Instabilities and Fluctuations in Systems Far from Thermodynamic Equilibrium

  • H. Thomas
Conference paper
Part of the Springer Series in Electrophysics book series (SSEP, volume 2)

Abstract

Instabilities are phase-transition-like phenomena occurring in systems away from thermodynamic equilibrium, when the physical behaviour changes discontinuously at a critical value of an external control parameter. A phase transition in an equilibrium system is usually characterized by a softening of a normal mode, leading to bifurcation into a new phase of broken symmetry, and similar phenomena can occur in a nonequilibrium system. However, in contrast to systems in thermodynamic equilibrium, where some time-independent state exists for any value of the control parameter, in nonequilibrium systems breaking of time translation symmetry can give rise to a bifurcation into time-dependent “dynamical structures”.

Keywords

Convection Hexa GaAs Autocorrelation Neon 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. /1/.
    / Synergetics, ed. by H. Haken, Teubner, Stuttgart 1973CrossRefMATHGoogle Scholar
  2. /2/.
    / Cooperative Effects, ed. by H. Haken, North-Holland, Amsterdam-Oxford American Elsevier, New York 1974Google Scholar
  3. /3/.
    / Fluctuations, Instabilities, and Phase Transitions, ed. by T. Riste, Plenum Press, New York and London 1975CrossRefGoogle Scholar
  4. /4/.
    / Turbulence and Navier Stokes Equation, ed. by R. Temam. Lecture Notes in Mathematics, Springer Verlag, Berlin, Heidelberg, New York 1976CrossRefGoogle Scholar
  5. /5/.
    Synergetics, ed. by H. Haken, Springer-Verlag, Berlin, Heidelberg,New York 1977CrossRefGoogle Scholar
  6. /6/.
    H. Haken, Rev. Mod. Phys. 47, 67 (1975)MathSciNetADSCrossRefGoogle Scholar
  7. /7/.
    C. Normand, Y. Pomeau, M.G. Velarde, Rev. Mod. Phys. 49, 581 (1977)MathSciNetADSCrossRefGoogle Scholar
  8. /8/.
    J.A. Whitehead, Jr., in Ref. /3/, p. 153Google Scholar
  9. /9/.
    G. Ahlers, in Ref. /3/, p. 181Google Scholar
  10. /10/.
    R. Graham, in Ref. /3/, p. 215Google Scholar
  11. /11/.
    P. Bergê, in Ref. /3/, p. 323Google Scholar
  12. /12/.
    E.L. Kaschmieder, in Ref. /5/, p. 70Google Scholar
  13. /13/.
    H.L. Swinney, P.R. Fenstermacher, J.P. Gollup, in Ref. /5/, p. 60Google Scholar
  14. /14/.
    J.C. McGroddy, M.I. Nathan, J.E. Smith, Jr., IBM J.Res. Develop. 13, 543 (1969)CrossRefGoogle Scholar
  15. J.E. Smith, Jr., M.I. Nathan, J.C. McGroddy, IBM J.Res. Develop. 13, 554 (1969)Google Scholar
  16. /15/.
    H. Thomas, in Ref. /1/, p. 87 and in Ref. /2/, p. 171Google Scholar
  17. /16/.
    J.B. Gunn, Solid State Comm. 1, 88 (1963); IBM J.Res. Develop. 8,141(1964)Google Scholar
  18. /17/.
    H. Risken, K. Nummedal, J. Appl. Phys. 39, 4662 (1968)CrossRefGoogle Scholar
  19. /18/.
    A.M.Turing,Phil,Trabs.Roy.soc.London,237B,37(1952)ADSCrossRefGoogle Scholar
  20. /19/.
    G. Nicolis, in Ref. /2/, p. 197Google Scholar
  21. /20/.
    / R. Lefever, in Ref. /3/, p. 353Google Scholar
  22. /21/.
    Y. Kuramoto, in Ref. /5/, p. 164Google Scholar
  23. /22/.
    R. Landauer, Ferroelectrics 2, 47 (1971)CrossRefGoogle Scholar
  24. /23/.
    R. Landauer, J.W.F. Woo, in: Statistical Mechanics: New Concepts,New Problems, New ApplicationsGoogle Scholar
  25. S.A. Rice, K.T. Freed, J.C. Light, University of Chicago Press 1972, and in Ref. /1/, p. 97Google Scholar
  26. /24/.
    H.R. Wilson, in Ref. /1/, p. 207, and in Ref. /2/, p. 247Google Scholar
  27. /25/.
    W. Weidlich, in Ref. /2/, p. 269Google Scholar
  28. /26/.
    P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure,Stability and Fluctuations, Wiley Interscience, London, New York, Sidney, Toronto 1971MATHGoogle Scholar
  29. /27/.
    F. Schlögl, Z. Physik 243, 303 (1971), 248, 446 (1971)Google Scholar
  30. /28/.
    R. Landauer, J. Statist. Phys. 9, 351 (1973), 11, 523 (1974), 13, 1and Phys. Rev. Al2, 636(1975)Google Scholar
  31. /29/.
    R. Landauer, J. Appl. Phys. 33, 2209 (1962)CrossRefGoogle Scholar
  32. /30/.
    V.M. Zaitsev, M.I. Shliomis, Sov. Phys. JETP 32, 866 (1971)ADSGoogle Scholar
  33. /31/.
    R. Graham, in Springer Tracts in Modern Physics, Vol. 66, Springer-Verlag, Berlin, Heidelberg, New York 1973, and Phys. Rev. A10, 1762 (1974)Google Scholar
  34. /32/.
    H.K. Janssen, Z. Physik 270, 67 (1974)ADSCrossRefGoogle Scholar
  35. /33/.
    I. Matheson, D.F. Walls, C.W. Gardiner, J. Statist. Phys. 12, 21 (1975)ADSCrossRefGoogle Scholar
  36. /34/.
    C.W. Gardiner, K.J. McNeill, D.F. Walls, I.S. Matheson, J. Statist. Phys. 14, 307 (1976)ADSCrossRefGoogle Scholar
  37. /35/.
    H.N.W. Lekkerkerker, J.-P. Boon, in Ref. /3/, p. 205Google Scholar
  38. /36/.
    C.P. Enz, Physica 89A, 1 (1977)MathSciNetADSCrossRefGoogle Scholar
  39. /36/.
    E. Pytte, H. Thomas, Phys. Rev. 179, 431 (1969)ADSCrossRefGoogle Scholar
  40. /38/.
    K. Pfundtner, H. Thomas, Phys. kondens. Materie 16, 245 (1973)ADSGoogle Scholar
  41. /39/.
    M. Büttiker, H. Thomas, Phys. Rev. Letters 38, 78 (1977),Solid State Electronics 21, 95 (1978) and present volumeGoogle Scholar
  42. /40/.
    R. Landauer, J.W.F. Woo, Comments on Solid State Physics 4, 139 (1972))Google Scholar
  43. /41/.
    B. Ross, J.D. Litster, Phys. Rev. A15, 1246 (1977)ADSCrossRefGoogle Scholar
  44. /42/.
    R. Landauer, Phys. Rev. A15, 2117 (1977)ADSCrossRefGoogle Scholar
  45. /43/.
    H. Haken, in Ref. /5/, p. 2Google Scholar
  46. /44/.
    H.Thomes,IEEE Transactions on Magetics MAG-5,874(1969)ADSCrossRefGoogle Scholar
  47. /45/.
    E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)ADSCrossRefGoogle Scholar
  48. /46/.
    J.B. McLaughlin, P.C. Martin, Phys. Rev. Letters 33, 1189 (1974)ADSCrossRefGoogle Scholar
  49. /47/.
    P.C. Martin, in: Statistical Physics, ed. by L. Pal and P. Szépfalusy,Akademiai Kiado, Budapest 1976Google Scholar
  50. /47/.
    D. Ruelle, F. Takens, Commun. Math. Phys. 20, 167 (1971)MathSciNetADSCrossRefMATHGoogle Scholar
  51. /49/.
    /D. Ruelle, in Ref. /3/, p. 146Google Scholar
  52. /50/.
    M. Henon, Y. Pomeau, in Ref. /3/, p. 29Google Scholar
  53. /51/.
    G. Ahlers, Phys. Rev. Letters 33, 1185 (1974)ADSCrossRefGoogle Scholar
  54. /52/.
    G. Ahlers, R.P. Behringer, Phys. Rev. Letters 40, 712 (1978)ADSCrossRefGoogle Scholar
  55. /53/.
    H.K. Moffat, in: Fluid Dynamics, ed. by R. Balian and J.L. Peube,Gordon & Breach, London, New York, Paris 1977Google Scholar
  56. /54/.
    H. Haken, Physics Letters 53A, 77 (1975)ADSGoogle Scholar
  57. /55/.
    E. Rössler, in Ref. /5/, p. 174Google Scholar
  58. /56/.
    R. Landauer, “Poor Man’s Chaos”, private communicationGoogle Scholar
  59. /57/.
    E. Rössler, in Ref. /5/, p. 184Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • H. Thomas
    • 1
  1. 1.Institut für PhysikUniversität BaselBaselSwitzerland

Personalised recommendations