 5 ; ; PUNCT cana-6326 199 6 393 393 NUM cana-6326 199 7 - - SYM cana-6326 199 8 408 408 NUM cana-6326 199 9 . . PUNCT cana-6326 200 1 communications communication NOUN cana-6326 200 2 on on ADP cana-6326 200 3 applied apply VERB cana-6326 200 4 nonlinear nonlinear ADJ cana-6326 200 5 analysis analysis NOUN cana-6326 200 6 issn issn NOUN cana-6326 200 7 : : PUNCT cana-6326 200 8 1074 1074 NUM cana-6326 200 9 - - PUNCT cana-6326 200 10 133x 133x NUM cana-6326 200 11 vol vol VERB cana-6326 200 12 32 32 NUM cana-6326 200 13 no no NOUN cana-6326 200 14 . . PUNCT cana-6326 201 1 10s 10 NOUN cana-6326 201 2 ( ( PUNCT cana-6326 201 3 2025 2025 NUM cana-6326 201 4 ) ) PUNCT cana-6326 201 5 3726 3726 NUM cana-6326 201 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 202 1 [ [ X cana-6326 202 2 7 7 X cana-6326 202 3 ] ] X cana-6326 202 4 eringen eringen PROPN cana-6326 202 5 , , PUNCT cana-6326 202 6 a.c a.c PROPN cana-6326 202 7 . . PROPN cana-6326 202 8 : : PUNCT cana-6326 203 1 memory memory NOUN cana-6326 203 2 dependent dependent ADJ cana-6326 203 3 nonlocal nonlocal ADJ cana-6326 203 4 electrodynamics electrodynamic NOUN cana-6326 203 5 , , PUNCT cana-6326 203 6 mechanical mechanical ADJ cana-6326 203 7 modelling modelling NOUN cana-6326 203 8 of of ADP cana-6326 203 9 new new ADJ cana-6326 203 10 electromagnetic electromagnetic ADJ cana-6326 203 11 materials material NOUN cana-6326 203 12 , , PUNCT cana-6326 203 13 proceedings proceeding NOUN cana-6326 203 14 of of ADP cana-6326 203 15 iutam iutam PROPN cana-6326 203 16 symposium symposium NOUN cana-6326 203 17 ( ( PUNCT cana-6326 203 18 hsieh hsieh PROPN cana-6326 203 19 r.k.t r.k.t PROPN cana-6326 203 20 . . PUNCT cana-6326 203 21 ,ed ,ed PROPN cana-6326 203 22 . . PUNCT cana-6326 203 23 ) ) PUNCT cana-6326 204 1 elsevier elsevier NOUN cana-6326 204 2 , , PUNCT cana-6326 204 3 amsterdam amsterdam PROPN cana-6326 204 4 , , PUNCT cana-6326 204 5 ( ( PUNCT cana-6326 204 6 1990 1990 NUM cana-6326 204 7 ) ) PUNCT cana-6326 204 8 ; ; PUNCT cana-6326 204 9 45 45 NUM cana-6326 204 10 - - SYM cana-6326 204 11 49 49 NUM cana-6326 204 12 . . PUNCT cana-6326 205 1 [ [ X cana-6326 205 2 8 8 NUM cana-6326 205 3 ] ] X cana-6326 205 4 eringen eringen PROPN cana-6326 205 5 , , PUNCT cana-6326 205 6 a.c a.c PROPN cana-6326 205 7 . . PROPN cana-6326 205 8 : : PUNCT cana-6326 205 9 memory memory NOUN cana-6326 205 10 dependent dependent ADJ cana-6326 205 11 nonlocal nonlocal ADJ cana-6326 205 12 electromagnetic electromagnetic ADJ cana-6326 205 13 elastic elastic ADJ cana-6326 205 14 solids solid NOUN cana-6326 205 15 and and CCONJ cana-6326 205 16 super super ADJ cana-6326 205 17 conduct conduct NOUN cana-6326 205 18 ivity ivity NOUN cana-6326 205 19 . . PUNCT cana-6326 206 1 journal journal PROPN cana-6326 206 2 of of ADP cana-6326 206 3 mathematical mathematical ADJ cana-6326 206 4 physics physics NOUN cana-6326 206 5 , , PUNCT cana-6326 206 6 32(3 32(3 NUM cana-6326 206 7 ) ) PUNCT cana-6326 206 8 , , PUNCT cana-6326 206 9 ( ( PUNCT cana-6326 206 10 1991);787 1991);787 NUM cana-6326 206 11 - - SYM cana-6326 206 12 796 796 NUM cana-6326 206 13 . . PUNCT cana-6326 207 1 https://doi.org/10.1063/1.529372 https://doi.org/10.1063/1.529372 VERB cana-6326 208 1 [ [ X cana-6326 208 2 9 9 NUM cana-6326 208 3 ] ] SYM cana-6326 208 4 mccay mccay NOUN cana-6326 208 5 , , PUNCT cana-6326 208 6 b. b. PROPN cana-6326 208 7 m. m. NOUN cana-6326 208 8 and and CCONJ cana-6326 208 9 narsimhan narsimhan NOUN cana-6326 208 10 , , PUNCT cana-6326 208 11 m. m. PROPN cana-6326 208 12 l. l. PROPN cana-6326 208 13 n. n. PROPN cana-6326 208 14 : : PUNCT cana-6326 208 15 theory theory NOUN cana-6326 208 16 of of ADP cana-6326 208 17 nonlocal nonlocal ADJ cana-6326 208 18 electromagnetic electromagnetic ADJ cana-6326 208 19 fluids fluid NOUN cana-6326 208 20 , , PUNCT cana-6326 208 21 archives archive NOUN cana-6326 208 22 of of ADP cana-6326 208 23 mechanics mechanic NOUN cana-6326 208 24 . . PUNCT cana-6326 209 1 33 33 NUM cana-6326 209 2 ( ( PUNCT cana-6326 209 3 3 3 NUM cana-6326 209 4 ) ) PUNCT cana-6326 209 5 ( ( PUNCT cana-6326 209 6 1981);365 1981);365 NUM cana-6326 209 7 - - SYM cana-6326 209 8 384 384 NUM cana-6326 209 9 . . PUNCT cana-6326 209 10 wa727_89260_p.262b wa727_89260_p.262b NOUN cana-6326 209 11 - - PUNCT cana-6326 209 12 mccay mccay NOUN cana-6326 209 13 - - NOUN cana-6326 209 14 theory theory NOUN cana-6326 209 15 [ [ X cana-6326 209 16 10 10 NUM cana-6326 209 17 ] ] SYM cana-6326 209 18 narsimhan narsimhan NOUN cana-6326 209 19 , , PUNCT cana-6326 209 20 m. m. NOUN cana-6326 209 21 l. l. PROPN cana-6326 209 22 n. n. PROPN cana-6326 209 23 and and CCONJ cana-6326 209 24 mccay mccay PROPN cana-6326 209 25 , , PUNCT cana-6326 209 26 b. b. PROPN cana-6326 209 27 m. m. NOUN cana-6326 209 28 : : PUNCT cana-6326 209 29 dispersion dispersion NOUN cana-6326 209 30 of of ADP cana-6326 209 31 surface surface NOUN cana-6326 209 32 waves wave NOUN cana-6326 209 33 in in ADP cana-6326 209 34 nonlocal nonlocal ADJ cana-6326 209 35 dielectric dielectric ADJ cana-6326 209 36 fluids fluid NOUN cana-6326 209 37 , , PUNCT cana-6326 209 38 archives archive NOUN cana-6326 209 39 of of ADP cana-6326 209 40 mechanics mechanic NOUN cana-6326 209 41 , , PUNCT cana-6326 209 42 33 33 NUM cana-6326 209 43 ( ( PUNCT cana-6326 209 44 3 3 NUM cana-6326 209 45 ) ) PUNCT cana-6326 209 46 ( ( PUNCT cana-6326 209 47 1981 1981 NUM cana-6326 209 48 ) ) PUNCT cana-6326 209 49 385 385 NUM cana-6326 209 50 - - PUNCT cana-6326 209 51 400.wa727_89260_p.262b 400.wa727_89260_p.262b NUM cana-6326 209 52 - - PUNCT cana-6326 209 53 mccay mccay NOUN cana-6326 209 54 - - PUNCT cana-6326 209 55 theory theory NOUN cana-6326 209 56 [ [ X cana-6326 209 57 11]eringen 11]eringen NUM cana-6326 209 58 , , PUNCT cana-6326 209 59 a.c a.c PROPN cana-6326 209 60 . . PROPN cana-6326 209 61 : : PUNCT cana-6326 209 62 nonlocal nonlocal ADJ cana-6326 209 63 continuum continuum ADJ cana-6326 209 64 field field NOUN cana-6326 209 65 theories theory NOUN cana-6326 209 66 , , PUNCT cana-6326 209 67 springer springer NOUN cana-6326 209 68 ( ( PUNCT cana-6326 209 69 2002 2002 NUM cana-6326 209 70 ) ) PUNCT cana-6326 209 71 https://doi.org/10.1007/b97697 https://doi.org/10.1007/b97697 VERB cana-6326 209 72 . . PUNCT cana-6326 210 1 [ [ X cana-6326 210 2 12 12 NUM cana-6326 210 3 ] ] PUNCT cana-6326 210 4 tzou tzou PROPN cana-6326 210 5 , , PUNCT cana-6326 210 6 d. d. PROPN cana-6326 210 7 y. y. PROPN cana-6326 210 8 : : PUNCT cana-6326 210 9 thermal thermal ADJ cana-6326 210 10 shock shock NOUN cana-6326 210 11 phenomena phenomenon NOUN cana-6326 210 12 under under ADP cana-6326 210 13 high high ADJ cana-6326 210 14 rate rate NOUN cana-6326 210 15 response response NOUN cana-6326 210 16 in in ADP cana-6326 210 17 solids solid NOUN cana-6326 210 18 , , PUNCT cana-6326 210 19 annual annual ADJ cana-6326 210 20 review review NOUN cana-6326 210 21 of of ADP cana-6326 210 22 heat heat NOUN cana-6326 210 23 transfer transfer NOUN cana-6326 210 24 , , PUNCT cana-6326 210 25 4 4 NUM cana-6326 210 26 ( ( PUNCT cana-6326 210 27 1992 1992 NUM cana-6326 210 28 ) ) PUNCT cana-6326 210 29 111 111 NUM cana-6326 210 30 - - SYM cana-6326 210 31 185 185 NUM cana-6326 210 32 . . PUNCT cana-6326 211 1 doi doi NOUN cana-6326 211 2 : : PUNCT cana-6326 211 3 10.1615 10.1615 NUM cana-6326 211 4 / / SYM cana-6326 211 5 annualrevheattransfer.v4.50 annualrevheattransfer.v4.50 NOUN cana-6326 212 1 [ [ X cana-6326 212 2 13 13 NUM cana-6326 212 3 ] ] SYM cana-6326 212 4 cao cao PROPN cana-6326 212 5 , , PUNCT cana-6326 212 6 b.y b.y PROPN cana-6326 212 7 . . PROPN cana-6326 212 8 and and CCONJ cana-6326 212 9 guo guo PROPN cana-6326 212 10 , , PUNCT cana-6326 212 11 z. z. PROPN cana-6326 212 12 y. y. PROPN cana-6326 212 13 : : PUNCT cana-6326 212 14 equation equation NOUN cana-6326 212 15 of of ADP cana-6326 212 16 motion motion NOUN cana-6326 212 17 of of ADP cana-6326 212 18 a a DET cana-6326 212 19 phonon phonon NOUN cana-6326 212 20 gas gas NOUN cana-6326 212 21 and and CCONJ cana-6326 212 22 non non ADJ cana-6326 212 23 - - ADJ cana-6326 212 24 fourier fourier ADJ cana-6326 212 25 heat heat NOUN cana-6326 212 26 conduction conduction NOUN cana-6326 212 27 , , PUNCT cana-6326 212 28 journal journal NOUN cana-6326 212 29 of of ADP cana-6326 212 30 applied applied ADJ cana-6326 212 31 physics physic NOUN cana-6326 212 32 , , PUNCT cana-6326 212 33 102(5 102(5 NUM cana-6326 212 34 ) ) PUNCT cana-6326 212 35 ( ( PUNCT cana-6326 212 36 2007 2007 NUM cana-6326 212 37 ) ) PUNCT cana-6326 212 38 053503.https://doi.org/10.1063/1.2775215 053503.https://doi.org/10.1063/1.2775215 NUM cana-6326 213 1 [ [ X cana-6326 213 2 14 14 NUM cana-6326 213 3 ] ] X cana-6326 213 4 guo guo PROPN cana-6326 213 5 , , PUNCT cana-6326 213 6 z. z. PROPN cana-6326 213 7 y. y. PROPN cana-6326 213 8 and and CCONJ cana-6326 213 9 hou hou PROPN cana-6326 213 10 , , PUNCT cana-6326 213 11 q.w q.w PROPN cana-6326 213 12 . . PROPN cana-6326 213 13 : : PUNCT cana-6326 213 14 thermal thermal ADJ cana-6326 213 15 wave wave NOUN cana-6326 213 16 based base VERB cana-6326 213 17 on on ADP cana-6326 213 18 the the DET cana-6326 213 19 thermomass thermomass NOUN cana-6326 213 20 model model NOUN cana-6326 213 21 , , PUNCT cana-6326 213 22 journal journal NOUN cana-6326 213 23 of of ADP cana-6326 213 24 heat heat NOUN cana-6326 213 25 transfer transfer NOUN cana-6326 213 26 . . PUNCT cana-6326 214 1 132(7 132(7 NUM cana-6326 214 2 ) ) PUNCT cana-6326 214 3 ( ( PUNCT cana-6326 214 4 2010 2010 NUM cana-6326 214 5 ) ) PUNCT cana-6326 214 6 ; ; PUNCT cana-6326 214 7 072403 072403 NUM cana-6326 214 8 . . PUNCT cana-6326 215 1 https://doi.org/10.1115/1.4000987 https://doi.org/10.1115/1.4000987 PROPN cana-6326 216 1 [ [ X cana-6326 216 2 15 15 NUM cana-6326 216 3 ] ] PUNCT cana-6326 216 4 tzou tzou NOUN cana-6326 216 5 , , PUNCT cana-6326 216 6 d.y d.y PROPN cana-6326 216 7 . . PROPN cana-6326 216 8 and and CCONJ cana-6326 216 9 guo guo PROPN cana-6326 216 10 , , PUNCT cana-6326 216 11 z.y z.y PROPN cana-6326 216 12 . . PUNCT cana-6326 216 13 : : PUNCT cana-6326 216 14 nonlocal nonlocal ADJ cana-6326 216 15 behavior behavior NOUN cana-6326 216 16 in in ADP cana-6326 216 17 thermal thermal ADJ cana-6326 216 18 lagging lagging NOUN cana-6326 216 19 , , PUNCT cana-6326 216 20 international international ADJ cana-6326 216 21 journal journal NOUN cana-6326 216 22 of of ADP cana-6326 216 23 thermal thermal ADJ cana-6326 216 24 sciences sciences PROPN cana-6326 216 25 , , PUNCT cana-6326 216 26 49(7 49(7 NUM cana-6326 216 27 ) ) PUNCT cana-6326 216 28 ( ( PUNCT cana-6326 216 29 2010);1133 2010);1133 NOUN cana-6326 216 30 - - SYM cana-6326 216 31 1137 1137 NUM cana-6326 216 32 . . PUNCT cana-6326 217 1 https://doi.org/10.1016/j.ijthermalsci.2010.01.022 https://doi.org/10.1016/j.ijthermalsci.2010.01.022 NOUN cana-6326 218 1 [ [ X cana-6326 218 2 16 16 NUM cana-6326 218 3 ] ] PUNCT cana-6326 218 4 tzou tzou PROPN cana-6326 218 5 , , PUNCT cana-6326 218 6 d.y d.y PROPN cana-6326 218 7 . . PROPN cana-6326 218 8 : : PUNCT cana-6326 219 1 a a DET cana-6326 219 2 unified unified ADJ cana-6326 219 3 field field NOUN cana-6326 219 4 approach approach NOUN cana-6326 219 5 for for ADP cana-6326 219 6 heat heat NOUN cana-6326 219 7 conduction conduction NOUN cana-6326 219 8 from from ADP cana-6326 219 9 macro macro ADJ cana-6326 219 10 to to ADP cana-6326 219 11 micro micro NOUN cana-6326 219 12 scales scale NOUN cana-6326 219 13 , , PUNCT cana-6326 219 14 journal journal NOUN cana-6326 219 15 of of ADP cana-6326 219 16 heat heat NOUN cana-6326 219 17 transfer transfer NOUN cana-6326 219 18 , , PUNCT cana-6326 219 19 117(1 117(1 NUM cana-6326 219 20 ) ) PUNCT cana-6326 219 21 ( ( PUNCT cana-6326 219 22 1995 1995 NUM cana-6326 219 23 ) ) PUNCT cana-6326 219 24 ; ; PUNCT cana-6326 219 25 8 8 NUM cana-6326 219 26 - - SYM cana-6326 219 27 16 16 NUM cana-6326 219 28 . . PUNCT cana-6326 219 29 https://doi.org/10.1115/1.2822329 https://doi.org/10.1115/1.2822329 X cana-6326 220 1 [ [ X cana-6326 220 2 17 17 NUM cana-6326 220 3 ] ] PUNCT cana-6326 220 4 tzou tzou PROPN cana-6326 220 5 , , PUNCT cana-6326 220 6 d.y d.y PROPN cana-6326 220 7 . . PROPN cana-6326 220 8 : : PUNCT cana-6326 221 1 the the DET cana-6326 221 2 generalised generalise VERB cana-6326 221 3 lagging lagging ADJ cana-6326 221 4 response response NOUN cana-6326 221 5 in in ADP cana-6326 221 6 small small ADJ cana-6326 221 7 scale scale NOUN cana-6326 221 8 and and CCONJ cana-6326 221 9 high high ADJ cana-6326 221 10 rate rate NOUN cana-6326 221 11 heating heating NOUN cana-6326 221 12 , , PUNCT cana-6326 221 13 international international ADJ cana-6326 221 14 journal journal NOUN cana-6326 221 15 of of ADP cana-6326 221 16 heat heat NOUN cana-6326 221 17 and and CCONJ cana-6326 221 18 mass mass NOUN cana-6326 221 19 transfer transfer NOUN cana-6326 221 20 , , PUNCT cana-6326 221 21 38(17 38(17 NUM cana-6326 221 22 ) ) PUNCT cana-6326 221 23 ( ( PUNCT cana-6326 221 24 1995 1995 NUM cana-6326 221 25 ) ) PUNCT cana-6326 221 26 ; ; PUNCT cana-6326 221 27 3231 3231 NUM cana-6326 221 28 - - SYM cana-6326 221 29 3240 3240 NUM cana-6326 221 30 . . PUNCT cana-6326 222 1 https://doi.org/10.1016/0017-9310(95)00052-b https://doi.org/10.1016/0017-9310(95)00052-b X cana-6326 222 2 [ [ X cana-6326 222 3 18 18 NUM cana-6326 222 4 ] ] X cana-6326 222 5 sherief sherief NOUN cana-6326 222 6 , , PUNCT cana-6326 222 7 h.h h.h PROPN cana-6326 222 8 . . PROPN cana-6326 222 9 , , PUNCT cana-6326 222 10 hamza hamza PROPN cana-6326 222 11 , , PUNCT cana-6326 222 12 f.a f.a PROPN cana-6326 222 13 . . PROPN cana-6326 222 14 and and CCONJ cana-6326 222 15 saleh saleh NOUN cana-6326 222 16 , , PUNCT cana-6326 222 17 h. h. PROPN cana-6326 222 18 a. a. PROPN cana-6326 222 19 : : PUNCT cana-6326 222 20 the the DET cana-6326 222 21 theory theory NOUN cana-6326 222 22 of of ADP cana-6326 222 23 generalised generalise VERB cana-6326 222 24 thermoelastic thermoelastic ADJ cana-6326 222 25 diffusion diffusion NOUN cana-6326 222 26 , , PUNCT cana-6326 222 27 international international ADJ cana-6326 222 28 journal journal NOUN cana-6326 222 29 of of ADP cana-6326 222 30 engineering engineering NOUN cana-6326 222 31 science science NOUN cana-6326 222 32 . . PUNCT cana-6326 223 1 42(5 42(5 NUM cana-6326 223 2 - - SYM cana-6326 223 3 6 6 NUM cana-6326 223 4 ) ) PUNCT cana-6326 223 5 ( ( PUNCT cana-6326 223 6 2004 2004 NUM cana-6326 223 7 ) ) PUNCT cana-6326 223 8 591 591 NUM cana-6326 223 9 - - SYM cana-6326 223 10 608 608 NUM cana-6326 223 11 . . PUNCT cana-6326 224 1 https://doi.org/10.1016/j.ijengsci.2003.05.001 https://doi.org/10.1016/j.ijengsci.2003.05.001 PROPN cana-6326 224 2 [ [ X cana-6326 224 3 19 19 NUM cana-6326 224 4 ] ] X cana-6326 224 5 sherief sherief NOUN cana-6326 224 6 , , PUNCT cana-6326 224 7 h.h h.h PROPN cana-6326 224 8 . . PROPN cana-6326 224 9 and and CCONJ cana-6326 224 10 saleh saleh PROPN cana-6326 224 11 , , PUNCT cana-6326 224 12 h. h. PROPN cana-6326 224 13 : : PUNCT cana-6326 224 14 a a DET cana-6326 224 15 half half NOUN cana-6326 224 16 space space NOUN cana-6326 224 17 problem problem NOUN cana-6326 224 18 in in ADP cana-6326 224 19 the the DET cana-6326 224 20 theory theory NOUN cana-6326 224 21 of of ADP cana-6326 224 22 generalised generalise VERB cana-6326 224 23 thermoelastic thermoelastic ADJ cana-6326 224 24 diffusion diffusion NOUN cana-6326 224 25 , , PUNCT cana-6326 224 26 international international ADJ cana-6326 224 27 journal journal NOUN cana-6326 224 28 of of ADP cana-6326 224 29 solids solid NOUN cana-6326 224 30 and and CCONJ cana-6326 224 31 structures structure NOUN cana-6326 224 32 , , PUNCT cana-6326 224 33 42(15 42(15 NUM cana-6326 224 34 ) ) PUNCT cana-6326 224 35 ( ( PUNCT cana-6326 224 36 2005 2005 NUM cana-6326 224 37 ) ) PUNCT cana-6326 224 38 ; ; PUNCT cana-6326 224 39 4484 4484 NUM cana-6326 224 40 - - SYM cana-6326 224 41 4493 4493 NUM cana-6326 224 42 . . PUNCT cana-6326 225 1 https://doi.org/10.1016/j.ijsolstr.2005.01.001 https://doi.org/10.1016/j.ijsolstr.2005.01.001 X cana-6326 225 2 [ [ X cana-6326 225 3 20 20 NUM cana-6326 225 4 ] ] PUNCT cana-6326 225 5 sharma sharma PROPN cana-6326 225 6 , , PUNCT cana-6326 225 7 k. k. VERB cana-6326 225 8 : : PUNCT cana-6326 225 9 boundary boundary ADJ cana-6326 225 10 value value NOUN cana-6326 225 11 problem problem NOUN cana-6326 225 12 in in ADP cana-6326 225 13 generalized generalize VERB cana-6326 225 14 thermodiffusive thermodiffusive PRON cana-6326 225 15 elastic elastic ADJ cana-6326 225 16 medium medium NOUN cana-6326 225 17 , , PUNCT cana-6326 225 18 journal journal NOUN cana-6326 225 19 of of ADP cana-6326 225 20 solid solid ADJ cana-6326 225 21 mechanics mechanic NOUN cana-6326 225 22 , , PUNCT cana-6326 225 23 2 2 NUM cana-6326 225 24 ( ( PUNCT cana-6326 225 25 5 5 NUM cana-6326 225 26 ) ) PUNCT cana-6326 225 27 ( ( PUNCT cana-6326 225 28 2010 2010 NUM cana-6326 225 29 ) ) PUNCT cana-6326 225 30 ; ; PUNCT cana-6326 226 1 348 348 NUM cana-6326 226 2 - - SYM cana-6326 226 3 362 362 NUM cana-6326 226 4 , , PUNCT cana-6326 226 5 https://oiccpress.com/jsm/article/view/12348 https://oiccpress.com/jsm/article/view/12348 PROPN cana-6326 226 6 [ [ X cana-6326 226 7 21 21 NUM cana-6326 226 8 ] ] X cana-6326 226 9 sharma sharma PROPN cana-6326 226 10 , , PUNCT cana-6326 226 11 k. k. X cana-6326 226 12 : : PUNCT cana-6326 226 13 reflection reflection NOUN cana-6326 226 14 of of ADP cana-6326 226 15 plane plane NOUN cana-6326 226 16 waves wave NOUN cana-6326 226 17 in in ADP cana-6326 226 18 thermodiffusive thermodiffusive PRON cana-6326 226 19 elastic elastic ADJ cana-6326 226 20 half half NOUN cana-6326 226 21 space space NOUN cana-6326 226 22 with with ADP cana-6326 226 23 voids voids NOUN cana-6326 226 24 , , PUNCT cana-6326 226 25 multidiscipline multidiscipline VERB cana-6326 226 26 modeling modeling NOUN cana-6326 226 27 in in ADP cana-6326 226 28 materials material NOUN cana-6326 226 29 and and CCONJ cana-6326 226 30 structures structure NOUN cana-6326 226 31 . . PUNCT cana-6326 227 1 8(3 8(3 NUM cana-6326 227 2 ) ) PUNCT cana-6326 227 3 ( ( PUNCT cana-6326 227 4 2012 2012 NUM cana-6326 227 5 ) ) PUNCT cana-6326 227 6 ; ; PUNCT cana-6326 227 7 269 269 NUM cana-6326 227 8 - - SYM cana-6326 227 9 296 296 NUM cana-6326 227 10 . . PUNCT cana-6326 228 1 https://doi.org/10.1108/15736101211269113 https://doi.org/10.1108/15736101211269113 NOUN cana-6326 228 2 https://rcin.org.pl/ippt/content/70834/pdf/wa727_89260_p.262b-mccay-theory.pdf https://rcin.org.pl/ippt/content/70834/pdf/wa727_89260_p.262b-mccay-theory.pdf PROPN cana-6326 228 3 https://rcin.org.pl/ippt/content/70834/pdf/wa727_89260_p.262b-mccay-theory.pdf https://rcin.org.pl/ippt/content/70834/pdf/wa727_89260_p.262b-mccay-theory.pdf PROPN cana-6326 228 4 https://doi.org/10.1007/b97697 https://doi.org/10.1007/b97697 NUM cana-6326 228 5 https://doi.org/10.1115/1.4000987 https://doi.org/10.1115/1.4000987 NOUN cana-6326 228 6 communications communication NOUN cana-6326 228 7 on on ADP cana-6326 228 8 applied apply VERB cana-6326 228 9 nonlinear nonlinear ADJ cana-6326 228 10 analysis analysis NOUN cana-6326 228 11 issn issn NOUN cana-6326 228 12 : : PUNCT cana-6326 228 13 1074 1074 NUM cana-6326 228 14 - - PUNCT cana-6326 228 15 133x 133x NUM cana-6326 228 16 vol vol VERB cana-6326 228 17 32 32 NUM cana-6326 228 18 no no NOUN cana-6326 228 19 . . PUNCT cana-6326 229 1 10s 10 NOUN cana-6326 229 2 ( ( PUNCT cana-6326 229 3 2025 2025 NUM cana-6326 229 4 ) ) PUNCT cana-6326 229 5 3727 3727 NUM cana-6326 229 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 230 1 [ [ X cana-6326 230 2 22 22 NUM cana-6326 230 3 ] ] PUNCT cana-6326 230 4 sharma sharma PROPN cana-6326 230 5 , , PUNCT cana-6326 230 6 s. s. PROPN cana-6326 230 7 , , PUNCT cana-6326 230 8 sharma sharma PROPN cana-6326 230 9 , , PUNCT cana-6326 230 10 k. k. PROPN cana-6326 230 11 and and CCONJ cana-6326 230 12 bhargava bhargava PROPN cana-6326 230 13 , , PUNCT cana-6326 230 14 r. r. PROPN cana-6326 230 15 : : PUNCT cana-6326 230 16 effect effect NOUN cana-6326 230 17 of of ADP cana-6326 230 18 viscosity viscosity NOUN cana-6326 230 19 on on ADP cana-6326 230 20 wave wave NOUN cana-6326 230 21 propagation propagation NOUN cana-6326 230 22 in in ADP cana-6326 230 23 anisotropic anisotropic NOUN cana-6326 230 24 thermoelastic thermoelastic ADJ cana-6326 230 25 with with ADP cana-6326 230 26 green green ADJ cana-6326 230 27 - - PUNCT cana-6326 230 28 naghdi naghdi NOUN cana-6326 230 29 theory theory NOUN cana-6326 230 30 type type NOUN cana-6326 230 31 - - PUNCT cana-6326 230 32 ii ii NOUN cana-6326 230 33 and and CCONJ cana-6326 230 34 type type NOUN cana-6326 230 35 - - PUNCT cana-6326 230 36 iii iii NOUN cana-6326 230 37 , , PUNCT cana-6326 230 38 material material NOUN cana-6326 230 39 physics physics NOUN cana-6326 230 40 mechanics mechanic NOUN cana-6326 230 41 . . PUNCT cana-6326 231 1 16 16 NUM cana-6326 231 2 ( ( PUNCT cana-6326 231 3 2013 2013 NUM cana-6326 231 4 ) ) PUNCT cana-6326 231 5 ; ; PUNCT cana-6326 232 1 144 144 NUM cana-6326 232 2 - - SYM cana-6326 232 3 158 158 NUM cana-6326 232 4 . . PUNCT cana-6326 233 1 [ [ X cana-6326 233 2 23 23 NUM cana-6326 233 3 ] ] PUNCT cana-6326 233 4 sharma sharma PROPN cana-6326 233 5 , , PUNCT cana-6326 233 6 k. k. PROPN cana-6326 233 7 , , PUNCT cana-6326 233 8 marin marin NOUN cana-6326 233 9 , , PUNCT cana-6326 233 10 m. m. NOUN cana-6326 233 11 : : PUNCT cana-6326 233 12 reflection reflection NOUN cana-6326 233 13 and and CCONJ cana-6326 233 14 transmission transmission NOUN cana-6326 233 15 of of ADP cana-6326 233 16 waves wave NOUN cana-6326 233 17 from from ADP cana-6326 233 18 imperfect imperfect ADJ cana-6326 233 19 boundary boundary NOUN cana-6326 233 20 between between ADP cana-6326 233 21 two two NUM cana-6326 233 22 heat heat NOUN cana-6326 233 23 conducting conduct VERB cana-6326 233 24 micropolar micropolar ADJ cana-6326 233 25 thermoelastic thermoelastic ADJ cana-6326 233 26 solids solid NOUN cana-6326 233 27 , , PUNCT cana-6326 233 28 an an PROPN cana-6326 233 29 . . PUNCT cana-6326 233 30 st st PROPN cana-6326 233 31 . . PROPN cana-6326 233 32 univ univ PROPN cana-6326 233 33 . . PUNCT cana-6326 234 1 ovidius ovidius PROPN cana-6326 234 2 constanta constanta PROPN cana-6326 234 3 , , PUNCT cana-6326 234 4 22(2),(2014);151 22(2),(2014);151 PROPN cana-6326 234 5 - - SYM cana-6326 234 6 175 175 NUM cana-6326 234 7 . . PUNCT cana-6326 235 1 doi doi NOUN cana-6326 235 2 : : PUNCT cana-6326 235 3 10.2478 10.2478 NUM cana-6326 235 4 / / SYM cana-6326 235 5 auom-2014 auom-2014 NOUN cana-6326 235 6 - - PUNCT cana-6326 235 7 0040 0040 NUM cana-6326 235 8 [ [ X cana-6326 235 9 24 24 NUM cana-6326 235 10 ] ] PUNCT cana-6326 235 11 abouelregal abouelregal ADJ cana-6326 235 12 , , PUNCT cana-6326 235 13 a. a. PROPN cana-6326 235 14 e. e. PROPN cana-6326 235 15 and and CCONJ cana-6326 235 16 zenkour zenkour PROPN cana-6326 235 17 , , PUNCT cana-6326 235 18 a. a. NOUN cana-6326 235 19 m. m. NOUN cana-6326 235 20 : : PUNCT cana-6326 235 21 effect effect NOUN cana-6326 235 22 of of ADP cana-6326 235 23 phase phase NOUN cana-6326 235 24 lags lag VERB cana-6326 235 25 on on ADP cana-6326 235 26 thermoelastic thermoelastic ADJ cana-6326 235 27 functionally functionally ADV cana-6326 235 28 graded grade VERB cana-6326 235 29 microbeams microbeam NOUN cana-6326 235 30 subjected subject VERB cana-6326 235 31 to to ADP cana-6326 235 32 ramp ramp NOUN cana-6326 235 33 - - PUNCT cana-6326 235 34 type type NOUN cana-6326 235 35 heating heating NOUN cana-6326 235 36 , , PUNCT cana-6326 235 37 iranian iranian ADJ cana-6326 235 38 journal journal PROPN cana-6326 235 39 of of ADP cana-6326 235 40 science science NOUN cana-6326 235 41 and and CCONJ cana-6326 235 42 technology technology NOUN cana-6326 235 43 , , PUNCT cana-6326 235 44 transactions transaction NOUN cana-6326 235 45 of of ADP cana-6326 235 46 mechanical mechanical ADJ cana-6326 235 47 engineering engineering NOUN cana-6326 235 48 . . PUNCT cana-6326 236 1 38(m2 38(m2 X cana-6326 236 2 ) ) PUNCT cana-6326 236 3 ( ( PUNCT cana-6326 236 4 2014);321 2014);321 NUM cana-6326 236 5 - - PUNCT cana-6326 236 6 335 335 NUM cana-6326 236 7 . . PUNCT cana-6326 237 1 [ [ X cana-6326 237 2 25 25 NUM cana-6326 237 3 ] ] PUNCT cana-6326 237 4 sharma sharma PROPN cana-6326 237 5 , , PUNCT cana-6326 237 6 s. s. PROPN cana-6326 237 7 and and CCONJ cana-6326 237 8 sharma sharma PROPN cana-6326 237 9 , , PUNCT cana-6326 237 10 k. k. VERB cana-6326 237 11 : : PUNCT cana-6326 237 12 influence influence NOUN cana-6326 237 13 of of ADP cana-6326 237 14 heat heat NOUN cana-6326 237 15 sources source NOUN cana-6326 237 16 and and CCONJ cana-6326 237 17 relaxation relaxation NOUN cana-6326 237 18 time time NOUN cana-6326 237 19 on on ADP cana-6326 237 20 temperature temperature NOUN cana-6326 237 21 distribution distribution NOUN cana-6326 237 22 in in ADP cana-6326 237 23 tissues tissue NOUN cana-6326 237 24 , , PUNCT cana-6326 237 25 international international ADJ cana-6326 237 26 journal journal NOUN cana-6326 237 27 of of ADP cana-6326 237 28 applied apply VERB cana-6326 237 29 mechanical mechanical ADJ cana-6326 237 30 engineering engineering NOUN cana-6326 237 31 , , PUNCT cana-6326 237 32 19(2 19(2 NUM cana-6326 237 33 ) ) PUNCT cana-6326 237 34 ( ( PUNCT cana-6326 237 35 2014 2014 NUM cana-6326 237 36 ) ) PUNCT cana-6326 237 37 427 427 NUM cana-6326 237 38 - - SYM cana-6326 237 39 433 433 NUM cana-6326 237 40 . . PUNCT cana-6326 238 1 doi doi NOUN cana-6326 238 2 : : PUNCT cana-6326 238 3 10.2478 10.2478 NUM cana-6326 238 4 / / SYM cana-6326 238 5 ijame-2014 ijame-2014 NOUN cana-6326 238 6 - - PUNCT cana-6326 238 7 0029 0029 NUM cana-6326 239 1 [ [ X cana-6326 239 2 26 26 NUM cana-6326 239 3 ] ] X cana-6326 239 4 marin marin NOUN cana-6326 239 5 , , PUNCT cana-6326 239 6 m. m. NOUN cana-6326 239 7 , , PUNCT cana-6326 239 8 abbas abbas PROPN cana-6326 239 9 , , PUNCT cana-6326 239 10 i. i. PROPN cana-6326 239 11 a. a. PROPN cana-6326 239 12 and and CCONJ cana-6326 239 13 kumar kumar PROPN cana-6326 239 14 , , PUNCT cana-6326 239 15 r. r. PROPN cana-6326 239 16 : : PUNCT cana-6326 239 17 relaxed relaxed ADJ cana-6326 239 18 saint saint PROPN cana-6326 239 19 - - PUNCT cana-6326 239 20 venant venant NOUN cana-6326 239 21 principle principle NOUN cana-6326 239 22 for for ADP cana-6326 239 23 thermoelastic thermoelastic ADJ cana-6326 239 24 micropolar micropolar ADJ cana-6326 239 25 diffusion diffusion NOUN cana-6326 239 26 , , PUNCT cana-6326 239 27 structural structural ADJ cana-6326 239 28 engineering engineering NOUN cana-6326 239 29 and and CCONJ cana-6326 239 30 mechanics mechanic NOUN cana-6326 239 31 , , PUNCT cana-6326 239 32 51(4 51(4 NUM cana-6326 239 33 ) ) PUNCT cana-6326 239 34 ( ( PUNCT cana-6326 239 35 2014 2014 NUM cana-6326 239 36 ) ) PUNCT cana-6326 239 37 ; ; PUNCT cana-6326 239 38 651 651 NUM cana-6326 239 39 - - SYM cana-6326 239 40 662 662 NUM cana-6326 239 41 . . PUNCT cana-6326 240 1 https://doi.org/10.12989/sem.2014.51.4.651 https://doi.org/10.12989/sem.2014.51.4.651 X cana-6326 241 1 [ [ X cana-6326 241 2 27 27 NUM cana-6326 241 3 ] ] X cana-6326 241 4 yu yu PROPN cana-6326 241 5 , , PUNCT cana-6326 241 6 y.j y.j PROPN cana-6326 241 7 . . PROPN cana-6326 241 8 , , PUNCT cana-6326 241 9 tian tian PROPN cana-6326 241 10 , , PUNCT cana-6326 241 11 x.g x.g PROPN cana-6326 241 12 . . PROPN cana-6326 241 13 and and CCONJ cana-6326 241 14 xiong xiong PROPN cana-6326 241 15 , , PUNCT cana-6326 241 16 q. q. PROPN cana-6326 241 17 l. l. PROPN cana-6326 241 18 : : PUNCT cana-6326 241 19 nonlocal nonlocal ADJ cana-6326 241 20 thermoelasticity thermoelasticity NOUN cana-6326 241 21 based base VERB cana-6326 241 22 on on ADP cana-6326 241 23 nonlocal nonlocal ADJ cana-6326 241 24 heat heat NOUN cana-6326 241 25 conduction conduction NOUN cana-6326 241 26 and and CCONJ cana-6326 241 27 nonlocal nonlocal ADJ cana-6326 241 28 elasticity elasticity NOUN cana-6326 241 29 , , PUNCT cana-6326 241 30 european european ADJ cana-6326 241 31 journal journal PROPN cana-6326 241 32 of of ADP cana-6326 241 33 mechanics-/ mechanics-/ PROPN cana-6326 241 34 a a DET cana-6326 241 35 solids solid NOUN cana-6326 241 36 . . PUNCT cana-6326 242 1 60 60 NUM cana-6326 242 2 ( ( PUNCT cana-6326 242 3 2016);238253 2016);238253 ADJ cana-6326 242 4 . . PUNCT cana-6326 243 1 https://doi.org/10.1016/j.euromechsol.2016.08.004 https://doi.org/10.1016/j.euromechsol.2016.08.004 VERB cana-6326 244 1 [ [ X cana-6326 244 2 28 28 NUM cana-6326 244 3 ] ] X cana-6326 244 4 kumar kumar PROPN cana-6326 244 5 , , PUNCT cana-6326 244 6 r. r. PROPN cana-6326 244 7 , , PUNCT cana-6326 244 8 abbas abbas PROPN cana-6326 244 9 , , PUNCT cana-6326 244 10 i.a i.a PROPN cana-6326 244 11 . . PROPN cana-6326 244 12 : : PUNCT cana-6326 245 1 disturbance disturbance NOUN cana-6326 245 2 due due ADP cana-6326 245 3 to to ADP cana-6326 245 4 thermomechanical thermomechanical ADJ cana-6326 245 5 sources source NOUN cana-6326 245 6 in in ADP cana-6326 245 7 porothermoelastic porothermoelastic ADJ cana-6326 245 8 medium medium NOUN cana-6326 245 9 , , PUNCT cana-6326 245 10 strength strength NOUN cana-6326 245 11 of of ADP cana-6326 245 12 materials material NOUN cana-6326 245 13 48(2 48(2 NUM cana-6326 245 14 ) ) PUNCT cana-6326 245 15 ( ( PUNCT cana-6326 245 16 2016 2016 NUM cana-6326 245 17 ) ) PUNCT cana-6326 245 18 ; ; PUNCT cana-6326 245 19 315-332.https://doi.org/10.1007/s11223-0169767-y 315-332.https://doi.org/10.1007/s11223-0169767-y NUM cana-6326 245 20 [ [ X cana-6326 245 21 29 29 NUM cana-6326 245 22 ] ] X cana-6326 245 23 kumar kumar PROPN cana-6326 245 24 , , PUNCT cana-6326 245 25 r. r. PROPN cana-6326 245 26 , , PUNCT cana-6326 245 27 devi devi PROPN cana-6326 245 28 , , PUNCT cana-6326 245 29 s. s. PROPN cana-6326 245 30 and and CCONJ cana-6326 245 31 sharma sharma PROPN cana-6326 245 32 , , PUNCT cana-6326 245 33 v. v. CCONJ cana-6326 245 34 : : PUNCT cana-6326 245 35 effect effect NOUN cana-6326 245 36 of of ADP cana-6326 245 37 hall hall PROPN cana-6326 245 38 current current NOUN cana-6326 245 39 and and CCONJ cana-6326 245 40 rotation rotation NOUN cana-6326 245 41 in in ADP cana-6326 245 42 modified modify VERB cana-6326 245 43 couple couple NOUN cana-6326 245 44 stress stress NOUN cana-6326 245 45 generalised generalise VERB cana-6326 245 46 thermoelastic thermoelastic ADJ cana-6326 245 47 half half NOUN cana-6326 245 48 space space NOUN cana-6326 245 49 due due ADP cana-6326 245 50 to to ADP cana-6326 245 51 ramp ramp NOUN cana-6326 245 52 type type NOUN cana-6326 245 53 heating heating NOUN cana-6326 245 54 , , PUNCT cana-6326 245 55 journal journal NOUN cana-6326 245 56 of of ADP cana-6326 245 57 solid solid ADJ cana-6326 245 58 mechanics mechanic NOUN cana-6326 245 59 , , PUNCT cana-6326 245 60 9(3 9(3 NUM cana-6326 245 61 ) ) PUNCT cana-6326 245 62 ( ( PUNCT cana-6326 245 63 2017 2017 NUM cana-6326 245 64 ) ) PUNCT cana-6326 245 65 ; ; PUNCT cana-6326 245 66 527 527 NUM cana-6326 245 67 - - SYM cana-6326 245 68 542 542 NUM cana-6326 245 69 . . PUNCT cana-6326 246 1 [ [ X cana-6326 246 2 30 30 NUM cana-6326 246 3 ] ] X cana-6326 246 4 kumar kumar PROPN cana-6326 246 5 , , PUNCT cana-6326 246 6 r. r. PROPN cana-6326 246 7 , , PUNCT cana-6326 246 8 miglani miglani PROPN cana-6326 246 9 , , PUNCT cana-6326 246 10 a. a. NOUN cana-6326 246 11 , , PUNCT cana-6326 246 12 rani rani PROPN cana-6326 246 13 , , PUNCT cana-6326 246 14 r. r. PROPN cana-6326 246 15 : : PUNCT cana-6326 246 16 transient transient VERB cana-6326 246 17 analysis analysis NOUN cana-6326 246 18 of of ADP cana-6326 246 19 nonlocal nonlocal ADJ cana-6326 246 20 microstretch microstretch VERB cana-6326 246 21 thermoelastic thermoelastic ADJ cana-6326 246 22 thick thick ADJ cana-6326 246 23 circular circular ADJ cana-6326 246 24 plate plate NOUN cana-6326 246 25 with with ADP cana-6326 246 26 phase phase NOUN cana-6326 246 27 lags lag VERB cana-6326 246 28 , , PUNCT cana-6326 246 29 mediterranean mediterranean PROPN cana-6326 246 30 journal journal NOUN cana-6326 246 31 of of ADP cana-6326 246 32 modeling modeling NOUN cana-6326 246 33 and and CCONJ cana-6326 246 34 simulation simulation NOUN cana-6326 246 35 . . PUNCT cana-6326 247 1 09 09 NUM cana-6326 247 2 ( ( PUNCT cana-6326 247 3 2018 2018 NUM cana-6326 247 4 ) ) PUNCT cana-6326 247 5 025 025 NUM cana-6326 247 6 - - SYM cana-6326 247 7 042 042 NUM cana-6326 247 8 . . PUNCT cana-6326 247 9 1983-1522252589.pdf 1983-1522252589.pdf X cana-6326 248 1 [ [ X cana-6326 248 2 31 31 NUM cana-6326 248 3 ] ] X cana-6326 248 4 kumar kumar PROPN cana-6326 248 5 , , PUNCT cana-6326 248 6 r. r. PROPN cana-6326 248 7 , , PUNCT cana-6326 248 8 devi devi PROPN cana-6326 248 9 , , PUNCT cana-6326 248 10 s. s. PROPN cana-6326 248 11 and and CCONJ cana-6326 248 12 sharma sharma PROPN cana-6326 248 13 , , PUNCT cana-6326 248 14 v. v. NOUN cana-6326 248 15 : : PUNCT cana-6326 248 16 resonance resonance NOUN cana-6326 248 17 of of ADP cana-6326 248 18 nanoscale nanoscale NOUN cana-6326 248 19 beam beam NOUN cana-6326 248 20 due due ADP cana-6326 248 21 to to ADP cana-6326 248 22 various various ADJ cana-6326 248 23 sources source NOUN cana-6326 248 24 in in ADP cana-6326 248 25 modified modified ADJ cana-6326 248 26 couple couple NOUN cana-6326 248 27 stress stress NOUN cana-6326 248 28 thermoelastic thermoelastic ADJ cana-6326 248 29 diffusion diffusion NOUN cana-6326 248 30 with with ADP cana-6326 248 31 phase phase NOUN cana-6326 248 32 lags lag NOUN cana-6326 248 33 , , PUNCT cana-6326 248 34 mechanics mechanic NOUN cana-6326 248 35 and and CCONJ cana-6326 248 36 mechanical mechanical ADJ cana-6326 248 37 engineering engineering NOUN cana-6326 248 38 . . PUNCT cana-6326 249 1 23(1 23(1 X cana-6326 249 2 ) ) PUNCT cana-6326 249 3 ( ( PUNCT cana-6326 249 4 2019 2019 NUM cana-6326 249 5 ) ) PUNCT cana-6326 249 6 ; ; PUNCT cana-6326 250 1 36 36 NUM cana-6326 250 2 - - SYM cana-6326 250 3 49 49 NUM cana-6326 250 4 . . PUNCT cana-6326 250 5 doi:10.2478 doi:10.2478 PROPN cana-6326 250 6 / / SYM cana-6326 250 7 mme-2019 mme-2019 NOUN cana-6326 250 8 - - PUNCT cana-6326 250 9 0006 0006 NUM cana-6326 250 10 [ [ X cana-6326 250 11 32 32 NUM cana-6326 250 12 ] ] SYM cana-6326 250 13 marin marin NOUN cana-6326 250 14 , , PUNCT cana-6326 250 15 m. m. NOUN cana-6326 250 16 , , PUNCT cana-6326 250 17 sharma sharma PROPN cana-6326 250 18 , , PUNCT cana-6326 250 19 s. s. PROPN cana-6326 250 20 , , PUNCT cana-6326 250 21 kumar kumar PROPN cana-6326 250 22 , , PUNCT cana-6326 250 23 r r NOUN cana-6326 250 24 and and CCONJ cana-6326 250 25 vlase vlase PROPN cana-6326 250 26 s. s. PROPN cana-6326 250 27 : : PUNCT cana-6326 250 28 fundamental fundamental ADJ cana-6326 250 29 solution solution NOUN cana-6326 250 30 and and CCONJ cana-6326 250 31 green green PROPN cana-6326 250 32 ’s ’s PART cana-6326 250 33 function function NOUN cana-6326 250 34 in in ADP cana-6326 250 35 orthotropic orthotropic ADJ cana-6326 250 36 photothermoelastic photothermoelastic ADJ cana-6326 250 37 media medium NOUN cana-6326 250 38 with with ADP cana-6326 250 39 temperature temperature NOUN cana-6326 250 40 - - PUNCT cana-6326 250 41 dependent dependent ADJ cana-6326 250 42 properties property NOUN cana-6326 250 43 under under ADP cana-6326 250 44 the the DET cana-6326 250 45 moore moore PROPN cana-6326 250 46 - - PUNCT cana-6326 250 47 gibson gibson PROPN cana-6326 250 48 - - PUNCT cana-6326 250 49 thompson thompson PROPN cana-6326 250 50 model model NOUN cana-6326 250 51 . . PUNCT cana-6326 251 1 zamm zamm PROPN cana-6326 251 2 - - PUNCT cana-6326 251 3 j. j. PROPN cana-6326 251 4 of of ADP cana-6326 251 5 appl appl PROPN cana-6326 251 6 . . PUNCT cana-6326 252 1 math math PROPN cana-6326 252 2 . . PUNCT cana-6326 253 1 mech.105(6 mech.105(6 NUM cana-6326 253 2 ) ) PUNCT cana-6326 254 1 ( ( PUNCT cana-6326 254 2 2025 2025 NUM cana-6326 254 3 ) ) PUNCT cana-6326 254 4 e70124 e70124 PROPN cana-6326 254 5 . . PUNCT cana-6326 254 6 https://doi.org/10.1002/zamm.70124 https://doi.org/10.1002/zamm.70124 X cana-6326 255 1 [ [ X cana-6326 255 2 33 33 NUM cana-6326 255 3 ] ] PUNCT cana-6326 255 4 sharma sharma PROPN cana-6326 255 5 , , PUNCT cana-6326 255 6 k. k. PROPN cana-6326 255 7 marin marin PROPN cana-6326 255 8 , , PUNCT cana-6326 255 9 m. m. NOUN cana-6326 255 10 and and CCONJ cana-6326 255 11 kumar kumar PROPN cana-6326 255 12 , , PUNCT cana-6326 255 13 r. r. PROPN cana-6326 255 14 : : PUNCT cana-6326 255 15 thermomechanical thermomechanical ADJ cana-6326 255 16 deformation deformation NOUN cana-6326 255 17 in in ADP cana-6326 255 18 a a DET cana-6326 255 19 micropolar micropolar ADJ cana-6326 255 20 thermoviscoelastic thermoviscoelastic ADJ cana-6326 255 21 solid solid ADJ cana-6326 255 22 under under ADP cana-6326 255 23 the the DET cana-6326 255 24 moore moore PROPN cana-6326 255 25 - - PUNCT cana-6326 255 26 gibson gibson PROPN cana-6326 255 27 - - PUNCT cana-6326 255 28 thompson thompson PROPN cana-6326 255 29 heat heat NOUN cana-6326 255 30 equation equation NOUN cana-6326 255 31 with with ADP cana-6326 255 32 non non ADJ cana-6326 255 33 - - ADJ cana-6326 255 34 local local ADJ cana-6326 255 35 https://oaji.net/articles/2017/1983-1522252589.pdf https://oaji.net/articles/2017/1983-1522252589.pdf PROPN cana-6326 255 36 http://dx.doi.org/10.2478/mme-2019-0006 http://dx.doi.org/10.2478/mme-2019-0006 NOUN cana-6326 255 37 https://doi.org/10.1002/zamm.70124 https://doi.org/10.1002/zamm.70124 NOUN cana-6326 255 38 communications communication NOUN cana-6326 255 39 on on ADP cana-6326 255 40 applied apply VERB cana-6326 255 41 nonlinear nonlinear ADJ cana-6326 255 42 analysis analysis NOUN cana-6326 255 43 issn issn NOUN cana-6326 255 44 : : PUNCT cana-6326 255 45 1074 1074 NUM cana-6326 255 46 - - PUNCT cana-6326 255 47 133x 133x NUM cana-6326 255 48 vol vol VERB cana-6326 255 49 32 32 NUM cana-6326 255 50 no no NOUN cana-6326 255 51 . . PUNCT cana-6326 256 1 10s 10 NOUN cana-6326 256 2 ( ( PUNCT cana-6326 256 3 2025 2025 NUM cana-6326 256 4 ) ) PUNCT cana-6326 256 5 3728 3728 NUM cana-6326 256 6 https://internationalpubls.com https://internationalpubls.com X cana-6326 256 7 and and CCONJ cana-6326 256 8 hyperbolic hyperbolic ADJ cana-6326 256 9 two two NUM cana-6326 256 10 - - PUNCT cana-6326 256 11 temperature temperature NOUN cana-6326 256 12 effects effect NOUN cana-6326 256 13 , , PUNCT cana-6326 256 14 journal journal NOUN cana-6326 256 15 of of ADP cana-6326 256 16 computational computational ADJ cana-6326 256 17 applied apply VERB cana-6326 256 18 mechanics mechanic NOUN cana-6326 256 19 , , PUNCT cana-6326 256 20 56(4 56(4 NOUN cana-6326 256 21 ) ) PUNCT cana-6326 256 22 ( ( PUNCT cana-6326 256 23 2025 2025 NUM cana-6326 256 24 ) ) PUNCT cana-6326 256 25 720 720 NUM cana-6326 256 26 - - NUM cana-6326 256 27 736 736 NUM cana-6326 256 28 . . PUNCT cana-6326 257 1 doi doi NOUN cana-6326 257 2 : : PUNCT cana-6326 257 3 10.22059 10.22059 NUM cana-6326 257 4 / / SYM cana-6326 257 5 jcamech jcamech NOUN cana-6326 257 6 ( ( PUNCT cana-6326 257 7 2025).397650.1525 2025).397650.1525 NUM cana-6326 257 8 [ [ X cana-6326 257 9 34 34 NUM cana-6326 257 10 ] ] X cana-6326 257 11 abouelregal abouelregal ADJ cana-6326 257 12 , , PUNCT cana-6326 257 13 a a DET cana-6326 257 14 e e NOUN cana-6326 257 15 , , PUNCT cana-6326 257 16 marin marin NOUN cana-6326 257 17 m m PROPN cana-6326 257 18 , , PUNCT cana-6326 257 19 alhassan alhassan ADJ cana-6326 257 20 , , PUNCT cana-6326 257 21 y y PROPN cana-6326 257 22 and and CCONJ cana-6326 257 23 atta atta PROPN cana-6326 257 24 , , PUNCT cana-6326 257 25 d. d. PROPN cana-6326 257 26 : : PUNCT cana-6326 257 27 a a DET cana-6326 257 28 novel novel ADJ cana-6326 257 29 space space NOUN cana-6326 257 30 - - PUNCT cana-6326 257 31 time time NOUN cana-6326 257 32 nonlocal nonlocal ADJ cana-6326 257 33 thermo thermo NOUN cana-6326 257 34 - - PUNCT cana-6326 257 35 viscoelastic viscoelastic ADJ cana-6326 257 36 model model NOUN cana-6326 257 37 with with ADP cana-6326 257 38 two two NUM cana-6326 257 39 - - PUNCT cana-6326 257 40 phase phase NOUN cana-6326 257 41 - - PUNCT cana-6326 257 42 lags lag NOUN cana-6326 257 43 for for ADP cana-6326 257 44 analysing analyse VERB cana-6326 257 45 heat heat NOUN cana-6326 257 46 diffusion diffusion NOUN cana-6326 257 47 in in ADP cana-6326 257 48 a a DET cana-6326 257 49 half half ADJ cana-6326 257 50 space space NOUN cana-6326 257 51 subjected subject VERB cana-6326 257 52 to to ADP cana-6326 257 53 a a DET cana-6326 257 54 heat heat NOUN cana-6326 257 55 source source NOUN cana-6326 257 56 , , PUNCT cana-6326 257 57 iranian iranian ADJ cana-6326 257 58 journal journal PROPN cana-6326 257 59 of of ADP cana-6326 257 60 science science NOUN cana-6326 257 61 and and CCONJ cana-6326 257 62 technology technology NOUN cana-6326 257 63 , , PUNCT cana-6326 257 64 transactions transaction NOUN cana-6326 257 65 of of ADP cana-6326 257 66 mechanical mechanical ADJ cana-6326 257 67 engineering engineering NOUN cana-6326 257 68 49(2025 49(2025 NUM cana-6326 257 69 ) ) PUNCT cana-6326 257 70 ; ; PUNCT cana-6326 257 71 1315 1315 NUM cana-6326 257 72 - - SYM cana-6326 257 73 1332 1332 NUM cana-6326 257 74 . . PUNCT cana-6326 258 1 https://doi.org/10.1007/s40997-02500835-9 https://doi.org/10.1007/s40997-02500835-9 NOUN