Extinction and Long-Time Relaxation

  • Alexander S. Mikhailov
  • Alexander Yu. Loskutov
Part of the Springer Series in Synergetics book series (SSSYN, volume 52)

Abstract

Complex patterns can be produced during the processes of relaxation to a steady uniform state. In this case one finds the relative selective amplification of certain spatial modes due to variations in their damping rates. The hierarchy of characteristic relaxation times of different modes, including very long scales, reveals itself in more complicated laws of relaxation. For instance, a simple exponential dependence can be replaced by some power law.

Keywords

Combustion Recombination Expense 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 11.1
    B. Felderhof, I. Deutch: J. Chem. Phys. 64, 4551–4558 (1976)ADSCrossRefGoogle Scholar
  2. 11.2
    J.R. Lebenhaft, R. Kapral: J. Stat. Phys. B 20, 125 (1979)MathSciNetGoogle Scholar
  3. 11.3
    M. Bixon, R. Zwanzig: J. Chem. Phys. 75, 2354 (1981)ADSCrossRefGoogle Scholar
  4. 11.4
    M. Muthukumar, R.J. Cukier: J. Stat. Phys. 26, 453 (1981)ADSCrossRefGoogle Scholar
  5. 11.5
    B. Felderhof, I. Deutch, U. Titulauer: J. Chem. Phys. 76, 4178–4184 (1982)ADSCrossRefGoogle Scholar
  6. 11.6
    T.R. Kirkpatrick: J. Chem. Phys. 76, 4255–4259 (1982)ADSCrossRefGoogle Scholar
  7. 11.7
    M. Tokuyama, R.I. Cukier: J. Chem. Phys. 76, 6202 (1982)ADSCrossRefGoogle Scholar
  8. 11.8
    B.Ya. Balagurov, V.G. Vaks: Zh. Eksp. Teor. Fiz. 65, 1939–1945 (1973)Google Scholar
  9. 11.9
    P. Grassberger, I. Procaccia: J. Chem. Phys. 77, 6281–6284 (1982)ADSCrossRefGoogle Scholar
  10. 11.10
    I.M. Lifshitz, S.A. Gredeskul, L.A. Pastur: Introduction to the Theory of Disordered Systems (Nauka, Moscow 1982)Google Scholar
  11. 11.11
    I.M. Lifshitz: Usp. Fiz. Nauk. 83, 617 (1964)Google Scholar
  12. 11.12
    I.M. Lifshitz: Zh. Eksp. Teor. Fiz. 53, 743 (1967)Google Scholar
  13. 11.13
    A.S. Mikhailov, I.V. Uporov: Sov. Phys. Usp. 27, 695 (1984)ADSCrossRefGoogle Scholar
  14. 11.14
    R.F. Kayser, J.B. Hubbard: Phys. Rev. Lett. 51, 79–82 (1983)MathSciNetADSCrossRefGoogle Scholar
  15. 11.15
    R.F. Kayser, J.B. Hubbard: J. Chem. Phys. 80, 1127–1130 (1984)ADSCrossRefGoogle Scholar
  16. 11.16
    A. Blumen, J. Klafter, G. Zumofen: Phys. Rev. B 28, 6112–6115 (1983)ADSCrossRefGoogle Scholar
  17. 11.17
    J. Klafter, A. Blumen: J. Chem. Phys. 80, 875–877 (1984)ADSCrossRefGoogle Scholar
  18. 11.18
    T.R. Waite: Phys. Rev. 107, 463–470 (1957)ADSCrossRefGoogle Scholar
  19. 11.19
    S.A. Rice: Diffision-Limited Reactions (Elsevier, Amsterdam 1985)Google Scholar
  20. 11.20
    Ya.B. Zeldovich: Sov. Electrochem. 13, 581 (1977)Google Scholar
  21. 11.21
    A.A. Ovchinnikov, Ya.B. Zeldovich: Chem. Phys. 28, 215 (1978)CrossRefGoogle Scholar
  22. 11.22
    D. Toussaint, F. Wilczec: J. Chem. Phys. 78, 2642–2647 (1983)ADSCrossRefGoogle Scholar
  23. 11.23
    S.F. Burlatskii, A.A. Ovchinnikov: Zh. Eksp. Teor. Fiz. 92, 1618–1635 (1987)Google Scholar
  24. 11.24
    Ya.B. Zeldovich, A.S. Mikhailov: Sov. Phys. Usp. 30, 977–992 (1987)ADSCrossRefGoogle Scholar
  25. 11.25
    Ya.B. Zeldovich: Zh. Tekh. Fiz. 19, 1199 (1949)Google Scholar
  26. 11.26
    I.M. Sokolov: JETP Lett. 44, 67 (1986)ADSGoogle Scholar
  27. 11.27
    Ya.B. Zeldovich, A.S. Mikhailov: “Chirality wave propagation and the first evolutionary catastrophe”, in Thermodynamics and Pattern Formation in Biology, ed. by I. Lamprecht, A.I. Zotin (de Gruyter, Berlin 1988) pp. 57–68Google Scholar
  28. 11.28
    A.S. Mikhailov: Phys. Rep. 184, 308–374 (1989)ADSCrossRefGoogle Scholar
  29. 11.29
    Ya.B. Zeldovich, A.A. Ovchinnikov: Sov. Phys. JETP 65, 535 (1978)Google Scholar
  30. 11.30
    Ya.B. Zeldovich, A.A. Ovchinnikov: JETP Lett. 26, 440 (1977)ADSGoogle Scholar
  31. 11.31
    S.F. Burlatskii: Fluctuational Kinetics ofDiffusional Processes, Dr. Sc. Thesis (Institute for Chemical Physics, Moscow 1988)Google Scholar
  32. 11.32
    S.F. Burlatskii, A.A. Ovchinnikov, G.S. Oshanin: Zh. Eksp. Teor. Fiz. 95, 1993–2008 (1989)Google Scholar
  33. 11.33
    G.S. Oshanin, S.F. Burlatskii, A.A. Ovchinnikov: J. Phys. A 22, 977 (1989)ADSCrossRefGoogle Scholar
  34. 11.34
    A.A. Ovchinnikov, S.F. Burlatskii: Sov. Phys. JETP Lett. 43, 638 (1986)ADSGoogle Scholar
  35. 11.35
    A.M. Gutin, A.S. Mikhailov, V.V. Yashin: Sov. Phys. JETP 65, 535 (1987)Google Scholar
  36. 11.36
    Y.C. Zhang: Phys. Rev. Lett. 59, 1726–1728 (1987)ADSCrossRefGoogle Scholar
  37. 11.37
    V.L. Vinetskii, A.V. Kondrachuk: Ukr. Fiz. Zh. 27, 383–387 (1982)Google Scholar
  38. 11.38
    Yu.H. Kalnins, Yu.Yu. Krikis: Izv. Akad. Nauk Latv. SSR. Ser. Fiz.-Tekh. Nauk. No. 1, 104–106 (1983)Google Scholar
  39. 11.39
    F.V. Pirogov, E.I. Palagishvili: Izv. Akad. Nauk Latv. SSR. Ser. Fiz.-Tekh. Nauk. No. 4, 46–53 (1984)Google Scholar
  40. 11.40
    L.W. Anacker, R. Kopelman: Phys. Rev. Lett. 58, 289–291 (1987)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alexander S. Mikhailov
    • 1
    • 2
  • Alexander Yu. Loskutov
    • 1
  1. 1.Department of PhysicsMoscow State UniversityMoscowUSSR
  2. 2.Institut für Theoretische Physik und SynergetikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

Personalised recommendations