Lecture Notes On Mathematical Theory Of The Boltzmann Equation
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Direct Methods For Solving The Boltzmann Equation And Study Of Nonequilibrium Flows
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Author : V.V. Aristov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Direct Methods For Solving The Boltzmann Equation And Study Of Nonequilibrium Flows written by V.V. Aristov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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 The Mathematical Theory Of The Boltzmann Equation
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Author : N. Bellomo
language : en
Publisher: World Scientific
Release Date : 1995
Lecture Notes On The Mathematical Theory Of The Boltzmann Equation written by N. Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
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.
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models
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Author : Nicola Bellomo
language : en
Publisher: World Scientific
Release Date : 2000-01-11
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by Nicola Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-11 with Mathematics categories.
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.
Entropy Methods For The Boltzmann Equation
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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2007
Entropy Methods For The Boltzmann Equation written by and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Handbook Of Differential Equations Evolutionary Equations
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Author : C.M. Dafermos
language : en
Publisher: Gulf Professional Publishing
Release Date : 2004
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous, and in depth surveys on the most important aspects of the present theory.
A Quest Towards A Mathematical Theory Of Living Systems
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Author : Nicola Bellomo
language : en
Publisher: Birkhäuser
Release Date : 2017-07-13
A Quest Towards A Mathematical Theory Of Living Systems written by Nicola Bellomo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-13 with Mathematics categories.
This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field. A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.
Stochastic Numerics For The Boltzmann Equation
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Author : Sergej Rjasanow
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-04
Stochastic Numerics For The Boltzmann Equation written by Sergej Rjasanow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-04 with Mathematics categories.
Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.
Handbook Of Mathematical Fluid Dynamics
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Author : S. Friedlander
language : en
Publisher: Elsevier
Release Date : 2002-07-09
Handbook Of Mathematical Fluid Dynamics written by S. Friedlander and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-09 with Science categories.
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Boltzmann S Legacy
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Author : Jakob Yngvason
language : en
Publisher: European Mathematical Society
Release Date : 2008
Boltzmann S Legacy written by Jakob Yngvason and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Biography & Autobiography categories.
Ludwig Eduard Boltzmann (1844-1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. To commemorate the 100th anniversary of his death in Duino, the International Symposium ``Boltzmann's Legacy'' was held at the Erwin Schrodinger International Institute for Mathematical Physics in June 2006. This text covers a broad spectrum of topics ranging from equilibrium statistical and nonequilibrium statistical physics, ergodic theory and chaos to basic questions of biology and historical accounts of Boltzmann's work. Besides the lectures presented at the symposium the volume also contains contributions specially written for this occasion. The articles give a broad overview of Boltzmann's legacy to the sciences from the standpoint of some of today's leading scholars in the field. The book addresses students and researchers in mathematics, physics, and the history of science.
Mathematical Methods For The Natural And Engineering Sciences
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Author : Ronald E Mickens
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-04-13
Mathematical Methods For The Natural And Engineering Sciences written by Ronald E Mickens and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-13 with Science categories.
This book provides a variety of methods required for the analysis and solution of equations which arise in the modeling of phenomena from the natural and engineering sciences. It can be used productively by both undergraduate and graduate students, as well as others who need to learn and understand these techniques. A detailed discussion is also presented for several topics that are usually not included in standard textbooks at this level: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations, and various perturbation methods. Each chapter contains a large number of worked examples and provides references to the appropriate literature.