The Mathematical Theory of Dilute Gases

The Mathematical Theory of Dilute Gases

Author: Carlo Cercignani

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 357

ISBN-13: 1441985247

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The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.


Transport Phenomena and Kinetic Theory

Transport Phenomena and Kinetic Theory

Author: Carlo Cercignani

Publisher: Springer Science & Business Media

Published: 2007-12-03

Total Pages: 274

ISBN-13: 0817645543

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The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.


Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

Author: V.V. Aristov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 9401008663

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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.


Lecture Notes On Mathematical Theory Of The Boltzmann Equation

Lecture Notes On Mathematical Theory Of The Boltzmann Equation

Author: Nicola Bellomo

Publisher: World Scientific

Published: 1995-08-31

Total Pages: 273

ISBN-13: 9814500844

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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

Transport Processes in Multicomponent Plasma

Author: V.M. Zhdanov

Publisher: CRC Press

Published: 2002-04-11

Total Pages: 294

ISBN-13: 9780415279208

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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.


Transport Theory

Transport Theory

Author: James J. Duderstadt

Publisher: John Wiley & Sons

Published: 1979

Total Pages: 630

ISBN-13:

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Problems after each chapter


Kinetic Theory of Granular Gases

Kinetic Theory of Granular Gases

Author: Nikolai V. Brilliantov

Publisher: Oxford University Press

Published: 2010-11-11

Total Pages: 343

ISBN-13: 0199588139

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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.