非平衡统计力学
2003-12
World Scientific Publishing Co Pte Ltd
Chen, Tian-Quan
420
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This book presents the construction of an asymptotic technique for solving the Liouville equation, which is to some degree an analogue of the Enskog–Chapman technique for solving the Boltzmann equation. Because the assumption of molecular chaos has been given up at the outset, the macroscopic variables at a point, defined as arithmetic means of the corresponding microscopic variables inside a small neighborhood of the point, are random in general. They are the best candidates for the macroscopic variables for turbulent flows. The outcome of the asymptotic technique for the Liouville equation reveals some new terms showing the intricate interactions between the velocities and the internal energies of the turbulent fluid flows, which have been lost in the classical theory of BBGKY hierarchy.
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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