Generalized Boltzmann Physical Kinetics

Boris V. Alexeev9780444515827, 0444515828

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

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Table of contents :
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