The Boltzmann Equation And Its Applications PDF Download
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Author | : Carlo Cercignani |
Publisher | : Springer Science & Business Media |
Total Pages | : 467 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461210399 |
Download The Boltzmann Equation and Its Applications Book in PDF, ePub and Kindle
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.
Author | : E.G.D. Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 647 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3709183367 |
Download The Boltzmann Equation Book in PDF, ePub and Kindle
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.
Author | : Stewart Harris |
Publisher | : Courier Corporation |
Total Pages | : 242 |
Release | : 2012-12-27 |
Genre | : Science |
ISBN | : 0486143821 |
Download An Introduction to the Theory of the Boltzmann Equation Book in PDF, ePub and Kindle
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.
Author | : Gilberto M. Kremer |
Publisher | : Springer Science & Business Media |
Total Pages | : 313 |
Release | : 2010-08-18 |
Genre | : Technology & Engineering |
ISBN | : 3642116965 |
Download An Introduction to the Boltzmann Equation and Transport Processes in Gases Book in PDF, ePub and Kindle
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.
Author | : Carlo Cercignani |
Publisher | : Birkhäuser |
Total Pages | : 391 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3034881657 |
Download The Relativistic Boltzmann Equation: Theory and Applications Book in PDF, ePub and Kindle
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.
Author | : Carlo Cercignani |
Publisher | : |
Total Pages | : 436 |
Release | : 1975 |
Genre | : Science |
ISBN | : |
Download Theory and Application of the Boltzmann Equation Book in PDF, ePub and Kindle
Appendix after each chapter
Author | : V.V. Aristov |
Publisher | : Springer Science & Business Media |
Total Pages | : 305 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401008663 |
Download Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows Book in PDF, ePub and Kindle
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.
Author | : Alexander Sinitsyn |
Publisher | : Elsevier |
Total Pages | : 320 |
Release | : 2011-06-17 |
Genre | : Mathematics |
ISBN | : 0123877806 |
Download Kinetic Boltzmann, Vlasov and Related Equations Book in PDF, ePub and Kindle
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
Author | : S. Succi |
Publisher | : Oxford University Press |
Total Pages | : 308 |
Release | : 2001-06-28 |
Genre | : Mathematics |
ISBN | : 9780198503989 |
Download The Lattice Boltzmann Equation Book in PDF, ePub and Kindle
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.
Author | : Jun Li |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2020-09-06 |
Genre | : Technology & Engineering |
ISBN | : 9783030264680 |
Download Multiscale and Multiphysics Flow Simulations of Using the Boltzmann Equation Book in PDF, ePub and Kindle
This book provides a comprehensive introduction to the kinetic theory for describing flow problems from molecular scale, hydrodynamic scale, to Darcy scale. The author presents various numerical algorithms to solve the same Boltzmann-like equation for different applications of different scales, in which the dominant transport mechanisms may differ. This book presents a concise introduction to the Boltzmann equation of the kinetic theory, based on which different simulation methods that were independently developed for solving problems of different fields can be naturally related to each other. Then, the advantages and disadvantages of different methods will be discussed with reference to each other. It mainly covers four advanced simulation methods based on the Boltzmann equation (i.e., direct simulation Monte Carlo method, direct simulation BGK method, discrete velocity method, and lattice Boltzmann method) and their applications with detailed results. In particular, many simulations are included to demonstrate the applications for both conventional and unconventional reservoirs. With the development of high-resolution CT and high-performance computing facilities, the study of digital rock physics is becoming increasingly important for understanding the mechanisms of enhanced oil and gas recovery. The advanced methods presented here have broad applications in petroleum engineering as well as mechanical engineering , making them of interest to researchers, professionals, and graduate students alike. At the same time, instructors can use the codes at the end of the book to help their students implement the advanced technology in solving real industrial problems.