Advances in Kinetic Theory and Continuum Mechanics

Advances in Kinetic Theory and Continuum Mechanics
Author: Renee Gatignol
Publisher: Springer Science & Business Media
Total Pages: 307
Release: 2012-12-06
Genre: Science
ISBN: 3642502350

This volume contains the proceedings of the symposium held on Friday 6 July 1990 at the University Pierre et Marie Curie (Paris VI), France, in honor of Professor Henri Cabannes on the occasion of his retirement. There were about one hundred participants from nine countries: Canada, France, Germany, Italy, Japan, Norway, Portugal, the Netherlands, and the USA. Many of his past students or his colleagues were among the participants. The twenty-six papers in this volume are written versions submitted by the authors and cover almost all the fields in which Professor Cabannes has actively worked for more than forty-five years. The papers are presented in four chapters: classical kinetic theory and fluid dynamics, discrete kinetic theory, applied fluid mechanics, and continuum mechanics. The editors would like to take this opportunity to thank the generous spon sors of the symposium: the University Pierre et Marie Curie, Commissariat a l'Energie Atomique (especially Academician R. Dautray and Dr. N. Camarcat) and Direction des Recherches et Etudes Techniques (especially Professor P. Lallemand). Many thanks are also due to all the participants for making the symposium a success. Finally, we thank Professor W. Beiglbock and his team at Springer-Verlag for producing this volume.

Advances in Kinetic Theory and Computing

Advances in Kinetic Theory and Computing
Author: B. Perthame
Publisher: World Scientific
Total Pages: 232
Release: 1994
Genre: Mathematics
ISBN: 9789810216719

This selection of 8 papers discusses ?Equations of Kinetic Physics? with emphasis on analysis, modelling and computing. The first 3 papers are on numerical methods for Vlasov-Poisson and Vlasov-Maxwell Equations ? Comparison between Particles and Eulerian Methods (G Manfredi and M R Feix), Computing BGK Instability with Eulerian Codes (M R Feix, Pertrand & A Ghieco) and Coupling Particles and Eulerian Methods (S Mas-Gallic and P A Raviart) ? Followed by a survey of kinetic and macroscopic models for semiconductor devices ? Boltzmann Equation, Drift-Diffusion Models (F Poupaud). In addition, there are 2 papers on the modelling and analysis of singular perturbation problems arising in plasma physics ? Derivation of the Child-Lagmuyr Emission Laws (P Degond) and Euler Models with Small Pressure Terms (F Bouchut) ? followed by two papers on the analysis and numerical analysis of the Boltzmann equations ? Symmetry Properties in the Polynomials Arising in Chapman-Enskog Expansion (L Desvillettes and F Golse) and A General Introduction to Computing the Boltzmann Equations with Random Particle Methods (B Perthame).

Continuum Mechanics

Continuum Mechanics
Author: I-Shih Liu
Publisher: Springer Science & Business Media
Total Pages: 303
Release: 2013-04-17
Genre: Science
ISBN: 3662050560

This concise textbook develops step by step the fundamental principles of continuum mechanics. Emphasis is on mathematical clarity, and an extended appendix provides the required background knowledge in linear algebra and tensor calculus. After introducing the basic notions about general kinematics, balance equations, material objectivity and constitutive functions, the book turns to the presentation of rational thermodynamics by stressing the role of Lagrange multipliers in deriving constitutive funcitions from the underlying entropy principle. A brief lecture on extended thermodynamics closes the book. Many examples and exercises round off the material presendted in the chapters. The book addresses primarily advanced undergraduate students in theoretical physics, applied mathematics and materials sciences.

Kinetic Theory and Fluid Dynamics

Kinetic Theory and Fluid Dynamics
Author: Yoshio Sone
Publisher: Springer Science & Business Media
Total Pages: 358
Release: 2012-12-06
Genre: Science
ISBN: 146120061X

This 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.

Handbook of Mathematical Fluid Dynamics

Handbook of Mathematical Fluid Dynamics
Author: S. Friedlander
Publisher: Gulf Professional Publishing
Total Pages: 627
Release: 2003-03-27
Genre: Science
ISBN: 008053354X

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.

Mathematics Applied to Continuum Mechanics

Mathematics Applied to Continuum Mechanics
Author: Lee A. Segel
Publisher: SIAM
Total Pages: 598
Release: 2007-07-12
Genre: Science
ISBN: 0898716209

This classic work gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text for both classroom use and independent study.

Kinetic Theory

Kinetic Theory
Author: R.L. Liboff
Publisher: Springer Science & Business Media
Total Pages: 587
Release: 2006-03-30
Genre: Science
ISBN: 0387217754

This book goes beyond the scope of other works in the field with its thorough treatment of applications in a wide variety of disciplines. The third edition features a new section on constants of motion and symmetry and a new appendix on the Lorentz-Legendre expansion.

Dynamics of Polymeric Liquids, Volume 1

Dynamics of Polymeric Liquids, Volume 1
Author: R. Byron Bird
Publisher: Wiley-Interscience
Total Pages: 680
Release: 1987-05-27
Genre: Science
ISBN:

This revision of an introductory text examines Newtonian liquids and polymer fluid mechanics. It begins with a review of the main ideas of fluid dynamics as well as key points of Newtonian fluids.