# Generalized Boltzmann Physical Kinetics

**By**

- Boris Alexeev, Physics Department, Moscow Lomonosov University of Fine Chemical Technologies, Moscow, Russia
- Boris Alexeev, Physics Department, Moscow Lomonosov University of Fine Chemical Technologies, Moscow, Russia

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.

View full description### Audience

Specialists working in the theory of transport processes in physical systems

### Book information

- Published: May 2004
- Imprint: ELSEVIER
- ISBN: 978-0-444-51582-7

### Table of Contents

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.PrefaceHistorical introduction and the problem formulationChapter 1. Generalized Boltzmann EquationChapter 2. Theory of generalized hydrodynamic equationsChapter 3. Strict theory of turbulence and some applications of the generalized hydrodynamic theoryChapter 4. Physics of a weakly ionized gasChapter 5. Kinetic coefficients in the theory of the generalized kinetic equationsChapter 6. Some applications of the generalized Boltzmann physical kineticsChapter 7. Numerical simulation of vortex gas flow using the generalized Euler equationsChapter 8. Generalized Boltzmann physical kinetics in physics of plasma and liquidsAppendix 1. Derivation of energy equation for invariant E_alpha = (m_alpha V_alpha^2)/2 + epsilon_alphaAppendix 2. Three-diagonal method of Gauss elimination technique for the differential third order equationAppendix 3. Some integral calculations in the generalized Navier-Stokes approximationAppendix 4. Three-diagonal method of Gauss elimination technique for the differential second order equationAppendix 5. Characteristic scales in plasma physicsAppendix 6. Dispersion relations in the generalized Boltzmann kinetic theory neglecting the integral collision termReferencesSubject index