非平衡统计力学

作者简介

This work presents the construction of an asymptotic technique for solving the Liouville equation, which is an analogue of the Enskog-Chapman technique for the Boltzmann equation. Because the assumption of molecular chaos has not been introduced, the macroscopic variables defined by the arithmetic means of the corresponding microscopic variables are random in general. Therefore, it is convenient for describing the turbulence phenomena. The asymptotic technique for the Liouville equation reveals a term showing the interaction between the temperature and the velocity of the fluid flows, which will be lost under the assumption of molecular chaos.

书籍目录

ForewordPreface1 Introduction  1.1 Historical Background  1.2 Outline of the Book2 H-Functional  2.1 Hydrodynamic Random Fields  2.2 H-Functional3 H-Functional Equation  3.1 Derivation of H-Functional Equation  3.2 H-Functional Equation  3.3 Balance Equations  3.4 Reformulation4 K-Functional  4.1 Definition of K-Functional5 Some Useful Formulas  5.1 Some Useful Formulas  5.2 A Remark on H-Functional Equation6 Turbulent Gibbs Distributions  6.1 Asymptotic Analysis for Liouville Equation  6.2 Turbulent Gibbs Distributions  6.3 Gibbs Mean7 Euler K-Functional Equation  7.1 Expressions of B2 and B3  7.2 Euler K-Functional Equation  7.3 Reformulation  7.4 Special Cases  7.5 Case of Deterministic Flows8 Functionals and Distributions  8.1 K-Functionals and Turbulent Gibbs Distributions  8.2 Turbulent Gibbs Measures  8.3 Asymptotic Analysis9 Local Stationary Liouville Equation  9.1 Gross Determinism  9.2 Temporal Part of Material Derivative of TN  9.3 Spatial Part of Material Derivative of TN  9.4 Stationary Local Liouville equation10 Second Order Approximate Solutions  10.1 Case of Reynolds-Gibbs Distributions  10.2 A Poly-spherical Coordinate System  10.3 A Solution to the Equation (10.24)1  ……11 A Finer K-Functional Equation12 ConclusionsA Some Facts About Spherical HarmonicsBibliographyIndex

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