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The Relativistic Boltzmann Equation: Theory and Applications
Progress in Mathematical Physics 22
ISBN/EAN: 9783034894630
Umbreit-Nr.: 5524173
Sprache:
Englisch
Umfang: x, 384 S., 2 s/w Illustr.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 30.10.2012
Auflage: 1/2002
- Zusatztext
- Inhaltsangabe1 Special Relativity.- 1.1 Introduction.- 1.2 Lorentz transformations.- 1.3 Tensors in Minkowski spaces.- 1.4 Relativistic mechanics.- 1.4.1 Four-velocity.- 1.4.2 Minkowski force.- 1.4.3 Elastic collisions.- 1.4.4 Relative velocity.- 1.5 Electrodynamics in free space.- 1.5.1 Maxwell equations.- 1.5.2 Energy-momentum tensor.- 1.5.3 Retarded potentials.- 2 Relativistic Boltzmann Equation.- 2.1 Single non-degenerate gas.- 2.2 Single degenerate gas.- 2.3 General equation of transfer.- 2.4 Summational invariants.- 2.5 Macroscopic description.- 2.6 Local Lorentz rest frame.- 2.7 Equilibrium distribution function.- 2.8 Trend to equilibrium. H-theorem.- 2.9 The projector ???.- 2.10 Equilibrium states.- 3 Fields in Equilibrium.- 3.1 The general case.- 3.2 Non-degenerate gas.- 3.2.1 Modified Bessel function of second kind.- 3.2.2 Expressions for n, e and p.- 3.2.3 Non-relativistic limit.- 3.2.4 Ultra-relativistic limit.- 3.3 Degenerate relativistic Fermi gas.- 3.3.1 Completely degenerate relativistic Fermi gas.- 3.3.2 White dwarf stars.- 3.3.3 Strongly degenerate relativistic Fermi gas.- 3.4 Degenerate relativistic Bose gas.- 3.4.1 Some useful integrals.- 3.4.2 Relativistic Bose-Einstein condensation.- 4 Thermomechanics of Relativistic Fluids.- 4.1 Introduction.- 4.2 Thermodynamics of perfect fluids.- 4.3 Eckart decomposition.- 4.4 Landau and Lifshitz decomposition.- 4.5 Thermodynamics of a single fluid.- 5 Chapman-Enskog Method.- 5.1 Introduction.- 5.2 Simplified version.- 5.3 The integrals Il, I2 and I3.- 5.4 Transport coefficients.- 5.4.1 Hard-sphere particles.- 5.4.2 Israel particles.- 5.5 Formal version.- 5.5.1 Integral equations.- 5.5.2 Second approximation.- 5.5.3 Orthogonal polynomials.- 5.5.4 Expansion in orthogonal polynomials.- 5.6 Appendix.- 6 Method of Moments.- 6.1 Introduction.- 6.2 Grad distribution function.- 6.3 Constitutive equations for Taßry and Paß.- 6.4 Linearized field equations.- 6.5 Five-field theory.- 6.5.1 Laws of Navier-Stokes and Fourier.- 6.5.2 Linearized Burnett equations.- 6.6 Maxwellian particles.- 6.7 Combined method of Chapman-Enskog and Grad.- 7 Chemically Reacting Gas Mixtures.- 7.1 Introduction.- 7.2 Boltzmann and transfer equations.- 7.3 Maxwell-Jüttner distribution function.- 7.4 Thermodynamics of mixtures.- 7.5 Transport coefficients.- 7.6 Onsager reciprocity relations.- 8 Model Equations.- 8.1 Introduction.- 8.2 The characteristic time.- 8.3 Single non-degenerate gas.- 8.3.1 The model of Marle.- 8.3.2 The model of Anderson and Witting.- 8.3.3 Comparison of the models.- 8.4 Single degenerate gas.- 8.4.1 Non-zero rest mass.- 8.4.2 Zero rest mass.- 8.5 Relativistic ionized gases.- 8.5.1 Boltzmann and balance equations.- 8.5.2 Decomposition with respect to the four-velocity.- 8.5.3 Ohm's law.- 8.6 Appendix.- 9 Wave Phenomena in a Relativistic Gas.- 9.1 Introduction.- 9.2 Propagation of discontinuities.- 9.3 Small oscillations.- 9.3.1 Boltzmann equation.- 9.3.2 Continuum-like theories.- 9.4 Shock waves.- 9.4.1 Continuum theory.- 9.4.2 Boltzmann equation.- 10 Tensor Calculus in General Coordinates.- 10.1 Introduction.- 10.2 Tensor components in general coordinates.- 10.3 Affine connection.- 10.4 Covariant differentiation.- 10.5 Spatial metric tensor.- 10.6 Special relativity in general coordinates.- 11 Riemann Spaces and General Relativity.- 11.1 Introduction.- 11.2 Tensors in Riemannian spaces.- 11.3 Curvature tensor.- 11.4 Physical principles of general relativity.- 11.5 Mechanics in gravitational fields.- 11.5.1 Four-velocity.- 11.5.2 Equations of motion.- 11.6 Electrodynamics in gravitational fields.- 11.7 Perfect fluids.- 11.8 Einstein's field equations.- 11.9 Solution for weak fields.- 11.10 Exact solutions of Einstein's field equations.- 11.11 Robertson-Walker metric.- 11.11.1 Geometrical meaning.- 11.11.2 Determination of the energy density.- 11.11.3 Determination of K(t).- 12 Boltzmann Equation in Gravitational Fields.- 12.1 Introduction.- 12.2 Transformation of volume elements.- 12.3 Boltzm