Generalized Boltzmann Physical Kinetics
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Table of contents
- Cover
- Contentsv
- Prefacevii
- Historical Introduction and the Problem Formulation1
- Chapter 1 Generalized Boltzmann Equation21
- Mathematical introduction. Method of many scales21
- Hierarchy of Bogolubov kinetic equations33
- Derivation of the generalized Boltzmann equation39
- Generalized Boltzmann H-theorem and the problem of irreversibility of time61
- Generalized Boltzmann equation and iterative construction of higher-order equations in the Boltzmann79
- Generalized Boltzmann equation and the theory of non-local kinetic equations with time delay83
- Chapter 2 Theory of Generalized Hydrodynamic Equations91
- Transport of molecular characteristics91
- Hydrodynamic Enskog equations94
- Transformations of the generalized Boltzmann equation96
- Generalized continuity equation98
- Generalized momentum equation for component101
- Generalized energy equation for component106
- Generalized hydrodynamic Euler equations112
- Boundary conditions in the theory of the generalized hydrodynamic equations124
- Chapter 3 Strict Theory of Turbulence and Some Applications of the Generalized Hydrodynamic Theory133
- About principles of classical theory of turbulent flows133
- Theory of turbulence and generalized Euler equations136
- Theory of turbulence and the generalized Enskog equations149
- Generalized hydrodynamic equations and quantum mechanics153
- Chapter 4 Physics of a Weakly Ionized Gas161
- Relaxation of charged particles in ``Maxwellian'' gas and the hydrodynamic aspects of the theory161
- Distribution function of the charged particles in the ``Lorentz'' gas168
- Charged particles in alternating electric field176
- Conductivity of a weakly ionized gas in crossed electric and magnetic fields179
- Chapter 5 Kinetic Coefficients in the Theory of the Generalized Kinetic Equations187
- Linearization of the generalized Boltzmann equation187
- Approximate modified Chapman-Enskog method195
- Kinetic coefficient calculation with taking into account the statistical fluctuations208
- Chapter 6 Some Applications of the Generalized Boltzmann Physical Kinetics215
- Investigation of the generalized Boltzmann equation for electron energy distribution in a constant e215
- Sound propagation studied with the generalized equations of fluid dynamics226
- Shock wave structure examined with the generalized equations of fluid dynamics238
- Chapter 7 Numerical Simulation of Vortex Gas Flow Using the Generalized Euler Equations241
- Unsteady flow of a compressible gas in a cavity241
- Application of the generalized hydrodynamic equations: to the investigation of gas flows in channels254
- Vortex and turbulent flow of viscous gas in channel with flat plate266
- Chapter 8 Generalized Boltzmann Physical Kinetics in Physics of Plasma and Liquids287
- Extension of generalized Boltzmann physical kinetics for the transport processes description in plas287
- Dispersion equations of plasma in generalized Boltzmann theory297
- Generalized dispersion relations for plasma: theory and experiment313
- To the kinetic and hydrodynamic theory of liquids323
- Appendix 1. Derivation of energy equation for invariant Ealpha= malphaValpha2/2 + epsilonalpha339
- Appendix 2. Three-diagonal method of Gauss elimination technics for the differential third-order eq347
- Appendix 3. Some integral calculations in the generalized Navier-Stokes approximation352
- Appendix 4. Three-diagonal method of Gauss elimination technique for the differential second-order e354
- Appendix 5. Characteristic scales in plasma physics356
- Appendix 6. Dispersion relations in the generalized Boltzmann kinetic theory neglecting the integral357
- Referencesvi
- Subject Indexvi
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
· 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