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| GENERALIZED BOLTZMANN PHYSICAL KINETICS
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By
Boris Alexeev, Moscow Fine Chemical Technology Institute, Moscow, Russia
Description
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.
Audience
Specialists working in the theory of transport processes in physical systems
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.
Preface
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
References
Subject index
| Bibliographic details |
Hardbound, 376 pages, publication date: MAY-2004
ISBN-13: 978-0-444-51582-7
ISBN-10: 0-444-51582-8
Imprint: ELSEVIER
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USD 190
EUR 135.95
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Last update: 30 Nov 2009
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