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A Possible Solution For The Boltzmann Equation
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Book Synopsis A Possible Solution for the Boltzmann Equation by : Fredrick Zia Michael
Download or read book A Possible Solution for the Boltzmann Equation written by Fredrick Zia Michael and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been an interest in utilizing recent advances in nonlinear partial differential equations solution methods, the equivalent description by stochastic calculus methods, and the state function level of information entropy to the solution of several nonlinear PDEs that are well known in application to problems of gases and fluids and regular to turbulent flow in physics. A recent reported solution has been to the Boltzmann equation. Previously advances were made in solutions to the Navier-Stokes equations of gaseous flow. In this article we derive a possible solution to the 3D Boltzmann equation utilizing transformation methods at the macroscopic functional level, the PDF distribution and stochastic differential equation level. The collision integrals are evaluated utilizing the hypothesis of semiclassical collisions and are obtained from a maximum entropy approach. The collision integral evaluated beyond the molecular chaos approximation, it is 'added' to the phase space variational principle and the Boltzmann equation is transformed to a Fokker-Planck equation which is solved by several known methods both for computational and mathematical analytical applications.
Book Synopsis An Introduction to the Theory of the Boltzmann Equation by : Stewart Harris
Download or read book An Introduction to the Theory of the Boltzmann Equation written by Stewart Harris and published by Courier Corporation. This book was released on 2012-12-27 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solutions of the Boltzmann Equation in Two Space Dimensions by : E. L. Secrest
Download or read book Solutions of the Boltzmann Equation in Two Space Dimensions written by E. L. Secrest and published by . This book was released on 1959 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Boltzmann Equation and Its Applications by : Carlo Cercignani
Download or read book The Boltzmann Equation and Its Applications written by Carlo Cercignani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Solution of the Boltzmann Equation for a Shock Wave by : Harold Meade Mott-Smith
Download or read book The Solution of the Boltzmann Equation for a Shock Wave written by Harold Meade Mott-Smith and published by . This book was released on 1950 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Numerical Solution to the Angle-integrated Boltzmann Equation by : J. H. Bennett
Download or read book A Numerical Solution to the Angle-integrated Boltzmann Equation written by J. H. Bennett and published by . This book was released on 1958 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows by : V.V. Aristov
Download or read book Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows written by V.V. Aristov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New method of solution of a boltzmann equation by : K. B. Winterbon
Download or read book New method of solution of a boltzmann equation written by K. B. Winterbon and published by . This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Solutions of the Boltzmann Equation for Monoenergetic Neutron Transport in Spherical Geometry by : Walter Kofink
Download or read book New Solutions of the Boltzmann Equation for Monoenergetic Neutron Transport in Spherical Geometry written by Walter Kofink and published by . This book was released on 1961 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hydrodynamic Limits of the Boltzmann Equation by : Laure Saint-Raymond
Download or read book Hydrodynamic Limits of the Boltzmann Equation written by Laure Saint-Raymond and published by Springer. This book was released on 2009-04-20 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.
Book Synopsis The Relativistic Boltzmann Equation: Theory and Applications by : Carlo Cercignani
Download or read book The Relativistic Boltzmann Equation: Theory and Applications written by Carlo Cercignani and published by Birkhäuser. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis NUMERICAL SOLUTION OF THE BOLTZMANN EQUATION by : ALEXANDRE JOEL. CHORIN
Download or read book NUMERICAL SOLUTION OF THE BOLTZMANN EQUATION written by ALEXANDRE JOEL. CHORIN and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lecture Notes on the Discretization of the Boltzmann Equation by : N. Bellomo
Download or read book Lecture Notes on the Discretization of the Boltzmann Equation written by N. Bellomo and published by World Scientific. This book was released on 2003 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.
Book Synopsis The Boltzmann Equation by : E.G.D. Cohen
Download or read book The Boltzmann Equation written by E.G.D. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lecture Notes on the Mathematical Theory of the Boltzmann Equation by : N. Bellomo
Download or read book Lecture Notes on the Mathematical Theory of the Boltzmann Equation written by N. Bellomo and published by World Scientific. This book was released on 1995 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Equivalence of the Navier-Stokes and Nonlinear Boltzmann Equations by : Harold Grad
Download or read book Asymptotic Equivalence of the Navier-Stokes and Nonlinear Boltzmann Equations written by Harold Grad and published by . This book was released on 1964 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singular and Nonuniform Limits of Solutions of the Boltzmann Equation (Classic Reprint) by : Harold Grad
Download or read book Singular and Nonuniform Limits of Solutions of the Boltzmann Equation (Classic Reprint) written by Harold Grad and published by Forgotten Books. This book was released on 2016-10-20 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Singular and Nonuniform Limits of Solutions of the Boltzmann Equation For coherence in the oral presentation, the emphasis was placed on a broad survey rather than on the new material We reverse this emphasis in the written text since there are other sources available for the details of many of the nonuniform limits which are here The new material consists of a unified formal treatment of the small mean free path limit in steady boundary value problems (secs. 7-10) and an analysis of the profile of a very strong shock (sec. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
