The Boltzmann Equation and Its Applications

The Boltzmann Equation and Its Applications

Author: Carlo Cercignani

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 467

ISBN-13: 1461210399

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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.


The Boltzmann Equation

The Boltzmann Equation

Author: E.G.D. Cohen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 647

ISBN-13: 3709183367

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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.


The Relativistic Boltzmann Equation: Theory and Applications

The Relativistic Boltzmann Equation: Theory and Applications

Author: Carlo Cercignani

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 391

ISBN-13: 3034881657

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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.


An Introduction to the Theory of the Boltzmann Equation

An Introduction to the Theory of the Boltzmann Equation

Author: Stewart Harris

Publisher: Courier Corporation

Published: 2012-12-27

Total Pages: 242

ISBN-13: 0486143821

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This introductory graduate-level text emphasizes physical aspects of the theory of Boltzmann's equation in a detailed presentation that doubles as a practical resource for professionals. 1971 edition.


An Introduction to the Boltzmann Equation and Transport Processes in Gases

An Introduction to the Boltzmann Equation and Transport Processes in Gases

Author: Gilberto M. Kremer

Publisher: Springer Science & Business Media

Published: 2010-08-18

Total Pages: 313

ISBN-13: 3642116965

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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.


Kinetic Boltzmann, Vlasov and Related Equations

Kinetic Boltzmann, Vlasov and Related Equations

Author: Alexander Sinitsyn

Publisher: Elsevier

Published: 2011-06-17

Total Pages: 321

ISBN-13: 0123877806

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Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory.This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance. - Reviews the whole field from the beginning to today - Includes practical applications - Provides classical and modern (semi-analytical) solutions


Kinetic Equations

Kinetic Equations

Author: Alexander V. Bobylev

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-10-12

Total Pages: 275

ISBN-13: 3110550172

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The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences. The aim of the series is to be an active forum for the dissemination of up-to-date information in the form of authoritative works that will serve the applied mathematics community as the basis for further research. Editorial Board Rémi Abgrall, Universität Zürich, Switzerland José Antonio Carrillo de la Plata, University of Oxford, UK Jean-Michel Coron, Université Pierre et Marie Curie, Paris, France Athanassios S. Fokas, Cambridge University, UK Irene Fonseca, Carnegie Mellon University, Pittsburgh, USA


Hydrodynamic Limits of the Boltzmann Equation

Hydrodynamic Limits of the Boltzmann Equation

Author: Laure Saint-Raymond

Publisher: Springer Science & Business Media

Published: 2009-03-26

Total Pages: 203

ISBN-13: 3540928464

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"The material published in this volume comes essentially from a course given at the Conference on "Boltzmann equation and fluidodynamic limits", held in Trieste in June 2006." -- preface.


The Lattice Boltzmann Equation

The Lattice Boltzmann Equation

Author: S. Succi

Publisher: Oxford University Press

Published: 2001-06-28

Total Pages: 308

ISBN-13: 9780198503989

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Certain forms of the Boltzmann equation, have emerged, which relinquish most mathematical complexities of the true Boltzmann equation. This text provides a detailed survey of Lattice Boltzmann equation theory and its major applications.