Author : N. Bellomo
Publisher : World Scientific
Page : 276 pages
File Size : 39,63 MB
Release : 1995
Category : Science
ISBN : 9789810221669
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.
Author : N. Bellomo
Publisher : World Scientific
Page : 317 pages
File Size : 19,49 MB
Release : 2003
Category : Science
ISBN : 9812382259
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.
Author : Laure Saint-Raymond
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 36,28 MB
Release : 2009-03-26
Category : Mathematics
ISBN : 3540928464
"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.
Author : V.V. Aristov
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 12,28 MB
Release : 2012-12-06
Category : Science
ISBN : 9401008663
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 :
Publisher : Springer Science & Business Media
Page : 122 pages
File Size : 20,70 MB
Release : 2007
Category :
ISBN : 3540737049
Author : Nicola Bellomo
Publisher : World Scientific
Page : 355 pages
File Size : 39,17 MB
Release : 2000-01-11
Category : Mathematics
ISBN : 9814494259
This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.
Author : Carlo Cercignani
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 34,37 MB
Release : 2013-12-01
Category : Science
ISBN : 1441985247
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.
Author : Nicola Bellomo
Publisher : World Scientific
Page : 317 pages
File Size : 29,18 MB
Release : 2003-01-24
Category : Mathematics
ISBN : 9814487066
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.
Author : Stewart Harris
Publisher : Courier Corporation
Page : 242 pages
File Size : 10,40 MB
Release : 2012-12-27
Category : Science
ISBN : 0486143821
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 : Carlo Cercignani
Publisher : Birkhäuser
Page : 391 pages
File Size : 45,28 MB
Release : 2012-12-06
Category : Science
ISBN : 3034881657
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.
