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Prog. Theor. Phys. Vol. 57 No. 3 (1977) pp. 770-784

[ Full Text PDF : FREE ACCESS (1237K) ]

Critical Dimensionality for Normal Fluctuations of Macrovariables in Nonequilibrium States

Hazime Mori and Kenneth J. McNeil

Department of Physics, Kyushu University, Fukuoka 812

(Received August 21, 1976)

Abstract:

The scaling condition for the normal fluctuations of macrovariables is studied by regarding the spatial dimensionality d for fluctuations as a variable parameter. The critical dimensionality dc, above which the fluctuations are normal and obey a Gaussian process and below which they are anomalous and obey a nonlinear non-Gaussian process, is defined and explored for nonequilibrium inhomogeneous systems with the aid of a scaling theory of the dependence of macrovariables on their spatial cutoff. If is shown that dc=max µ[2αµ+γµ]. Where αµ and γµ are the scaling exponents of the deterministic part and those of the pair correlation functions for d≧dc, respectively. It turns out that dc=1 in the kinetic region of the particle density in µ space of low-density gases with short-range forces, dc=2 in the non-critical region of laminar hydrodynamic flows, and dc=4 in the critical region of the Bénard-Rayleigh instability and of the Schlögl chemical instability. It is shown that there are two types of critical fluctuations, both of which have an identical value of dc, but which have quite different features from each other.


URL : http://ptp.ipap.jp/link?PTP/57/770/
DOI : 10.1143/PTP.57.770

[ Full Text PDF : FREE ACCESS (1237K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 57 No. 3 (1977) pp. 734-745 :
    Theoretical Study of a Chemical Turbulence
    Hirokazu Fujisaka and Tomoji Yamada
  2. Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 92-112 :
    Kinetic Equations and Fluctuations in µ Space of One-Component Dilute Plasmas
    Michio Tokuyama and Hazime Mori
  3. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1493-1510 :
    Kinetic Equations of Dilute Electron Plasmas in the Coherent Region
    Terumitsu Morita, Hazime Mori and Michio Tokuyama
  4. Progress of Theoretical Physics Vol. 63 No. 4 (1980) pp. 1181-1189 :
    Critical Fluctuations of Schlögl's Chemical Model
    Yutaka Fukuyama and Hazime Mori
  5. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 1865-1884 :
    Contraction of State Variables in Non-Equilibrium Open Systems. I
    Hazime Mori, Terumitsu Morita and Kazuko T. Mashiyama
  6. Progress of Theoretical Physics Vol. 65 No. 6 (1981) pp. 1820-1834 :
    Anomalous Fluctuations near Nonequilibrium Soft Transitions. I
    Kazuko T. Mashiyama, Kiyohumi Takayoshi and Hazime Mori
  7. Progress of Theoretical Physics Supplement No.64 (1978) pp. 50-64 :
    Scalng for the Space-Time Coarse Graining and Kinetic Equations
    Hazime Mori, Michio Tokuyama and Terumitsu Morita

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