This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

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

Statistical mechanics may be naturally divided into two branches, one dealing with equilibrium systems, the other with nonequilibrium systems. The equilibrium properties of macroscopic systems are defined in principle by suitable averages in well-defined Gibbs's ensembles. This provides a frame work for both qualitative understanding and quantitative approximations to equilibrium behaviour. Nonequilibrium phenomena are much less understood at the present time. A notable exception is offered by the case of dilute gases. Here a basic equation was established by Ludwig Boltzmann in 1872. The Boltzmann equation still forms the basis for the kinetic theory of gases and has proved fruitful not only for a study of the classical gases Boltzmann had in mind but also, properly generalized, for studying electron transport in solids and plasmas, neutron transport in nuclear reactors, phonon transport in superfluids, and radiative transfer in planetary and stellar atmospheres. Research in both the new fields and the old one has undergone a considerable advance in the last thirty years.

Kinetic Processes in Gases and Plasmas provides a survey of studies on transport and chemical kinetic processes in high temperature gases and plasmas. The book is concerned with conditions produced by the interaction of an object with the atmosphere at hypersonic velocities. The text also provides a foundation for the flow field equations which include chemical reactions and other transport processes, and to present in some detail the microscopic considerations underlying these calculations. Chapters are devoted to the discussion of topics such as the molecular theory of transport equations; transport processes in ionized gases; and inelastic energy transfer processes and chemical kinetics. Aerospace engineers, physicists, chemists, and astrophysicists will find the book a good reference material.

Many areas of physics research depend upon a good physical understanding of charged particle transport processes in gases, a statement which is as true now as it was in the early part of the last century, when modern physics was taking shape. Gas lasers, multi-wire drift chambers used in high energy particle detectors, muon-catalysed fusion in hydrogen and its isotopes and low-temperature plasma processing technology are just a few examples of experiments and processes in which electrons, ions or muons play a key role. The macroscopic properties of these non-equilibrium systems can best be found by averaging microscopic collision properties over a velocity distribution function, calculated from solution of Boltzmann's kinetic equation, using recently developed techniques. This is the realm of the modern kinetic theory of gases, and is the theme of this book.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.

The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description. This book discusses classical and modern methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equation, for small and moderate Knudsen numbers, i.e. at and above the Navier-Stokes-Fourier level. The main methods discussed are the classical Chapman-Enskog and Grad approaches, as well as the new order of magnitude method, which avoids the short-comings of the classical methods, but retains their benefits. The relations between the various methods are carefully examined, and the resulting equations are compared and tested for a variety of standard problems. The book develops the topic starting from the basic description of an ideal gas, over the derivation of the Boltzmann equation, towards the various methods for deriving macroscopic transport equations, and the test problems which include stability of the equations, shock waves, and Couette flow.

In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D.

In contrast to molecular gases (for example, air), the particles of granular gases, such as a cloud of dust, lose part of their kinetic energy when they collide, giving rise to many exciting physical properties. The book provides a self-contained introduction to the theory of granular gases for advanced undergraduates and beginning graduates.

A thorough examination of kinetic theory and its successes in understanding and describing irreversible phenomena in physical systems.