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Nonequilibrium thermodynamics of autowave processes in a catalyst bed


G.K. Boreskov Institute of Catalysis, Siberian Branch of the Russian Academy of Sciences, prosp. akad. Lavrenteva 5, Novosibirsk, 630090, Russian Federation

A new description of the nature of autowave processes in a static catalyst bed is reviewed by analyzing two kinds of autowaves, fast and slow heat waves. The thermodynamic description of physico-chemical processes is considered and the entropy balance equation is constructed and analyzed taking the quasi-homogeneous (basic) model of an immobile catalyst bed as an approximation. For slow heat waves, the extremal autowave solution functional (total entropy production in the system) is found and a variational formulation of the problem is given. A space-time dissipative structure (a fast heat wave) is shown to exist near the system’s thermodynamic equilibrium.

Fulltext pdf (417 KB)
Fulltext is also available at DOI: 10.1070/PU2004v047n10ABEH001770
PACS: 05.45.−a, 05.70.Ln, 82.40.−g (all)
DOI: 10.1070/PU2004v047n10ABEH001770
URL: https://ufn.ru/en/articles/2004/10/b/
000226730200002
2004PhyU...47..991G
Citation: Gerasev A P "Nonequilibrium thermodynamics of autowave processes in a catalyst bed" Phys. Usp. 47 991–1016 (2004)
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Оригинал: Герасев А П «Неравновесная термодинамика автоволновых процессов в слое катализатора» УФН 174 1061–1087 (2004); DOI: 10.3367/UFNr.0174.200410b.1061

References (194) ↓ Cited by (12) Similar articles (20)

  1. Vasil’ev V A, Romanovskii Yu M, Yakhno V G Usp. Fiz. Nauk 128 625 (1979) [Sov. Phys. Usp. 22 615 (1979)]
  2. Vasil’ev V A, Romanovskii Yu M, Yakhno V G Avtovolnovye Protsessy (Autowave Processes, Ed. D S Chernavskii, Moscow: Nauka, 1987)
  3. Grekhova M T et al. (Eds) Avtovolnovye Protsessy (Autowave Processes, Gor’kii: Izd. IPF AN SSSR, 1981)
  4. Ivanitskii G R, Krinskii V I, Sel’kov E E Matematicheskaya Biofizika Kletki (Mathematical Biophysics of the Cell, Moscow: Nauka, 1978)
  5. Romanovskii Yu M, Stepanova N V, Chernavskii D S Matematicheskaya Biofizika (Mathematical Biophysics, Moscow: Nauka, 1984)
  6. Krinskii V I, Mikhailov A S Avtovolny (Autowaves, Moscow: Znanie, 1984)
  7. Bykov V I (Ed.) Dinamika Khimicheskikh i Biologicheskikh Sistem (Dynamics of Chemical and Biological Systems, Novosibirsk: Nauka, 1989)
  8. Kerner B S, Osipov V V Avtosolitony: Lokalizovannye Sil’no-neravnovesnye Oblasti v Odnorodnykh Dissipativnykh Sistemakh (Autosolitons: Localized Strongly Non-Equilibrium Regions in Homogeneous Dissipative Systems, Moscow: Nauka, 1991) [Translated into English: Autosolitons: A New Approach to Problems of Self-Organization and Turbulence (Dordrecht: Kluwer Acad., 1994)]; Dokl. Akad. Nauk SSSR 264 1366 (1982) [Sov. Phys. Dokl. 27 484 (1982)]
  9. Loskutov A Yu, Mikhailov A S Vvedenie v Sinergetiku (Introduction to Synergetics, Moscow: Nauka, 1990); see also Mikhailov A S, Loskutov A Yu Foundations of Synergetics (Berlin: Springer-Verlag, 1990)
  10. Zykov V S Modelirovanie Volnovykh Protsessov v Vozbudimykh Sredakh (Simulation of Wave Processes in Excitable Media, Moscow: Nauka, 1984) [Translated into English (Manchester: Manchester Univ. Press, 1987)]
  11. Gurevich A Vl, Mints R G Usp. Fiz. Nauk 142 61 (1984) [Sov. Phys. Usp. 27 19 (1984)]
  12. Merzhanov A G, Rumanov E N Usp. Fiz. Nauk 151 553 (1987) [Sov. Phys. Usp. 30 293 (1987)]
  13. Ivanitskii G R, Medvinskii A B, Tsyganov M A Usp. Fiz. Nauk 161 (4) 13 (1991); 164 1041 (1994) [Sov. Phys. Usp. 34 289 (1991); Phys. Usp. 37 961 (1994)]
  14. Davydov V A, Zykov V S, Mikhailov A S Usp. Fiz. Nauk 161 (8) 45 (1991) [Sov. Phys. Usp. 34 665 (1991)]
  15. Davydov V A, Morozov V G Usp. Fiz. Nauk 166 327 (1996) [Phys. Usp. 39 305 (1996)]
  16. Malygin G A Usp. Fiz. Nauk 169 979 (1999) [Phys. Usp. 42 887 (1999)]
  17. Antonyuk B P, Antonyuk V B Usp. Fiz. Nauk 171 61 (2001) [Phys. Usp. 44 53 (2001)]
  18. Berezovskaya F S, Karev G P Usp. Fiz. Nauk 169 1011 (1999) [Phys. Usp. 42 917 (1999)]; Dokl. Ross. Akad. Nauk 368 318 (1999) [Dokl. Math. 60 295 (1999)]
  19. Ataullakhanov F I et al. Usp. Fiz. Nauk 172 671 (2002) [Phys. Usp. 45 619 (2002)]
  20. Slin’ko M M, Jaeger N I Oscillating Heterogeneous Catalytic Systems (Amsterdam: Elsevier, 1994)
  21. Merzhanov A G, Rumanov E N Rev. Mod. Phys. 71 1173 (1999)
  22. Zhdanov V P Surf. Sci. Rep. 45 231 (2002)
  23. Zhdanov V P Surf. Sci. 500 966 (2002)
  24. Elokhin V I et al. Kinet. Katal. 44 755 (2003) [Kinet. Catal. 44 692 (2003)]
  25. Rabinovich M I, Trubetskov D I Vvedenie v Teoriyu Kolebanii i Voln (Introduction to the Theory of Oscillations and Waves, Moscow: Nauka, 1984) [Translated into English: Oscillations and Waves in Linear and Nonlinear Systems (Dordrecht: Kluwer Acad. Publ., 1989)]
  26. Kadomtsev B B Kollektivnye Yavleniya v Plazme (Collective Phenomena in Plasma, Moscow: Nauka, 1988) [Translated into English: "Cooperative effects in plasmas", in Reviews of Plasma Physics Vol. 22 (Ed. V D Shafranov, New York: Kluwer Acad./Consultants Bureau, 2001) p. 1]
  27. Zhabotinsky A M, Zaikin A N J. Theor. Biol. 40 45 (1973)
  28. Zhabotinskii A M Kontsentratsionnye Avtokolebaniya (Concentration Autooscillations, Moscow: Nauka, 1974)
  29. Field R J, Burger M (Eds) Oscillations and Traveling Waves in Chemical Systems (New York: Wiley, 1985)
  30. de Wit A Adv. Chem. Phys. 109 435 (1999)
  31. Nicolis G, Prigogine I Self-Organization in Nonequilibrium Systems (New York: Wiley, 1977) [Translated into Russian (Moscow: Mir, 1979)]
  32. Kolmogorov A N, Petrovskii I G, Piskunov N S Byull. Mosk. Gos. Univ. Matem. Mekh. 1 (6) 1 (1937)
  33. Fisher R A Ann. Eugenics 7 335 (1937)
  34. Turing A M Philos. Trans. R. Soc. London Ser. B 237 37 (1952)
  35. Hodgkin A L, Huxley A F J. Physiol. (London) 116 449 (1952)
  36. FitzHugh R A Biophys. J. 1 445 (1961)
  37. Nagumo J, Arimoto S, Yoshizawa S Proc. IRE 50 2061 (1962)
  38. Zotin A I (Ed.) Termodinamika i Kinetika Biologicheskikh Protsessov (Thermodynamics and Kinetics of Biological Processes, Moscow: Nauka, 1980)
  39. Svirezhev Yu M Nelineinye Volny, Dissipativnye Struktury i Katastrofy v Ekologii (Non-Linear Waves, Dissipative Structures and Catastrophes in Ecology, Moscow: Nauka, 1987)
  40. Zel’dovich Ya B, Frank-Kamenetskii D A Dokl. Akad. Nauk SSSR 19 963 (1938)
  41. Zel’dovich Ya B, Frank-Kamenetskii D A Zh. Fiz. Khim. 12 100 (1938)
  42. Zel’dovich Ya B Zh. Fiz. Khim. 22 27 (1948)
  43. Zel’dovich Ya B et al. Matematicheskaya Teoriya Goreniya i Vzryva (The Mathematical Theory of Combustion and Explosions, Moscow: Nauka, 1980) [Translated into English (New York: Consultants Bureau, 1985)]
  44. Aldushin A P et al. Dokl. Akad. Nauk SSSR 243 1434 (1978)
  45. Merzhanov A G, Khaikin B I Teoriya Voln Goreniya v Gomogennykh Sredakh (The Theory of Combustion Waves in Homogeneous Media, Chernogolovka: Inst. Strukturnoi Makrokinetiki, 1992)
  46. Dovzhenko A Yu, Maklakov S V, Rumanov E N Dokl. Ross. Akad. Nauk 374 321 (2000) [Dokl. Phys. 45 446 (2000)]
  47. Dovzhenko A Yu et al. Dokl. Ross. Akad. Nauk 378 466 (2001) [Dokl. Phys. 46 380 (2001)]
  48. Merzhanov A G Usp. Khim. 72 323 (2003) [Russ. Chem. Rev. 72 289 (2003)]
  49. Rumanov E N Dokl. Ross. Akad. Nauk 393 188 (2003) [Dokl. Phys. 48 619 (2003)]
  50. Wicke E, Vortmeyer D Z. Elektrochem. Ber. Bunsenges. Phys. Chem. 63 145 (1959)
  51. Vortmeyer D Z. Elektrochem. Ber. Bunsenges. Phys. Chem. 65 282 (1961)
  52. Padberg G, Wicke E Chem. Eng. Sci. 22 1035 (1967)
  53. Wicke E, Padberg G Chem. Ing. Tech. 40 1033 (1968)
  54. Fieguth P, Wicke E Chem. Ing. Tech. 43 604 (1971)
  55. Vortmeyer D, Jahnel W Chem. Ing. Tech. 43 461 (1971)
  56. Vortmeyer D, Jahnel W Chem. Eng. Sci. 27 1485 (1972)
  57. Eigeberger G Chem. Eng. Sci. 27 1909 (1972)
  58. Rhee H-K, Lewis R P, Amundson N R Ind. Eng. Chem. Fundam. 13 317 (1974)
  59. Rhee H-K, Foley D, Amundson N R Chem. Eng. Sci. 28 607 (1973)
  60. Simon B, Vortmeyer D Chem. Eng. Sci. 33 109 (1978)
  61. Boreskov G K, Kiselev O V, Matros Yu Sh Dokl. Akad. Nauk SSSR 248 406 (1979)
  62. Kiselev O V, Matros Yu Sh Fiz. Goreniya Vzryva 16 (2) 25 (1980)
  63. Puszyński J, Hlavacek V Chem. Eng. Sci. 39 681 (1984)
  64. Kiselev O V, Matros Yu Sh Fiz. Goreniya Vzryva 23 (5) 167 (1987)
  65. Kiselev O V, Matros Yu Sh, Chumakova N A, in Rasprostranenie Teplovykh Voln v Geterogennykh Sredakh (Heat Wave Propagation in Heterogeneous Media, Ed. Yu Sh Matros, Novosibirsk: Nauka, 1988) p. 145
  66. Kiselev O V et al., in Rasprostranenie Teplovykh Voln v Geterogennykh Sredakh (Heat Wave Propagation in Heterogeneous Media, Ed. Yu Sh Matros, Novosibirsk: Nauka, 1988) p. 203
  67. Kiselev O V, Matros Yu Sh Dokl. Akad. Nauk SSSR 308 667 (1989) [Dokl. Chem. Technol. 307/309 114 (1989)]
  68. Kiselev O V Teoreticheskoe Issledovanie Rasprostraneniya Teplovykh Voln v Sloe Katalizatora (Theoretical Study of Heat Wave Propagation in a Catalyst Bed, Novosibirsk: TOO ’Parallel’, 1993)
  69. Gerasev A P et al. Teor. Osnovy Khim. Tekhnol. 27 165 (1993) [Theor. Found. Chem. Eng. 27 149 (1993)]
  70. Gerasev A P, Chumakova N A, Matros Yu Sh Chem. Eng. Sci. 52 693 (1997)
  71. Gerasev A P, Chumakova N A Fiz. Goreniya Vzryva 33 (5) 52 (1997) [Combust. Explosion Shock Waves 33 556 (1997)]
  72. Frank-Kamenetskii D A Diffuziya i Teploperedacha v Khimicheskoi Kinetike (Diffusion and Heat Transfer in Chemical Kinetics) 3rd ed. (Moscow: Nauka, 1987) [Translated into English of the 2nd Russian ed. (New York: Plenum Press, 1969)]
  73. Aldushin A P et al. Protsessy Goreniya v Khimicheskoi Tekhnologii i Metallurgii (Combustion Processes in Chemical Technology and Metallurgy, Ed. A G Merzhanov, Chernogolovka: Izd. IKhF AN SSSR, 1976)
  74. Takeno T, Sato K, in Combustion in Reactive Systems (Prog. in Astronautics and Aeronautics, Vol. 76, Eds J R Bowen et al., New York: American Institute of Aeronautics and Astronautics, 1981) p. 596
  75. Babkin V S et al. Dokl. Akad. Nauk SSSR 265 1157 (1982)
  76. Babkin V S et al. Fiz. Goreniya Vzryva 19 (2) 17 (1983)
  77. Laevskii Yu M et al. Fiz. Goreniya Vzryva 20 (6) 3 (1984)
  78. Babkin V S, Laevskii Yu M Fiz. Goreniya Vzryva 23 (5) 49 (1987)
  79. Aldushin A P, Merzhanov A G, in Rasprostranenie Teplovykh Voln v Geterogennykh Sredakh (Heat Wave Propagation in Heterogeneous Media, Ed. Yu Sh Matros, Novosibirsk: Nauka, 1988) p. 9
  80. Laevskii Yu M, Babkin V S, in Rasprostranenie Teplovykh Voln v Geterogennykh Sredakh (Heat Wave Propagation in Heterogeneous Media, Ed. Yu Sh Matros, Novosibirsk: Nauka, 1988) p. 108
  81. Yoshizawa Y, Sasaki K, Echigo R Int. J. Heat Mass Transfer 31 311 (1988)
  82. Babkin V S Pure Appl. Chem. 65 (2) 335 (1993)
  83. Aldushin A P, Rumanov I E Dokl. Ross. Akad. Nauk 361 775 (1998) [Dokl. Phys. Chem. 361 264 (1998)]
  84. Burkina R S Fiz. Goreniya Vzryva 36 (4) 3 (2000) [Combust. Explosion Shock Waves 36 417 (2000)]
  85. Laevsky Yu M, Babkin V S Combust. Sci. Technol. 164 129 (2001)
  86. Babkin V S, Vierzba I, Karim G A Fiz. Goreniya Vzryva 38 (1) 3 (2002) [Combust. Explosion Shock Waves 38 1 (2002)]
  87. Futko S I Fiz. Goreniya Vzryva 39 (2) 15 (2003) [Combust. Explosion Shock Waves 39 130 (2003)]
  88. Babkin V S, Barannik G B, Ismagilov Z R Dokl. Akad. Nauk SSSR 304 630 (1989)
  89. Belyaev A F Zh. Fiz. Khim. 12 93 (1938)
  90. Novozhilov B V Dokl. Akad. Nauk SSSR 141 151 (1961)
  91. Novozhilov B V Dokl. Ross. Akad. Nauk 378 359 (2001) [Dokl. Phys. Chem. 378 141 (2001)]
  92. Aldushin A P, Merzhanov A G, Khaikin B I Dokl. Akad. Nauk SSSR 204 1139 (1972)
  93. Aldushin A P et al. Fiz. Goreniya Vzryva 8 (2) 202 (1972)
  94. Merzhanov A G Tverdoplamennoe Gorenie (Solid-Flame Combustion, Chernogolovka: Izd. ISMAN, 2000)
  95. Berman V S, Ryazantsev Yu S Fiz. Goreniya Vzryva 11 (2) 179 (1975)
  96. Galkina V I, Lyubchenko V I, Marchenko G N Dokl. Akad. Nauk SSSR 286 373 (1986)
  97. Merzhanov A G, Borovinskaya I P Dokl. Akad. Nauk SSSR 204 366 (1972)
  98. Merzhanov A G Dokl. Ross. Akad. Nauk 353 504 (1997) [Dokl. Phys. Chem. 353 135 (1997)]
  99. Merzhanov A G, Peregudov A N, Gontkovskaya V T Dokl. Ross. Akad. Nauk SSSR 360 217 (1998) [Dokl. Phys. Chem. 360 158 (1998)]
  100. Rogachev A S, Merzhanov A G Dokl. Ross. Akad. Nauk 365 788 (1999) [Dokl. Phys. Chem. 365 127 (1999)]
  101. Rogachev A S Fiz. Goreniya Vzryva 39 (2) 38 (2003) [Combust. Explosion Shock Waves 39 150 (2003)]
  102. Merzhnov A G et al. Dokl. Akad. Nauk SSSR 221 1114 (1975)
  103. Barelko V V, Volodin Yu E Dokl. Akad. Nauk SSSR 223 112 (1975)
  104. Barelko V V, Kurochka I I, Merzhnov A G Dokl. Akad. Nauk SSSR 229 898 (1976)
  105. Volodin Yu E, Barelko V V, Merzhnov A G Khim. Fiz. 1 670 (1982)
  106. Barelko V V et al. Chem. Eng. Sci. 38 1775 (1983)
  107. Ivanova A N, Andrianova Z S, Barelko V V Dokl. Ross. Akad. Nauk 386 789 (2002) [Dokl. Phys. Chem. 386 257 (2002)]
  108. Zel’dovich Ya B, Rachinskii V V Vvedenie v Obshchuyu Teoriyu Dinamiki Sorbtsii i Khromatografii (Introduction to the General Theory of Sorption Dynamics and Chromatography, Moscow: Nauka, 1964)
  109. Kel’tsev N V Osnovy Adsorbtsionnoi Tekhniki (Fundamentals of Adsorption Technique) 2nd ed. (Moscow: Khimiya, 1984)
  110. Babenko Yu I, Moshinskii A I Fiz. Goreniya Vzryva 33 (5) 62 (1997) [Combust. Explosion Shock Waves 33 565 (1997)]
  111. Zhukov S A, Barelko V V, Merzhanov A G Int. J. Heat Mass Transfer 24 47 (1981)
  112. Barelko V V et al. Dokl. Akad. Nauk SSSR 257 339 (1981)
  113. Glansdorff P, Prigogine I Thermodynamic Theory of Structure, Stability and Fluctuations (London: Wiley-Intersci., 1971) [Translated into Russian (Moscow: Mir, 1973)]
  114. Prigogine I Science 201 777 (1978); Usp. Fiz. Nauk 131 185 (1980)
  115. Gaponov-Grekhov A V, Rabinovich M I Usp. Fiz. Nauk 128 579 (1979) [Sov. Phys. Usp. 22 590 (1979)]
  116. Andronov A A et al. Kachestvennaya Teoriya Dinamicheskikh Sistem Vtorogo Poryadka (Qualitative Theory of Second-Order Dynamic Systems, Moscow: Nauka, 1966) [Translated into English (New York: J. Wiley, 1973)]
  117. Bautin N N, Leontovich E A Metody i Priemy Kachestvennogo Issledovaniya Dinamicheskikh Sistem na Ploskosti (Methods and Approaches for Qualitative Studies of Dynamic Systems on a Plane, Moscow: Nauka, 1976)
  118. Bykov V I, Shmidt A V Dokl. Ross. Akad. Nauk 375 188 (2000) [Phys. Dokl. 45 610 (2000)]
  119. Prigogine I, Nicolis G Usp. Fiz. Nauk 109 517 (1973)
  120. Nicolis G, Prigogine I Exploring Complexity: An Introduction (New York: W.H. Freeman, 1989) [Translated into Russian (Moscow: Mir, 1990)]
  121. Prigogine I From Being to Becoming: Time and Complexity in the Physical Sciences (San Francisco: W.H. Freeman, 1980) [Translated into Russian (Moscow: Editorial URSS, 2002)]
  122. Ebeling W Strukturbildung bei irreversiblen Prozessen: eine Einführung in der Theorie dissipativer Strukturen (Leipzig: BSB Teubner, 1976) [Translated into Russian (Moscow: Mir, 1979)]
  123. Eigen M Self-Organization Matter and the Evolution of Biological Macromolecules (Heidelberg: Springer-Verlag, 1971) [Translated into Russian (Moscow: Mir, 1973)]; Usp. Fiz. Nauk 109 545 (1973)
  124. Gaponov-Grekhov A V, Rabinovich M I (Eds) Nelineinye Volny: Samoorganizatsiya (NonLinear Waves: Self-Organization, Moscow: Nauka, 1983)
  125. Polak L S, Mikhailov A S Samoorganizatsiya v Neravnovesnykh Fiziko-Khimicheskikh Sistemakh (Self-Organization in Physico-Chemical Systems, Moscow: Nauka, 1983)
  126. Haken H Synergetics: An Introduction 2nd ed. (Berlin: Springer-Verlag, 1978) [Translated into Russian (Moscow: Mir, 1980)]
  127. Haken H Advanced Synergetics: Instability Hierarchies of Self-Organizing Systems and Devices (Berlin: Springer-Verlag, 1983) [Translated into Russian (Moscow: Mir, 1985)]
  128. Maslov V P, Danilov V G, Volosov K A Matematicheskoe Modelirovanie Protsessov Teplomassoperenosa (Mathematical Modelling of Heat and Mass Transfer Processes, Moscow: Nauka, 1987) [Translated into English (Dordrecht: Kluwer Acad. Publ., 1995)]
  129. Basin M A (Ed.) Sinergetika i Metody Nauki (Synergetics and Methods of Science, St. Petersburg: Nauka, 1998)
  130. Kondepudi D, Prigogine I Modern Thermodynamics. From Heat Engines to Dissipative Structures (Chichester: John Wiley & Sons, 1998) [Translated into Russian (Moscow: Mir, 2002)]
  131. Benard H Rev. Gen. Sci. Pures Appl. 12 1261 (1900)
  132. Klimontovich Yu L Usp. Fiz. Nauk 158 59 (1989) [Sov. Phys. Usp. 32 416 (1989)]
  133. Onsager L Phys. Rev. 37 405; 38 2265 (1931)
  134. Prigogine I Introduction to Thermodynamics of Irreversible Processes (Springfield, Ill.: Thomas, 1955) [Translated into Russian (Moscow: IL, 1960)]
  135. Stratonovich R L Nelineinaya Neravnovesnaya Termodinamika (Non-Linear Non-Equilibrium Thermodynamics, Moscow: Nauka, 1985)
  136. Machlup S, Onsager L Phys. Rev. 91 1512 (1953)
  137. Ziegler H Extremum Principles in Irreversible Thermodynamics, with Application to Continuum Mechanics (Amsterdam: North-Holland, 1963) [Translated into Russian (Moscow: Mir, 1966)]
  138. Münster A Chemishe Thermodynamik (Weinheim: Verlag Chemie, 1969) [Translated into Russian (Moscow: Mir, 1971)]
  139. Biot M A Phys. Rev. 97 1463 (1955)
  140. Gyarmati I Non-Equilibrium Thermodynamics (Berlin: Springer, 1970) [Translated into Russian (Moscow: Mir, 1974)]
  141. Gyarmati I J. Non-Equilib. Thermodyn. 2 233 (1977)
  142. Bakhareva I F Zh. Fiz. Khim. 41 1717 (1967)
  143. Bakhareva I F Inzh.-Fiz. Zh. 20 1105 (1971) [J. Eng. Phys. 20 1105 (1971)]
  144. Bakhareva I F Zh. Fiz. Khim. 42 2394 (1968)
  145. Bakhareva I F Nelineinaya Neravnovesnaya Termodinamika (Non-Linear Non-Equilibrium Thermodynamics, Saratov: Izd. SGU, 1976)
  146. Gurov K P Fenomenologicheskaya Termodinamika Neobratimykh Protsessov: Fizicheskie Osnovy (Phenomenological Thermodynamics of Irreversible Processes. Physical Principles, Moscow: Nauka, 1978)
  147. Shakhparonov M I Zh. Fiz. Khim. 53 3043 (1979)
  148. Vyrodov I P Zh. Fiz. Khim. 54 1601 (1980)
  149. Haase R Thermodynamik der irreversiblen Prozesse (Darmstadt: D. Steinkopff, 1963) [Translated into English: Thermodynamics of Irreversible Processes (Reading, Mass.: Addison-Wesley, 1969); translated into Russian (Moscow: Mir, 1967)]
  150. Bulatov N K, Lundin A B Termodinamika Neobratimykh Fiziko-Khimicheskikh Protsessov (Thermodynamics of Irreversible Physico-Chemical Processes, Moscow: Khimiya, 1984)
  151. Klimontovich Yu L Statisticheskaya Teoriya Otkrytykh Sistem (Statistical Theory of Open Systems) Vol. 1 (Moscow: Yanus, 1995) [Translated into English (Dordrecht: Kluwer Acad. Publ., 1995)]
  152. Gorban’ A N, Kaganovich B M, Filippov S P Termodinamicheskie Ravnovesiya i Ekstremumy: Analiz Oblastei Dostizhimosti i Chastichnykh Ravnovesii v Fiziko-Khimicheskikh i Tekhnicheskikh Sistemakh (Thermodynamic Equilibria and Extrema: Analysis of Attainability and Partial Equilibria Regions in Physico-Chemical and Technical Systems, Novosibirsk: Nauka, 2001)
  153. Lopushanskaya A I (Ed.) Termodinamika Neobratimykh Protsessov (Thermodynamics of Irreversible Processes, Moscow: Nauka, 1987)
  154. Gladyshev G P Termodinamika i Makrokinetika Prirodnykh Ierarkhicheskikh Protsessov (Thermodynamics and Macrokinetics of Natural Hierarchical Processes, Moscow: Nauka, 1988)
  155. Fekete D Zh. Fiz. Khim. 57 2700 (1983)
  156. Magomedov K M Dokl. Ross. Akad. Nauk 361 768 (1998) [Phys. Dokl. 43 512 (1998)]
  157. Martiouchev L M, Seleznev V D Dokl. Ross. Akad. Nauk 371 466 (2000) [Phys. Dokl. 45 129 (2000)]
  158. Pleshanov A S Dokl. Ross. Akad. Nauk 378 38 (2001) [Phys. Dokl. 46 304 (2001)]
  159. Vyrodov I P Zh. Fiz. Khim. 56 1329 (1982)
  160. Vyrodov I P Zh. Fiz. Khim. 62 865 (1988)
  161. Vyrodov I P Zh. Fiz. Khim. 72 225 (1998) [Russ. J. Phys. Chem. 72 164 (1998)]
  162. Parmon V N Russ. J. Phys. Chem. 77 (Suppl. 1) S128 (2003)
  163. Pleshanov A S Dokl. Ross. Akad. Nauk 371 175 (2000) [Dokl. Math. 61 289 (2000)]
  164. Barashev P P Khim. Fiz. 21 (4) 110 (2002)
  165. Zhdanov V M, Roldugin V I Usp. Fiz. Nauk 168 407 (1998) [Phys. Usp. 41 349 (1998)]
  166. Kafarov V V, Dorokhov I N, Kol’tsova E M Sistemnyi Analiz Khimicheskoi Tekhnologii. Entropiinyi i Variatsionnyi Metody Neravnovesnoi Termodinamiki v Zadachakh Khimicheskoi Tekhnologii (Systemic Analysis of Chemical Technology. Entropy and Variational Methods of Non-Equilibrium Thermodynamics in Chemical Technological Problems, Moscow: Nauka, 1988)
  167. Kol’tsova E M, Gordeev L S Metody Sinergetiki v Khimii i Khimicheskoi Tekhnologii (Methods of Synergetics in Chemistry and Chemical Technology, Moscow: Khimiya, 1999)
  168. Mironova V A, Amel’kin S A, Tsirlin A M Matematicheskie Metody Termodinamiki pri Konechnom Vremeni (Mathematical Methods of Themodynamics at Finite Time, Moscow: Khimiya, 2000)
  169. Karpov A I J. Non-Equilib. Thermodyn. 17 (1) 1 (1992)
  170. Gerasev A P Fiz. Goreniya Vzryva 37 (6) 13 (2001) [Combust. Explosion Shock Waves 37 626 (2001)]
  171. Gerasev A P Fiz. Goreniya Vzryva 39 (4) 67 (2003) [Combust. Explosion Shock Waves 39 423 (2003)]
  172. Gerasev A P Fiz. Goreniya Vzryva 40 (1) 64 (2004) [Combust. Explosion Shock Waves 40 57 (2004)]
  173. Gerasev A P Dokl. Ross. Akad. Nauk 359 495 (1998) [Dokl. Phys. Chem. 359 102 (1998)]
  174. Gerasev A P Fiz. Goreniya Vzryva 36 (3) 51 (2000) [Combust. Explosion Shock Waves 36 329 (2000)]
  175. Gerasev A P Zh. Fiz. Khim. 74 1203 (2000) [Russ. J. Phys. Chem. 74 1077 (2000)]
  176. Gerasev A P Zh. Fiz. Khim. 76 221 (2002) [Russ. J. Phys. Chem. 76 161 (2002)]
  177. Mornev O A Zh. Fiz. Khim. 72 124 (1998) [Russ. J. Phys. Chem. 72 112 (1998)]
  178. Mornev O A, Aliev R Zh. Fiz. Khim. 69 1466 (1995)
  179. Mornev O A Zh. Fiz. Khim. 71 2293 (1997) [Russ. J. Phys. Chem. 71 2077 (1997)]
  180. Matros Yu Sh, Bunimovich G A Catal. Rev. Sci. Eng. 38 (1) 1 (1996)
  181. Akramov T A et al. Teor. Osnovy Khim. Tekhnol. 34 295 (2000) [Theor. Found. Chem. Eng. 34 263 (2000)]
  182. Prigogine I, Defay R Chemical Thermodynamics (London: Longmans Green, 1954) [Translated into Russian (Novosibirsk: Nauka, 1966)]
  183. de Donder Th, Van Rysselberghe P Thermodynamic Theory of Affinity (London: H. Milford, Oxford Univ. Press, 1936) [Translated into Russian (Moscow: Metallurgiya, 1984)]
  184. Boreskov G K Geterogennyi Kataliz (Heterogeneous Catalysis, Moscow: Nauka, 1986) [Translated into English (Hauppauge, NY: Nova Science Publ., 2003)]
  185. Horiuti J J. Res. Inst. Catal. Hokkaido Univ. 5 1 (1957)
  186. Horiuti D, in Problemy Fizicheskoi Khimii (Problems of Physical Chemistry) No. 2 (Ed. Ya M Kolotyrkin, Moscow: Goskhimizdat, 1959) p. 39
  187. Gerasev A P Kinet. Katal. 30 803 (1989) [Kinet. Catal. 30 703 (1989)]
  188. Barenblatt G I Podobie, Avtomodel’nost’ i Promezhutochnaya Asimptotika (Similarity, Automodelling and Intermediate Asymptotics, Leningrad: Gidrometeoizdat, 1978) [Translated into English: Similarity, Self-Similarity, and Intermediate Asymptotics (New York: Consultants Bureau, 1979)]
  189. de Groot S R, Mazur P Non-Equilibrium Thermodynamics (Amsterdam: North-Holland, 1962) [Translated into Russian (Moscow: Mir, 1964)]
  190. Van Resselberghe P J. Chem. Phys. 36 1327, 1329 (1962)
  191. Casimir H B G Rev. Mod. Phys. 17 343 (1945)
  192. Ross J, Mazur P J. Chem. Phys. 35 19 (1961)
  193. Malin K M (Ed.) Spravochnik Sernokislotchika (Reference Book on Sulfuric Acid) 2nd ed. (Moscow: Khimiya, 1971)
  194. Malozemov Yu V et al. Teor. Osnovy Khim. Tekhnol. 28 34 (1994) [Theor. Found. Chem. Eng. 28 29 (1994)]
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