The Relativistic Boltzmann Equation: Theory and Applications 相对论性的伯磁曼等式:理论和应用

作者： Carlo Cercignani著

出 版 社：

出版时间： 2002-4-1字数：版次： 1页数： 384印刷时间： 2002/04/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783764366933包装： 精装内容简介

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

目录

Preface

1 Special Relativity

1.1Introduction

1.2Lorentz transformations

1.3Tensors in Minkowski spaces

1.4Relativistic mechanics

1.4.1Four-velocity

1.4.2Minkowski force

1.4.3Elastic collisions

1.4.4Relative velocity

1.5Electrodynamics in free space

1.5.1Maxwell equations

1.5.2Energy-momentum tensor

1.5.3Retarded potentials

2Relativistic Boltzmann Equation

2.1Single non-degenerate gas

2.2Single degenerate gas

2.3General equation of transfer

2.4Summational invariants

2.5Macroscopic description

2.6Local Lorentz rest frame

2.7 Equilibrium distribution function

2.8Trend to equilibrium. Htheorem

2.9The projector

2.10 Equilibrium states

3Fields in Equilibrium

3.1The general case

3.2Non-degenerate gas

3.2.1Modified Bessel function of second kind.

3.2.2Expressions for n, e and p

3.2.3Non-relativistic limit

3.2.4Ultra-relativistic limit

3.3Degenerate relativistic Fermi gas

3.3.1Completely degenerate relativistic Fermi gas

3.3.2White dwarf stars

3.3.3Strongly degenerate relativistic Fermi gas

3.4Degenerate relativistic Bose gas

3.4.1Some useful integrals

3.4.2Relativistic Bose-Einstein condensation

4Thermomechanics of Relativistic Fluids

4.1Introduction

4.2Thermodynamics of perfect fluids

4.3Eckart decomposition

4.4Landau and Lifshitz decomposition

4.5Thermodynamics of a single fluid

5Chapman-Enskog Method

5.1Introduction

5.2Simplified version

5.3The integrals I1, I2 and I3

5.4Transport coefficients

5.4.1Hard-sphere particles

5.4.2Israel particles

5.5Formal version

5.5.1Integral equations

5.5.2Second approximation

5.5.3Orthogonal polynomials

5.5.4Expansion in orthogonal polynomials

5.6Appendix

6 Method of Moments

6.1Introduction

6.2Grad distribution function

6.3Constitutive equations for Tαβr and Pαβ

6.4Linearized field equations

6.5Five-field theory

6.5.1Laws of Navier-Stokes and Fourier

6.5.2Linearized Burnett equations

6.6Maxwellian particles

6.7Combined method of Chapman Enskog and Grad

7 Chemically Reacting Gas Mixtures

7.1Introduction

7.2Boltzmann and transfer equations

7.3Maxwell-Jiittner distribution function

7.4Thermodynamics of mixtures

……

8Model Equations

9 Wave Phenomena in a Relativistic Gas

10 Tensor Calculus in General Coordinates

11 Riemann Spaces and General Relativity

12 Boltzmann Equation in Gravitational Fields

13 The Vlasov Equation and Related Systems

Physical Constants

Modified Bessel Function

Index