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Prog. Theor. Phys. Vol. 49 No. 3 (1973) pp. 764-775

[ Full Text PDF : FREE ACCESS (853K) ]

On Nonlinear Dynamics of Fluctuations

Hazime Mori and Hirokazu Fujisaka

Department of Physics, Kyushu University, Fukuoka

(Received July 22, 1972)

Abstract:

A projection-operator method is developed for renormalizing kinetic coefficients by the nonlinear interaction between macroscopic modes in a nonlinear Langevin equation which is often used in studying anomalous transport phenomena near critical points and anomalous transport coefficients in two dimension. It is shown that the renormalization term is given by the time correlation of a new fluctuating force. Other theories are derived from this expression by making approximations. A relation between the Langevin fluctuating force and the transport fluctuating force is derived to clarify the relation between the Fokker-Planck equation approach by Green and Zwanzig and the linear equation-of-motion approach by one of the authors.


URL : http://ptp.ipap.jp/link?PTP/49/764/
DOI : 10.1143/PTP.49.764

[ Full Text PDF : FREE ACCESS (853K) ] Citation:

References:

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  2. M. S. Green, J. Chem. Phys. 20 (1952), 1281[CrossRef]; ibid. 22 (1954), 398[CrossRef].
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Citing Article(s) :

  1. Journal of the Physical Society of Japan 59 (1990) pp. 1299-1304 :
    Density Fluctuations in Liquids -Application of a Dynamical Density Functional Theory-*
    Toyonori Munakata
  2. Progress of Theoretical Physics Vol. 49 No. 1 (1973) pp. 357-358 :
    Kinetic Equations for the Particle Density in µ Space
    Hazime Mori
  3. Progress of Theoretical Physics Vol. 49 No. 3 (1973) pp. 1062-1063 :
    Landau-Lifshitz Equation of Motion for Ferromagnetic Systems
    Tomoji Yamada, Hirokazu Fujisaka and Hazime Mori
  4. Progress of Theoretical Physics Vol. 49 No. 5 (1973) pp. 1516-1545 :
    Statistical-Mechanical Theory of Kinetic Equations
    Hazime Mori
  5. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 424-449 :
    On the Theory of Non-Equilibrium Thermodynamics
    Hiroshi Furukawa
  6. Progress of Theoretical Physics Vol. 51 No. 1 (1974) pp. 109-122 :
    A New Expansion of the Master Equation
    Hazime Mori, Hirokazu Fujisaka and Hideto Shigematsu
  7. Progress of Theoretical Physics Vol. 51 No. 4 (1974) pp. 1257-1259 :
    On the Derivation of the Dynamic Scaling Law by Means of Kadanoff's Cell Analysis and Coarse Graining of Time
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  8. Progress of Theoretical Physics Vol. 51 No. 6 (1974) pp. 1712-1730 :
    Renormalization Group Theory of Dynamic Critical Phenomena
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  9. Progress of Theoretical Physics Vol. 52 No. 2 (1974) pp. 433-452 :
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  10. Progress of Theoretical Physics Vol. 53 No. 6 (1975) pp. 1617-1640 :
    Stochastic Processes of Macroscopic Variables
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  11. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1093-1098 :
    Nonlinear Effects on the Linear Transport Coefficients
    Sture Nordholm
  12. Progress of Theoretical Physics Vol. 55 No. 2 (1976) pp. 430-437 :
    Fluctuation Renormalization in Nonlinear Dynamics
    Hirokazu Fujisaka
  13. Progress of Theoretical Physics Vol. 55 No. 6 (1976) pp. 2025-2027 :
    Hydrodynamical Behavior of the Bose-Einstein Condensate
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  14. Progress of Theoretical Physics Vol. 56 No. 3 (1976) pp. 754-772 :
    Reduction of Variables and Processes in Macrodynamics
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  15. Progress of Theoretical Physics Vol. 56 No. 5 (1976) pp. 1351-1359 :
    Hydrodynamical Behavior of Bose-Einstein Condensate near the Lambda Point
    Yukio Okwamoto
  16. Progress of Theoretical Physics Vol. 56 No. 6 (1976) pp. 1689-1704 :
    Dynamics of Bose-Einstein Condensate and Two-Fluid Hydrodynamics
    Kazumasa Miyake and Kazuo Yamada
  17. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 53-67 :
    Anomalous Relaxation in One-Dimensional Magnets. I
    Hisao Okamoto, Katsuhiko Nagano, Takashi Karasudani and Hazime Mori
  18. Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 37-51 :
    Variation Principle of Linear and Nonlinear Irreversible Processes
    Masakazu Ichiyanagi
  19. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1203-1208 :
    Continued Fraction Expansion of Fluctuation Spectrum and Generalized Time Correlation
    Hirokazu Fujisaka and Masayoshi Inoue
  20. Progress of Theoretical Physics Vol. 104 No. 5 (2000) pp. 925-941 :
    Modeling Chaotic Evolution with Nonlinear Langevin Dynamics
    Toshiaki Tao and Hirokazu Fujisaka
  21. Progress of Theoretical Physics Vol. 114 No. 1 (2005) pp. 1-21 :
    A New Expansion of Dynamical Correlations in Stochastic Processes and Chaotic Dynamics
    Hirokazu Fujisaka
  22. 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
  23. Progress of Theoretical Physics Supplement No.64 (1978) pp. 74-82 :
    Nonlinear Transport Equations from Statistical Mechanics
    Robert Zwanzig

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