RSS feeds
ÐóññêèéEnglish
Issue 7, 2026
Volume year page
Issues Authors PACS Subscription For authors

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 (132) ↓ Similar articles (20)

  1. Abouelregal A E, Alsaeed S S et al International Communications In Heat And Mass Transfer 172 110329 (2026)
  2. Tóth B International Communications In Heat And Mass Transfer 179 112101 (2026)
  3. Munafó C F Journal of Non-Equilibrium Thermodynamics 51 (3) 437 (2026)
  4. Vasiliev V V, Lurie S A, Salov V A J Appl Mech Tech Phy 66 (2) 382 (2025)
  5. Galovic S, Čukić M, Chevizovich D Membranes 15 (1) 11 (2025)
  6. Joseph A M J. Electron. Mater. 54 (12) 11461 (2025)
  7. Galovic S, Popovic M N, Chevizovich D Fractal Fract 9 (10) 653 (2025)
  8. Kryukov Yu A, Zaitsev S V et al Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 29 (4) 778 (2025)
  9. Yang Ch Sci Rep 15 (1) (2025)
  10. 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)]
  11. Sobolev S, Kudinov I Waves In Random And Complex Media 1 (2025)
  12. Tóth B International Journal Of Heat And Mass Transfer 238 126456 (2025)
  13. Sobolev S L Mechanics Research Communications 149 104512 (2025)
  14. Popovic M N, Galovic S P et al Fractal Fract 9 (7) 456 (2025)
  15. Pal S, Melnik R Physics Of Life Reviews 53 24 (2025)
  16. Zhmakin A I Springer Series In Biophysics Vol. Heat Transfer in VivoRegional Models: Skin and Deep Tissues27 Chapter 5 (2025) p. 185
  17. Garibyan B A Her. Russ. Acad. Sci. 95 (5) 823 (2025)
  18. Kartashov E M Rossijskij Tehnologičeskij žurnal 12 (6) 80 (2024)
  19. Sobolev S L Phys. Rev. E 109 (5) (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. Bogaºnko V O, Bulavats’kii V M Dopov. Nac. Akad. Nauk Ukr. (1) 21 (2024)
  23. Kudinov I V, Trubitsyn K V et al Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 28 (4) 773 (2024)
  24. Khankhasaev V N, Bairov S A Discrete And Continuous Models 32 (1) 112 (2024)
  25. Kovács R Physics Reports 1048 1 (2024)
  26. Zhukov V V, Kryukov Yu A et al Jour 31 (1) 88 (2024)
  27. Kartashov E M High Temp 61 (5) 652 (2023)
  28. Kartashov E M Rossijskij Tehnologičeskij žurnal 11 (5) 106 (2023)
  29. Kartashov E M Math Models Comput Simul 15 (S1) S86 (2023)
  30. Zhmakin A I Non-Fourier Heat Conduction Chapter 7 (2023) p. 187
  31. Kovács R International Communications In Heat And Mass Transfer 148 107028 (2023)
  32. Zhmakin A I Non-Fourier Heat Conduction Chapter 2 (2023) p. 39
  33. Tóth B International Journal Of Heat And Mass Transfer 217 124663 (2023)
  34. Kartashov E M Rossijskij Tehnologičeskij žurnal 11 (3) 70 (2023)
  35. Zhmakin A I Non-Fourier Heat Conduction Chapter 1 (2023) p. 1
  36. Kartashov E M, Kartashov E M Matematicheskoe Modelirovanie 35 (8) 14 (2023)
  37. Galovic S P, Djordjevic K L et al J. Appl. Phys. 133 (24) 245701 (2023)
  38. Čukić M, Galovic S Chaos, Solitons & Fractals 172 113584 (2023)
  39. Traytak S D The Journal of Chemical Physics 158 (4) (2023)
  40. Bora A, Dai W et al International Journal Of Heat And Mass Transfer 190 122791 (2022)
  41. Muthukunnil J A, Cao B Materials 15 (5) 1651 (2022)
  42. Kovács R, Fehér A, Sobolev S International Journal Of Heat And Mass Transfer 194 123021 (2022)
  43. Kartashov E M, Polyakov S V KIAM Prepr. (100) 1 (2022)
  44. Ivanov M, Brylevskiy V et al Journal of Applied Physics 131 (1) (2022)
  45. Fehér A, Kovács R IFAC-PapersOnLine 55 (18) 87 (2022)
  46. Eremin A V, Kishov E A, Popov A I International Communications In Heat And Mass Transfer 138 106346 (2022)
  47. Shomali Z, Kovács R et al Continuum Mech. Thermodyn. 34 (3) 637 (2022)
  48. Wang F, Zhang K, Zheng B Acta Mech. Solida Sin. 35 (1) 174 (2022)
  49. Formalev V F, Garibyan B A, Kolesnik S A HoBMSTU.SNS (4 (103)) 80 (2022)
  50. Tovbin Yu K Russ. J. Phys. Chem. 95 (4) 637 (2021)
  51. Kostrobij P, Tokarchuk M et al Journal of Mathematical Physics 62 (10) (2021)
  52. Sobolev S L, Kudinov I V International Journal Of Thermal Sciences 159 106632 (2021)
  53. Morozov A N HoBMSTU.SNS (5 (98)) 60 (2021)
  54. Buchbinder G L EPL 133 (5) 58003 (2021)
  55. Sobolev S L Nanoscale And Microscale Thermophysical Engineering 25 (3-4) 153 (2021)
  56. (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
  57. Zhmakin A I Tech. Phys. 66 (1) 1 (2021)
  58. Mikheeva G V, Pashin A V J. Phys.: Conf. Ser. 2094 (2) 022023 (2021)
  59. Sobolev S L, Cao B-Ya, Kudinov I V Physica E: Low-dimensional Systems And Nanostructures 128 114610 (2021)
  60. Fehér A, Kovács R International Journal Of Engineering Science 169 103577 (2021)
  61. Morozov A N HoBMSTU.SNS (1 (94)) 47 (2021)
  62. Gandolfi M, Giannetti C, Banfi F Phys. Rev. Lett. 125 (26) (2020)
  63. Sobolev S L, Kudinov I V Journal of Non-Equilibrium Thermodynamics 45 (3) 209 (2020)
  64. Urinov A K, Okboev A B Lobachevskii J Math 41 (9) 1886 (2020)
  65. Georgievskii D V Chebyshevskii Sbornik 20 (3) 134 (2020)
  66. Pavlov S A, Antipov E M et al J Anal Chem 75 (8) 975 (2020)
  67. (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
  68. Popov V I J Eng Phys Thermophy 92 (4) 929 (2019)
  69. Serdyukov S I, Sizova I A et al Pet. Chem. 59 (5) 518 (2019)
  70. Popov V I Theor Found Chem Eng 53 (2) 235 (2019)
  71. Umirzakov I H J Therm Anal Calorim 137 (6) 1841 (2019)
  72. Zimin B A, Sudenkov Yu V Dokl. Phys. 64 (4) 181 (2019)
  73. Kudinov V A, Eremin A V et al Combust Explos Shock Waves 54 (6) 649 (2018)
  74. Bulavatsky V M Cybern Syst Anal 54 (5) 727 (2018)
  75. Kudinov V A, Eremin A V et al Russ. Aeronaut. 61 (2) 252 (2018)
  76. Sobolev S L Phys. Rev. E 97 (2) (2018)
  77. Vázquez F, López de Haro Mariano, Figueroa A Continuum Mech. Thermodyn. 30 (6) 1201 (2018)
  78. Morozov A N Entropy 21 (1) 9 (2018)
  79. Kudinov I V, Kudinov I V Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya «Fiziko-matematicheskie Nauki» 22 (1) 116 (2018)
  80. Li H-L, Hua Yu-Ch, Cao B-Ya International Journal Of Heat And Mass Transfer 127 1014 (2018)
  81. Morozov A N Jetp Lett. 107 (12) 798 (2018)
  82. Serdyukov S Entropy 20 (10) 802 (2018)
  83. Sobolev S L International Journal Of Heat And Mass Transfer 108 933 (2017)
  84. Liu W, Saanouni Kh et al Journal of Non-Equilibrium Thermodynamics 42 (4) (2017)
  85. Vysotskii V I, Kornilova A A et al J. Surf. Investig. 11 (4) 749 (2017)
  86. Tovbin Yu K Russ. J. Phys. Chem. 91 (3) 403 (2017)
  87. Sobolev S L J. Exp. Theor. Phys. 124 (3) 459 (2017)
  88. Bulavatsky V M Cybern Syst Anal 53 (2) 204 (2017)
  89. Sobolev S L Physics Letters A 381 (35) 2893 (2017)
  90. Kudinov V A, Eremin A V, Kudinov I V Thermophys. Aeromech. 24 (6) 901 (2017)
  91. Eremin A V, Kudinov V A, Kudinov I V Fluid Dyn 51 (1) 33 (2016)
  92. Sobolev S L International Journal Of Heat And Mass Transfer 94 138 (2016)
  93. Sobolev S L Acta Materialia 116 212 (2016)
  94. Kharchenko D O, Kharchenko V O Radiation Effects And Defects In Solids 171 (11-12) 819 (2016)
  95. Gula I A, Samsonov A M Bioinformatics 31 (5) 714 (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, Shabanova M R, Akhmedov E N Chaos, Solitons & Fractals 75 29 (2015)
  99. Sobolev S L Acta Materialia 93 256 (2015)
  100. Sobolev S L Materials Science And Technology 31 (13) 1607 (2015)
  101. Bulavatsky V M Cybern Syst Anal 50 (1) 81 (2014)
  102. Sobolev S L International Journal Of Heat And Mass Transfer 71 295 (2014)
  103. Meilanov R P, Magomedov R A J Eng Phys Thermophy 87 (6) 1521 (2014)
  104. Rukolaine S A, Samsonov A M Phys. Rev. E 88 (6) (2013)
  105. Rukolaine S A, Samsonov A M Proceedings of the International Conference Days on Diffraction 2013, (2013) p. 125
  106. Gula I A, Samsonov A M Proceedings of the International Conference Days on Diffraction 2013, (2013) p. 72
  107. Uchaikin V V Fractional Derivatives for Physicists and Engineers Nonlinear Physical Science Chapter 1 (2013) p. 3
  108. Selivanova N Yu, Shamolin M V J Math Sci 189 (2) 274 (2013)
  109. Serdyukov S I Theor Found Chem Eng 47 (2) 89 (2013)
  110. Buchbinder G L, Volkov V A Physica A: Statistical Mechanics And Its Applications 391 (23) 5935 (2012)
  111. Popov V I J Appl Mech Tech Phy 53 (6) 880 (2012)
  112. Yakunkin M M Inorg. Mater. Appl. Res. 3 (2) 69 (2012)
  113. Bulavatsky V M Cybern Syst Anal 48 (6) 861 (2012)
  114. Meilanov R P, Shabanova M R Tech. Phys. 56 (7) 903 (2011)
  115. Malyshkina O V Phys. Solid State 52 (4) 756 (2010)
  116. Malyshkina O V, Movchikova A A et al Ferroelectrics 400 (1) 63 (2010)
  117. Indeitsev D A, Naumov V N et al Z Angew Math Mech 89 (4) 279 (2009)
  118. Sidorova E A, Vershinin G A et al J. Surf. Investig. 2 (2) 305 (2008)
  119. Indeitsev D A, Naumov V N, Semenov B N Mech. Solids 42 (5) 672 (2007)
  120. Stratilatova E N J Math Sci 145 (5) 5303 (2007)
  121. Mészáros C, Bálint Á et al Drying Technology 25 (7-8) 1297 (2007)
  122. Nakhusheva V A, Nakhusheva V A Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-matematicheskie Nauki 42 11 (2006)
  123. Buchbinder G L International Journal Of Heat And Mass Transfer 46 (9) 1665 (2003)
  124. Alekseev B V Uspekhi Fizicheskikh Nauk 173 (2) 145 (2003)
  125. Bondarenko I K, Markov V N, Solov’ev V G Instruments And Experimental Techniques 45 (3) 418 (2002)
  126. Uchaikin V V, Saenko V V Tech. Phys. 46 (2) 139 (2001)
  127. Gabaraev B A, Kovalev S A et al High Temperature 39 (2) 302 (2001)
  128. Noyola A P-G Journal of Non-Equilibrium Thermodynamics 24 (2) (1999)
  129. Dinariyev O Yu Journal Of Applied Mathematics And Mechanics 63 (4) 569 (1999)
  130. Zol’nikov K P, Kadyrov R I et al Tech. Phys. Lett. 25 (3) 230 (1999)
  131. Carballo S A F, González de la Cruz G et al Phys. Rev. B 59 (16) 10630 (1999)
  132. 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