This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

Transport Processes in Multicomponent Plasma is a revised and updated version of the original Russian edition. The book examines transport phenomena in multicomponent plasma and looks at important issues such as partially ionized gases, molecular gas mixtures and methods of calculating kinetic coefficients. It makes a logical progression from simpler to more general problems, and the results presented in the book may be used to calculate the kinetic coefficients of plasma in electric and magnetic fields. The author concludes by describing several practical applications such as electrical conductivity and Hall's effect in MHD-generators. Transport Processes in Multicomponent Plasma will be of interest to advanced students and specialized researchers working in various aspects of plasma physics, including both cold plasmas for industrial research and high temperature plasmas in fusion.

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.

This book presents theoretical and experimental investigations of mechanical behavior of solids under shock loading and highlights a multi-scale exchange process of energy and momentum between meso and macroscopic hierarchy. It also widely covers experimental approaches for the multi-scale response of solids to impacts including uniaxial strain conditions and high-velocity penetration processes. The content comprises two parts. The first part overviews modeling and theory of dynamically deformed solids from the multi-scale point of view. The second part describes experimental characterization of shock-induced solids and experimental probing of mesostructured and mesoscale dynamic processes in solids. The theory presented in the first part is then verified as it is compared with i) experiments of shock loading into different kinds of solids and ii) probed microstructure of post-shocked specimens by scanning electron microscopy, transmission electron microscopy and optical microscopy. The text is written on the basis of author’s lectures at universities and thus is concisely described for postgraduate students. It is also useful for researchers who work on the theory of multi-scale mechanics of solids and engineers who work on testing materials under dynamic loading.

Transport Phenomena has been revised to include deeper and more extensive coverage of heat transfer, enlarged discussion of dimensional analysis, a new chapter on flow of polymers, systematic discussions of convective momentum,and energy. Topics also include mass transport, momentum transport and energy transport, which are presented at three different scales: molecular, microscopic and macroscopic. If this is your first look at Transport Phenomena you'll quickly learn that its balanced introduction to the subject of transport phenomena is the foundation of its long-standing success.

In this volume, we have collected a series of reviews that cover both experimental and theoretical work geared toward the more exact requirements of current SFE applications. While we have artificially divided the volume into experimental and theoretical sections, natural overlaps will be apparent. Many of the papers on experimental and theoretical sections, natural overlaps will be apparent. Many of the papers on experimental technique contain discussions on equation of state correlations. Indeed, a good deal of the experimental work is intimately tied to a mathematical description of fluid mixtures. The theoretical section presents reviews that cover the modern theory of critical phenomena, methods to correlate near critical experimental results and approaches to understanding the behavior of near critical fluids from microscopic theory. It is hoped that the scope of these reviews will provide the reader with the basis to further develop our understanding of the behavior of supercritical fluids.