| |
| |
| Preface | |
| |
| |
| Historical Introduction | |
| |
| |
| |
| Statistical Mechanical Preliminaries | |
| |
| |
| |
| The Microscopic Description | |
| |
| |
| |
| Relationship Between Microscopic and Macroscopic Descriptions | |
| |
| |
| |
| The Gibbs Ensemble | |
| |
| |
| |
| The Liouville Equation | |
| |
| |
| |
| Proof of Liouville's Theorem | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Contraction of the Statistical Mechanical Description | |
| |
| |
| |
| Reduced Distribution Functions | |
| |
| |
| |
| Reduction of the First BBGKY Equation to the Boltzmann Equation | |
| |
| |
| |
| The Moments of f | |
| |
| |
| |
| The Hydrodynamical Equations | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Description of Binary Collisions | |
| |
| |
| |
| General Formulation | |
| |
| |
| |
| An Alternate Representation of the Collision Integral | |
| |
| |
| |
| Hard Sphere Molecules | |
| |
| |
| |
| General Intermolecular Potentials | |
| |
| |
| |
| Power Law Potentials | |
| |
| |
| |
| The Collision Cross Section | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Properties of the Collision Term | |
| |
| |
| |
| Symmetry Properties of J(f) | |
| |
| |
| |
| The Summational Invariants | |
| |
| |
| |
| The Linearized Collision Term, L(g) | |
| |
| |
| |
| An Alternate Representation of L(g) | |
| |
| |
| |
| The Eigentheory of L(g) | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| The H Theorem and Irreversibility | |
| |
| |
| |
| Spatially Homogeneous Systems | |
| |
| |
| |
| The H Theorem for a Nonuniform System | |
| |
| |
| |
| Irreversibility and Boltzmann's Equation | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Normal Solutions of Boltzmann's Equation | |
| |
| |
| |
| The Fredholm Theorems | |
| |
| |
| |
| Hilbert's Uniqueness Theorem | |
| |
| |
| |
| The Chapman-Enskog Procedure | |
| |
| |
| |
| The First-Order Chapman-Enskog Solution | |
| |
| |
| |
| The Second-Order Chapman-Enskog Solution | |
| |
| |
| |
| Expressions for the Thermal Conductivity and Viscosity | |
| |
| |
| |
| Calculation of the Transport Coefficients | |
| |
| |
| |
| Validity of the Chapman-Enskog Results | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Moment Method Solutions | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Multidimensional Hermite Tensor Polynomials | |
| |
| |
| |
| Maxwell's Moment Method | |
| |
| |
| |
| Grad's Moment Method | |
| |
| |
| |
| Some Applications of the Thirteen-Moment Equations | |
| |
| |
| |
| Evaluation of the Collision Terms | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Model Boltzmann Equations | |
| |
| |
| |
| The Simple BGK Model Equation | |
| |
| |
| |
| Generalized Model Equations | |
| |
| |
| |
| Some Other Model Equations | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Solutions of Special Problems | |
| |
| |
| |
| Solutions of Boltzmann's Equation | |
| |
| |
| |
| Boundary Conditions in Kinetic Theory | |
| |
| |
| |
| Plane Poiseuille Flow | |
| |
| |
| |
| The Density-Density Correlation Function | |
| |
| |
| |
| Shock Wave Structure | |
| |
| |
| |
| Half-Range Polynomial Expansions | |
| |
| |
| |
| Couette Flow | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Gas Mixtures | |
| |
| |
| |
| Description of Binary Mixtures | |
| |
| |
| |
| Transport Phenomena in Mixtures | |
| |
| |
| |
| Linearized and Model Boltzmann Equations | |
| |
| |
| |
| The Boltzmann Fokker-Planck Equation | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Generalized Boltzmann Equations | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The Wang Chang-Uhlenbeck Equation | |
| |
| |
| |
| Normal Solutions of the WCU Equation | |
| |
| |
| |
| Model Equations for Structured Particles | |
| |
| |
| |
| Enskog's Equation for Dense Gases | |
| |
| |
| |
| A Boltzmann Equation for Traffic Flow | |
| |
| |
| References | |
| |
| |
| Problems | |
| |
| |
| |
| Comparison of Theory with Experiment | |
| |
| |
| |
| Transport Coefficients | |
| |
| |
| |
| Special Flows | |
| |
| |
| |
| The Distribution Function | |
| |
| |
| |
| Computer Experiments | |
| |
| |
| References | |
| |
| |
| General References | |
| |
| |
| Indexes | |