Generalized Boltzmann Physical Kinetics

The most important result obtained by Prof. B. Alexeev and reflected in the book is connected with new theory of transport processes in gases, plasma and liquids. It was shown by Prof. B. Alexeev that well-known Boltzmann equation, which is the basement of the classical kinetic theory, is wrong in the definite sense. Namely in the Boltzmann equation should be introduced the additional terms which generally speaking are of the same order of value as classical ones. It leads to dramatic changing in transport theory. The coincidence of experimental and theoretical data became much better. Particularly it leads to the strict theory of turbulence and possibility to calculate the turbulent flows from the first principles of physics. · Boltzmann equation (BE) is valid only for particles, which can be considered as material points, generalized Boltzmann equation (GBE) removes this restriction. · GBE contains additional terms in comparison with BE, which cannot be omitted · GBE leads to strict theory of turbulence · GBE gives all micro-scale turbulent fluctuations in tabulated closed analytical form for all flows · GBE leads to generalization of electro-dynamic Maxwell equations · GBE gives new generalized hydrodynamic equations (GHE) more effective than classic Navier-Stokes equations · GBE can be applied for description of flows for intermediate diapason of Knudsen numbers · Asymptotical solutions of GBE remove contradictions in the theory of Landau damping in plasma Contents......Page 6 Preface......Page 8 Historical Introduction and the Problem Formulation......Page 10 Mathematical introduction. Method of many scales......Page 30 Hierarchy of Bogolubov kinetic equations......Page 42 Derivation of the generalized Boltzmann equation......Page 48 Generalized Boltzmann H-theorem and the problem of irreversibility of time......Page 70 Generalized Boltzmann equation and iterative construction of higher-order equations in the Boltzmann kinetic theory......Page 88 Generalized Boltzmann equation and the theory of non-local kinetic equations with time delay......Page 92 Transport of molecular characteristics......Page 100 Hydrodynamic Enskog equations......Page 103 Transformations of the generalized Boltzmann equation......Page 105 Generalized continuity equation......Page 107 Generalized momentum equation for component......Page 110 Generalized energy equation for component......Page 115 Generalized hydrodynamic Euler equations......Page 121 Boundary conditions in the theory of the generalized hydrodynamic equations......Page 133 About principles of classical theory of turbulent flows......Page 142 Theory of turbulence and generalized Euler equations......Page 145 Theory of turbulence and the generalized Enskog equations......Page 158 Generalized hydrodynamic equations and quantum mechanics......Page 162 Relaxation of charged particles in "Maxwellian" gas and the hydrodynamic aspects of the theory......Page 170 Distribution function of the charged particles in the "Lorentz" gas......Page 177 Charged particles in alternating electric field......Page 185 Conductivity of a weakly ionized gas in crossed electric and magnetic fields......Page 188 Linearization of the generalized Boltzmann equation......Page 196 Approximate modified Chapman-Enskog method......Page 204 Kinetic coefficient calculation with taking into account the statistical fluctuations......Page 217 Investigation of the generalized Boltzmann equation for electron energy distribution in a constant electric field with due regard for inelastic collisions......Page 224 Sound propagation studied with the generalized equations of fluid dynamics......Page 235 Shock wave structure examined with the generalized equations of fluid dynamics......Page 247 Unsteady flow of a compressible gas in a cavity......Page 250 Application of the generalized hydrodynamic equations: to the investigation of gas flows in channels with a step......Page 263 Vortex and turbulent flow of viscous gas in channel with flat plate......Page 275 Extension of generalized Boltzmann physical kinetics for the transport processes description in plasma......Page 296 Dispersion equations of plasma in generalized Boltzmann theory......Page 306 Generalized dispersion relations for plasma: theory and experiment......Page 322 To the kinetic and hydrodynamic theory of liquids......Page 332 Appendix 1. Derivation of energy equation for invariant Ealpha = malphaValpha2/2 + epsilonalpha......Page 348 Appendix 2. Three-diagonal method of Gauss elimination technics for the differential third-order equation......Page 356 Appendix 3. Some integral calculations in the generalized Navier-Stokes approximation......Page 361 Appendix 4. Three-diagonal method of Gauss elimination technique for the differential second-order equation......Page 363 Appendix 5. Characteristic scales in plasma physics......Page 365 Appendix 6. Dispersion relations in the generalized Boltzmann kinetic theory neglecting the integral collision term......Page 366 References......Page 370 Subject Index......Page 376 The most important result obtained by Prof. B. Alexeev and reflected in the book is connected with new theory of transport processes in gases, plasma and liquids. It was shown by Prof. B. Alexeev that well-known Boltzmann equation, which is the basement of the classical kinetic theory, is wrong in the definite sense. Namely in the Boltzmann equation should be introduced the additional terms which generally speaking are of the same order of value as classical ones. It leads to dramatic changing in transport theory. The coincidence of experimental and theoretical data became much better. Particularly it leads to the strict theory of turbulence and possibility to calculate the turbulent flows from the first principles of physics.

· Boltzmann equation (BE) is valid only for particles, which can be considered as material points, generalized Boltzmann equation (GBE) removes this restriction.
· GBE contains additional terms in comparison with BE, which cannot be omitted
· GBE leads to strict theory of turbulence
· GBE gives all micro-scale turbulent fluctuations in tabulated closed analytical form for all flows
· GBE leads to generalization of electro-dynamic Maxwell equations
· GBE gives new generalized hydrodynamic equations (GHE) more effective than classic Navier-Stokes equations
· GBE can be applied for description of flows for intermediate diapason of Knudsen numbers
· Asymptotical solutions of GBE remove contradictions in the theory of Landau damping in plasma