Kinetic Equations and Asymptotic Theory
Author: François Bouchut
Publisher: Elsevier Masson
Published: 2000
Total Pages: 180
ISBN-13:
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Author: François Bouchut
Publisher: Elsevier Masson
Published: 2000
Total Pages: 180
ISBN-13:
DOWNLOAD EBOOKAuthor: Yoshio Sone
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 358
ISBN-13: 146120061X
DOWNLOAD EBOOKThis monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit.
Author: J. R. Mika
Publisher: World Scientific
Published: 1995
Total Pages: 332
ISBN-13: 9789810221256
DOWNLOAD EBOOKIn recent years there appeared a large number of papers as well as chapters in more general monographs devoted to evolution equations containing small (or large) parameters. In this book it is intended to gather the existing results as well as to introduce new ones on the field of initial value problems for singularly perturbed evolution equations of the resonance type. Such equations are of great interest in the applied sciences, particularly in the kinetic theory which is chosen as the main field of application for the asymptotic theory developed in the monograph.
Author: Nicola Bellomo
Publisher: World Scientific Publishing Company
Published: 1991-04-30
Total Pages: 226
ISBN-13: 9813103620
DOWNLOAD EBOOKThis book deals with the relevant mathematical aspects related to the kinetic equations for moderately dense gases with particular attention to the Enskog equation.
Author: Pierre Degond
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 360
ISBN-13: 0817682007
DOWNLOAD EBOOKIn recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Author: Robert T. Glassey
Publisher: SIAM
Published: 1996-01-01
Total Pages: 246
ISBN-13: 0898713676
DOWNLOAD EBOOKStudies the basic equations of kinetic theory in all of space, and contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations. This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although describing very different phenomena, these equations share the same streaming term.
Author: N. Bellomo
Publisher: World Scientific
Published: 1995
Total Pages: 276
ISBN-13: 9789810221669
DOWNLOAD EBOOKThis 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: Nicola Bellomo
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 429
ISBN-13: 1461205131
DOWNLOAD EBOOKModeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis. Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations. An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications. This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process. Topics and Features: * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinetic traffic-flow models * Models of granular media * Large communication networks * Thorough discussion of numerical simulations of Boltzmann equation This new book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers, and postgraduates will find the book a modern and authoritative guide to the topic.
Author: Giacomo Albi
Publisher: Springer Nature
Published: 2021-07-15
Total Pages: 251
ISBN-13: 3030671046
DOWNLOAD EBOOKIn recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and recent advances in the field of kinetic theory of lecturers and speakers of the School “Trails in Kinetic Theory: Foundational Aspects and Numerical Methods”, hosted at Hausdorff Institute for Mathematics (HIM) of Bonn, Germany, 2019, during the Junior Trimester Program “Kinetic Theory”. Focusing on fundamental questions in both theoretical and numerical aspects, it also presents a broad view of related problems in socioeconomic sciences, pedestrian dynamics and traffic flow management.
Author: Richard L. Liboff
Publisher:
Published: 1969
Total Pages: 424
ISBN-13:
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