· 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
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.
Specialists working in the theory of transport processes in physical systems
Generalized Boltzmann Physical Kinetics, 1st Edition
The Boltzmann equation (BE) is the classical basis of the transport processes description in plasma, neutral gases, liquids and physics of solid state. But the BE has many shortcomings, for example, the BE is valid only for particles which can be considered as material points, and the appearance of cross-sections in the collision integral is one of the contradictions of the Boltzmann kinetic theory. In other words the BE is not valid in the scale connected with the time of collision. The theory delivered in this book is based on the generalized Boltzmann equation (GBE).
The following is realized in the book:
The fundamental fact is shown that the introduction of a third scale, which describes the distribution function variations on a time scale of the order of the collision time, leads to a single order terms in the BE prior to the Bogolyubov-chain-decoupling approximations, and to terms proportional to the mean time between collisions after these approximations. It follows that the BE requires a radical modification – which is exactly, what the GBE provides.
Many applications of the generalized Boltzmann kinetic theory are considered including transport processes in neutral and ionized gases and liquids. Applications correspond to different areas of physics: acoustics of rarefied gases, strict theory of turbulent flows, Landau damping in plasma and so on.
Historical introduction and the problem formulation
Chapter 1. Generalized Boltzmann Equation
Chapter 2. Theory of generalized hydrodynamic equations
Chapter 3. Strict theory of turbulence and some applications of the generalized hydrodynamic theory
Chapter 4. Physics of a weakly ionized gas
Chapter 5. Kinetic coefficients in the theory of the generalized kinetic equations
Chapter 6. Some applications of the generalized Boltzmann physical kinetics
Chapter 7. Numerical simulation of vortex gas flow using the generalized Euler equations
Chapter 8. Generalized Boltzmann physical kinetics in physics of plasma and liquids
Appendix 1. Derivation of energy equation for invariant E_alpha = (m_alpha V_alpha^2)/2 + epsilon_alpha
Appendix 2. Three-diagonal method of Gauss elimination technique for the differential third order equation
Appendix 3. Some integral calculations in the generalized Navier-Stokes approximation
Appendix 4. Three-diagonal method of Gauss elimination technique for the differential second order equation
Appendix 5. Characteristic scales in plasma physics
Appendix 6. Dispersion relations in the generalized Boltzmann kinetic theory neglecting the integral collision term