Generalized Boltzmann Physical Kinetics (eBook)

Front Cover 1
Generalized Boltzmann Physical Kinetics 4
Copyright Page 5
Contents 6
Preface 8
Historical Introduction and the Problem Formulation 10
Chapter 1. Generalized Boltzmann Equation 30
1.1. Mathematical introduction. Method of many scales 30
1.2. Hierarchy of Bogolubov kinetic equations 42
1.3. Derivation of the generalized Boltzmann equation 48
1.4. Generalized Boltzmann H-theorem and the problem of irreversibility of time 70
1.5. Generalized Boltzmann equation and iterative construction of higher-order equations in the Boltzmann kinetic theory 88
1.6. Generalized Boltzmann equation and the theory of non-local kinetic equations with time delay 92
Chapter 2. Theory of Generalized Hydrodynamic Equations 100
2.1. Transport of molecular characteristics 100
2.2. Hydrodynamic Enskog equations 103
2.3. Transformations of the generalized Boltzmann equation 105
2.4. Generalized continuity equation 107
2.5. Generalized momentum equation for component 110
2.6. Generalized energy equation for component 115
2.7. Generalized hydrodynamic Euler equations 121
2.8. Boundary conditions in the theory of the generalized hydrodynamic equations 133
Chapter 3. Strict Theory of Turbulence and Some Applications of the Generalized Hydrodynamic Theory 142
3.1. About principles of classical theory of turbulent flows 142
3.2 Theory of turbulence and generalized Euler equations 145
3.3. Theory of turbulence and the generalized Enskog equations 158
3.4. Generalized hydrodynamic equations and quantum mechanics 162
Chapter 4. Physics of a Weakly Ionized Gas 170
4.1. Relaxation of charged particles in "Maxwellian" gas and the hydrodynamic aspects of the theory 170
4.2. Distribution function of the charged particles in the "Lorentz'' gas 177
4.3. Charged particles in alternating electric field 185
4.4. Conductivity of a weakly ionized gas in crossed electric and magnetic fields 188
Chapter 5. Kinetic Coefficients in the Theory of the Generalized Kinetic Equations 196
5.1. Linearization of the generalized Boltzmann equation 196
5.2. Approximate modified Chapman…Enskog method 204
5.3. Kinetic coefficient calculation with taking into account the statistical fluctuations 217
Chapter 6. Some Applications of the Generalized Boltzmann Physical Kinetics 224
6.1. Investigation of the generalized Boltzmann equation for electron energy distribution in a constant electric field with due regard for inelastic collisions 224
6.2. Sound propagation studied with the generalized equations of fluid dynamics 235
6.3. Shock wave structure examined with the generalized equations of fluid dynamics 247
Chapter 7. Numerical Simulation of Vortex Gas Flow Using the Generalized Euler Equations 250
7.1. Unsteady flow of a compressible gas in a cavity 250
7.2. Application of the generalized hydrodynamic equations: to the investigation of gas flows in channels with a step 263
7.3. Vortex and turbulent flow of viscous gas in channel with flat plate 275
Chapter 8. Generalized Boltzmann Physical Kinetics in Physics of Plasma and Liquids 296
8.1. Extension of generalized Boltzmann physical kinetics for the transport processes description in plasma 296
8.2. Dispersion equations of plasma in generalized Boltzmann theory 306
8.3. Generalized dispersion relations for plasma: theory and experiment 322
8.4. To the kinetic and hydrodynamic theory of liquids 332
Appendices 348
A 1. Derivation of energy equation for invariant Ea= maV2/a/2 + e 348
A 2. Three-diagonal method of Gauss elimination technics for the differential third-order equation 356
A 3. Some integral calculations in the generalized Navier…Stokes approximation 361
A 4. Three-diagonal method of Gauss elimination technique for the differential second-order equation 363
A 5. Characteristic scales in plasma physics 365
A 6. Dispersion relations in the generalized Boltzmann kinetic theory neglecting the integral collision term 366
References 370
Subject Index 376