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Prog. Theor. Phys. Vol. 56 No. 1 (1976) pp. 77-94

[ Full Text PDF : FREE ACCESS (1367K) ]

Scaling Theory of Non-Equilibrium Systems near the Instability Point. I

— General Aspects of Transient Phenomena —

Masuo Suzuki

Department of Physics, University of Tokyo, Tokyo 113

(Received December 25, 1975)

Abstract:

A new idea of scaling for transient phenomena near the instability point is proposed. This scaling theory is based on a generalized scale transformation of time and is very useful in discussing the relaxation and fluctuation in non-equilibrium systems near the asymptotically unstable point. The whole range of time is divided into three regions: the initial regime in which the ordinary ε-expansion is valid, the scaling regime in which the fluctuation enhancement occurs and the evolution equations of scaling functions are obtained, and the final regime in which the system approaches the equilibrium state. As an example, the relaxation of the nonlinear Fokker-Planck equation is studied by the help of the present scaling theory. The possibility of applications of this general theory to various kinds of transient phenomena near the instability point is pointed out.


URL : http://ptp.ipap.jp/link?PTP/56/77/
DOI : 10.1143/PTP.56.77

[ Full Text PDF : FREE ACCESS (1367K) ] Citation:

References:

  1. R. Kubo, in Synergetics, ed. H. Haken (B. G. Teubner, Stuttgart, 1973).
  2. R. Kubo, K. Matsuo and K. Kitahara, J. Stat. Phys. 9 (1973), 51[CrossRef].
  3. M. Suzuki, Prog. Theor. Phys. 53 (1975), 1657[PTP]; J. Stat. Phys. 14 (1976), 129.
  4. M. Suzuki, Prog. Theor. Phys. 55 (1976), 383[PTP].
  5. M. Suzuki, Prog. Theor. Phys. 55 (1976), 1064[PTP].
  6. M. Suzuki, Physica A 84 (1976), 48[CrossRef].
  7. N. G. van Kampen, Can. J. Phys. 39 (1961), 551.
  8. M. Suzuki, Phys. Lett. A 56 (1976), 71[CrossRef].
  9. Y. Saito, Thesis (University of Tokyo).
  10. J. S. Langer, M. Bar-on and H. D. Miller, Phys. Rev. A 11 (1975), 1417[APS].

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