Issues

 / 

1997

 / 

October

  

Methodological notes


Local non-equilibrium transport models


Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, Russian Federation

Local non-equilibrium models of heat and mass transport processes are considered and shown to form a hierarchy of parabolic and hyperbolic equations whose order increases with deviation from local equilibrium. The basic features of these models, in particular their relationship to generalized irreversible thermodynamics, are discussed.

Fulltext pdf (235 KB)
Fulltext is also available at DOI: 10.1070/PU1997v040n10ABEH000292
PACS: 05.60.+w, 05.70.Ln
DOI: 10.1070/PU1997v040n10ABEH000292
URL: https://ufn.ru/en/articles/1997/10/e/
A1997YH86200006
Citation: Sobolev S L "Local non-equilibrium transport models" Phys. Usp. 40 1043–1053 (1997)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Îðèãèíàë: Ñîáîëåâ Ñ Ë «Ëîêàëüíî-íåðàâíîâåñíûå ìîäåëè ïðîöåññîâ ïåðåíîñà» ÓÔÍ 167 1095–1106 (1997); DOI: 10.3367/UFNr.0167.199710f.1095

References (50) Cited by (129) ↓ Similar articles (20)

  1. Abouelregal A E, Alsaeed S S et al International Communications In Heat And Mass Transfer 172 110329 (2026)
  2. Yang Ch Sci Rep 15 (1) (2025)
  3. Aristov V V, Zabelok S A, Frolova A A Uspekhi Fizicheskikh Nauk 195 (03) 276 (2025) [Aristov V V, Zabelok S A, Frolova A A Phys. Usp. 68 (03) 261 (2025)]
  4. Kryukov Yu A, Zaitsev S V et al Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 29 (4) 778 (2025)
  5. Vasiliev V V, Lurie S A, Salov V A J Appl Mech Tech Phy 66 (2) 382 (2025)
  6. Galovic S, Popovic M N, Chevizovich D Fractal Fract 9 (10) 653 (2025)
  7. Zhmakin A I Springer Series In Biophysics Vol. Heat Transfer in VivoRegional Models: Skin and Deep Tissues27 Chapter 5 (2025) p. 185
  8. Tóth B International Journal Of Heat And Mass Transfer 238 126456 (2025)
  9. Joseph A M J. Electron. Mater. 54 (12) 11461 (2025)
  10. Popovic M N, Galovic S P et al Fractal Fract 9 (7) 456 (2025)
  11. Galovic S, Čukić M, Chevizovich D Membranes 15 (1) 11 (2025)
  12. Pal S, Melnik R Physics Of Life Reviews 53 24 (2025)
  13. Sobolev S L Mechanics Research Communications 149 104512 (2025)
  14. Sobolev S, Kudinov I Waves In Random And Complex Media 1 (2025)
  15. Bogaºnko V O, Bulavats’kii V M Dopov. Nac. Akad. Nauk Ukr. (1) 21 (2024)
  16. Kartashov E M Rossijskij Tehnologičeskij žurnal 12 (6) 80 (2024)
  17. Kudinov I V, Trubitsyn K V et al Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 28 (4) 773 (2024)
  18. Sobolev S L Phys. Rev. E 109 (5) (2024)
  19. Kovács R Physics Reports 1048 1 (2024)
  20. Takhirov J O J Math Sci 284 (2) 266 (2024)
  21. Somer A, Galovic S et al International Journal Of Heat And Mass Transfer 223 125233 (2024)
  22. Zhukov V V, Kryukov Yu A et al Jour 31 (1) 88 (2024)
  23. Khankhasaev V N, Bairov S A Discrete And Continuous Models 32 (1) 112 (2024)
  24. Zhmakin A I Non-Fourier Heat Conduction Chapter 2 (2023) p. 39
  25. Tóth B International Journal Of Heat And Mass Transfer 217 124663 (2023)
  26. Kartashov E M Rossijskij Tehnologičeskij žurnal 11 (5) 106 (2023)
  27. Kartashov E M Rossijskij Tehnologičeskij žurnal 11 (3) 70 (2023)
  28. Kartashov E M Math Models Comput Simul 15 (S1) S86 (2023)
  29. Traytak S D The Journal of Chemical Physics 158 (4) (2023)
  30. Galovic S P, Djordjevic K L et al J. Appl. Phys. 133 (24) 245701 (2023)
  31. Kartashov E M High Temp 61 (5) 652 (2023)
  32. Zhmakin A I Non-Fourier Heat Conduction Chapter 1 (2023) p. 1
  33. Čukić M, Galovic S Chaos, Solitons & Fractals 172 113584 (2023)
  34. Zhmakin A I Non-Fourier Heat Conduction Chapter 7 (2023) p. 187
  35. Kovács R International Communications In Heat And Mass Transfer 148 107028 (2023)
  36. Kartashov E M, Kartashov E M Matematicheskoe Modelirovanie 35 (8) 14 (2023)
  37. Shomali Z, Kovács R et al Continuum Mech. Thermodyn. 34 (3) 637 (2022)
  38. Kovács R, Fehér A, Sobolev S International Journal Of Heat And Mass Transfer 194 123021 (2022)
  39. Ivanov M, Brylevskiy V et al Journal of Applied Physics 131 (1) (2022)
  40. Muthukunnil J A, Cao B Materials 15 (5) 1651 (2022)
  41. Kartashov E M, Polyakov S V KIAM Prepr. (100) 1 (2022)
  42. Wang F, Zhang K, Zheng B Acta Mech. Solida Sin. 35 (1) 174 (2022)
  43. Bora A, Dai W et al International Journal Of Heat And Mass Transfer 190 122791 (2022)
  44. Formalev V F, Garibyan B A, Kolesnik S A HoBMSTU.SNS (4 (103)) 80 (2022)
  45. Eremin A V, Kishov E A, Popov A I International Communications In Heat And Mass Transfer 138 106346 (2022)
  46. Fehér A, Kovács R IFAC-PapersOnLine 55 (18) 87 (2022)
  47. Sobolev S L, Kudinov I V International Journal Of Thermal Sciences 159 106632 (2021)
  48. Sobolev S L Nanoscale And Microscale Thermophysical Engineering 25 (3-4) 153 (2021)
  49. Mikheeva G V, Pashin A V J. Phys.: Conf. Ser. 2094 (2) 022023 (2021)
  50. Morozov A N HoBMSTU.SNS (5 (98)) 60 (2021)
  51. Tovbin Yu K Russ. J. Phys. Chem. 95 (4) 637 (2021)
  52. (CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2021 (CEST 2021)) Vol. CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2021 (CEST 2021)Mathematical modeling of local non-equilibrium hydrodynamics in moving liquidsIgor V.KudinovVasiliy K.TkachevAnton V.EreminKonstantin V.Trubitsyn2429 (2021) p. 020019
  53. Kostrobij P, Tokarchuk M et al Journal of Mathematical Physics 62 (10) (2021)
  54. Sobolev S L, Cao B-Ya, Kudinov I V Physica E: Low-dimensional Systems And Nanostructures 128 114610 (2021)
  55. Buchbinder G L EPL 133 (5) 58003 (2021)
  56. Fehér A, Kovács R International Journal Of Engineering Science 169 103577 (2021)
  57. Morozov A N HoBMSTU.SNS (1 (94)) 47 (2021)
  58. Zhmakin A I Tech. Phys. 66 (1) 1 (2021)
  59. Sobolev S L, Kudinov I V Journal of Non-Equilibrium Thermodynamics 45 (3) 209 (2020)
  60. Georgievskii D V Chebyshevskii Sbornik 20 (3) 134 (2020)
  61. Urinov A K, Okboev A B Lobachevskii J Math 41 (9) 1886 (2020)
  62. Gandolfi M, Giannetti C, Banfi F Phys. Rev. Lett. 125 (26) (2020)
  63. Pavlov S A, Antipov E M et al J Anal Chem 75 (8) 975 (2020)
  64. (CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2020 (CEST 2020)) Vol. CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2020 (CEST 2020)Study of the two-temperature heat transfer model in metal nanofilms exposed to ultrashort laser pulsesIgor V.KudinovSergey L.SobolevGalina V.Mikheeva2275 (2020) p. 020015
  65. Zimin B A, Sudenkov Yu V Dokl. Phys. 64 (4) 181 (2019)
  66. Popov V I Theor Found Chem Eng 53 (2) 235 (2019)
  67. Popov V I J Eng Phys Thermophy 92 (4) 929 (2019)
  68. Serdyukov S I, Sizova I A et al Pet. Chem. 59 (5) 518 (2019)
  69. Umirzakov I H J Therm Anal Calorim 137 (6) 1841 (2019)
  70. Li H-L, Hua Yu-Ch, Cao B-Ya International Journal Of Heat And Mass Transfer 127 1014 (2018)
  71. Kudinov V A, Eremin A V et al Combust Explos Shock Waves 54 (6) 649 (2018)
  72. Bulavatsky V M Cybern Syst Anal 54 (5) 727 (2018)
  73. Morozov A N Entropy 21 (1) 9 (2018)
  74. Kudinov V A, Eremin A V et al Russ. Aeronaut. 61 (2) 252 (2018)
  75. Sobolev S L Phys. Rev. E 97 (2) (2018)
  76. Vázquez F, López de Haro Mariano, Figueroa A Continuum Mech. Thermodyn. 30 (6) 1201 (2018)
  77. Morozov A N Jetp Lett. 107 (12) 798 (2018)
  78. Kudinov I V, Kudinov I V Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 22 (1) 116 (2018)
  79. Serdyukov S Entropy 20 (10) 802 (2018)
  80. Liu W, Saanouni Kh et al Journal of Non-Equilibrium Thermodynamics 42 (4) (2017)
  81. Sobolev S L Physics Letters A 381 (35) 2893 (2017)
  82. Sobolev S L J. Exp. Theor. Phys. 124 (3) 459 (2017)
  83. Kudinov V A, Eremin A V, Kudinov I V Thermophys. Aeromech. 24 (6) 901 (2017)
  84. Tovbin Yu K Russ. J. Phys. Chem. 91 (3) 403 (2017)
  85. Bulavatsky V M Cybern Syst Anal 53 (2) 204 (2017)
  86. Sobolev S L International Journal Of Heat And Mass Transfer 108 933 (2017)
  87. Vysotskii V I, Kornilova A A et al J. Surf. Investig. 11 (4) 749 (2017)
  88. Eremin A V, Kudinov V A, Kudinov I V Fluid Dyn 51 (1) 33 (2016)
  89. Sobolev S L Acta Materialia 116 212 (2016)
  90. Kharchenko D O, Kharchenko V O Radiation Effects And Defects In Solids 171 (11-12) 819 (2016)
  91. Sobolev S L International Journal Of Heat And Mass Transfer 94 138 (2016)
  92. Sobolev S L Materials Science And Technology 31 (13) 1607 (2015)
  93. Meilanov R P, Shabanova M R, Akhmedov E N Chaos, Solitons & Fractals 75 29 (2015)
  94. Gula I A, Samsonov A M Bioinformatics 31 (5) 714 (2015)
  95. Sobolev S L Acta Materialia 93 256 (2015)
  96. Kudinov I V, Kudinov V A J Eng Phys Thermophy 88 (2) 406 (2015)
  97. Popov V I J Eng Phys Thermophy 88 (1) 266 (2015)
  98. Meilanov R P, Magomedov R A J Eng Phys Thermophy 87 (6) 1521 (2014)
  99. Bulavatsky V M Cybern Syst Anal 50 (1) 81 (2014)
  100. Sobolev S L International Journal Of Heat And Mass Transfer 71 295 (2014)
  101. Serdyukov S I Theor Found Chem Eng 47 (2) 89 (2013)
  102. Uchaikin V V Fractional Derivatives for Physicists and Engineers Nonlinear Physical Science Chapter 1 (2013) p. 3
  103. Gula I A, Samsonov A M Proceedings of the International Conference Days on Diffraction 2013, (2013) p. 72
  104. Rukolaine S A, Samsonov A M Proceedings of the International Conference Days on Diffraction 2013, (2013) p. 125
  105. Rukolaine S A, Samsonov A M Phys. Rev. E 88 (6) (2013)
  106. Selivanova N Yu, Shamolin M V J Math Sci 189 (2) 274 (2013)
  107. Buchbinder G L, Volkov V A Physica A: Statistical Mechanics And Its Applications 391 (23) 5935 (2012)
  108. Yakunkin M M Inorg. Mater. Appl. Res. 3 (2) 69 (2012)
  109. Popov V I J Appl Mech Tech Phy 53 (6) 880 (2012)
  110. Bulavatsky V M Cybern Syst Anal 48 (6) 861 (2012)
  111. Meilanov R P, Shabanova M R Tech. Phys. 56 (7) 903 (2011)
  112. Malyshkina O V, Movchikova A A et al Ferroelectrics 400 (1) 63 (2010)
  113. Malyshkina O V Phys. Solid State 52 (4) 756 (2010)
  114. Indeitsev D A, Naumov V N et al Z Angew Math Mech 89 (4) 279 (2009)
  115. Sidorova E A, Vershinin G A et al J. Surf. Investig. 2 (2) 305 (2008)
  116. Stratilatova E N J Math Sci 145 (5) 5303 (2007)
  117. Indeitsev D A, Naumov V N, Semenov B N Mech. Solids 42 (5) 672 (2007)
  118. Mészáros C, Bálint Á et al Drying Technology 25 (7-8) 1297 (2007)
  119. Nakhusheva V A, Nakhusheva V A Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-matematicheskie Nauki 42 11 (2006)
  120. Buchbinder G L International Journal Of Heat And Mass Transfer 46 (9) 1665 (2003)
  121. Alekseev B V Uspekhi Fizicheskikh Nauk 173 (2) 145 (2003)
  122. Bondarenko I K, Markov V N, Solov’ev V G Instruments And Experimental Techniques 45 (3) 418 (2002)
  123. Uchaikin V V, Saenko V V Tech. Phys. 46 (2) 139 (2001)
  124. Gabaraev B A, Kovalev S A et al High Temperature 39 (2) 302 (2001)
  125. Noyola A P-G Journal of Non-Equilibrium Thermodynamics 24 (2) (1999)
  126. Zol’nikov K P, Kadyrov R I et al Tech. Phys. Lett. 25 (3) 230 (1999)
  127. Dinariyev O Yu Journal Of Applied Mathematics And Mechanics 63 (4) 569 (1999)
  128. Carballo S A F, González de la Cruz G et al Phys. Rev. B 59 (16) 10630 (1999)
  129. Jou D, Casas-Vázquez J, Lebon G Journal of Non-Equilibrium Thermodynamics 23 (3) (1998)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions