Contribution a l'etude mathematique des equations de Boltzmann et de Landau en theorie cinetique des gaz et des plasmas PDF Download

Author: Cédric Villani
Publisher:
ISBN:
Category :
Languages : fr
Pages : 0

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Author: Cédric Villani
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Nous étudions des équations cinétiques de la forme f/t + v. *#xf = q(f, f), t0, x, r#n, v, r#n, qui décrivent l'évolution d'un gaz ou d'un plasma dans lequel les particules subissent des collisions modélisées par l'opérateur q, dit - de Boltzmann : q(f, f) dv#* d b(v v#*,) (f'f'#* ff#*), - ou de Landau : q(f, f) = /v#i dv#*a#i#j(v v#*) (f♯*f/v#j ff#*/v#*#, #j). Les trois premières parties de cette thèse concernent les équations homogènes (indépendantes de x) #tf = q(f, f). On insiste particulièrement sur deux points : les collisions rasantes et la dissipation d'entropie. Dans la première partie, on étudie le problème de Cauchy associé aux équations de Boltzmann et de Landau homogènes (pour des sections efficaces réalistes et éventuellement singulières), des propriétés de régularité des solutions, ainsi que l'asymptotique des collisions rasantes qui permet de passer d'une équation à l'autre. La deuxième partie est consacrée au cas particulier des molécules maxwelliennes. Sous cette hypothèse, on effectue une étude détaillée du problème de Cauchy et du retour vers l'équilibre, ainsi que des liens entre théorie cinétique et théorie de l'information. Dans la troisième partie, on utilise les résultats précédents pour obtenir des estimations explicites sur la vitesse de retour vers l'équilibre dans le cas général. Dans la quatrième partie, on obtient des résultats partiels sur le problème de Cauchy pour l'équation de Landau inhomogène, et quelques estimations nouvelles sur l'équation de Boltzmann inhomogène. Enfin, dans la cinquième partie, on établit diverses formes conservatives de l'opérateur de Boltzmann, avec application à l'asymptotique des collisions rasantes.

Author: Cédric Villani
Publisher:
ISBN:
Category :
Languages : fr
Pages : 456

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Author: Roberto Monaco
Publisher: World Scientific
ISBN: 9789812702937
Category : Mathematics
Languages : en
Pages : 600

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This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Chaos in Some Linear Kinetic Models (J Banasiak); Inverse Problems in Photon Transport. Part I: Determination of Physical and Geometrical Features of an Interstellar Cloud (A Belleni-Morante et al.); Inverse Problems in Photon Transport. Part II: Features of a Source Inside an Interstellar Cloud (A Belleni-Morante & R Riganti); The Riemann Problem for a Binary Non-Reacting Mixture of Euler Fluids (F Brini & T Ruggeri); Rate of Convergence toward the Equilibrium in Degenerate Settings (L Desvillettes & C Villani); Asymptotic and Other Properties of Positive Definite Integral Measures for Nonlinear Diffusion (J N Flavin); Thermocapillary Fluid and Adiabatic Waves Near its Critical Point (H Gouin); Constitutive Models for Atactic Elastomers (C O Horgan & G Saccomandi); Considerations about the Gibbs Paradox (I Mller); Transport Coefficients in Stochastic Models of the Revised Enskog and Square-Well Kinetic Theories (J Polewczak & G Stell); Some Recent Mathematical Results in Mixtures Theory of Euler Fluids (T Ruggeri); From Kinetic Systems to Diffusion Equations (F Salvarani & J L Vizquez); Non-Boussinesq Convection in Porous Media (B Straughan); and other papers. Readership: Researchers, academics and graduate students working in the fields of continuum mechanics, wave propagation, stability in fluids, kinetic theory and computational fluid dynamics."

Author: Henri Berestycki
Publisher: Springer Science & Business Media
ISBN: 9781402009730
Category : Mathematics
Languages : en
Pages : 548

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Proceedings of the NATO Advanced Study Institute on PDEs in Models of Superfluidity, Superconductivity and Reactive Flows, held in Cargèse, France, from 21 June to 3 July 1999

Author: Lorenzo Pareschi
Publisher: Nova Publishers
ISBN: 9781594545030
Category : Science
Languages : en
Pages : 238

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The book is divided into three parts, which contain respectively recent results in the kinetic theory of granular gases, kinetic theory of chemically reacting gases, and numerical methods for kinetic systems. Part I is devoted to theoretical aspects of granular gases. Part II presents recent results on modelling of kinetic systems in which molecules can undergo binary collisions in presence of chemical reactions and/or in presence of quantum effects. Part III contains several contributions related to the construction of suitable numerical methods and simulations for granular gases.

Author: Elaine McKinnon Riehm
Publisher: American Mathematical Soc.
ISBN: 0821869140
Category : Mathematics
Languages : en
Pages : 287

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Despite the renown of the Fields Medals, J.C. Fields has been until now a rather obscure figure, and recovering details about his professional activities and personal life was not at all a simple task. This work is a triumph of persistence with far-flung archival and documentary sources, and provides a rich non-mathematical portrait of the man in all aspects of his life and career. Highly readable and replete with period detail, the book sheds useful light on the mathematical and scientific world of Fields' time, and is sure to remain the definitive biographical study. --Tom Archibald, Simon Fraser University, Burnaby, BC, Canada Drawing on a wide array of archival sources, Riehm and Hoffman provide a vivid account of Fields' life and his part in the founding of the highest award in mathematics. Filled with intriguing detail--from a childhood on the shores of Lake Ontario, through the mathematics seminars of late 19th century Berlin, to the post-WW1 years of the fragmented international mathematical community--it is a richly textured story engagingly and sympathetically told. Read this book and you will understand why Fields never wanted the medal to bear his name and yet why, quite rightly, it does. --June Barrow-Green, Open University, Milton Keynes, United Kingdom One of the little-known effects of World War I was the collapse of international scientific cooperation. In mathematics, the discord continued after the war's end and after the Treaty of Versailles had been signed in 1919. Many distinguished scientists were involved in the war and its aftermath, and from their letters and papers, now almost a hundred years old, we learn of their anguished wartime views and their struggles afterwards either to prolong the schism in mathematics or to end it. J.C. Fields, the foremost Canadian mathematician of his time, was educated in Canada, the United States, and Germany, and championed an international spirit of cooperation to further the frontiers of mathematics. It was during the awkward post-war period that J.C. Fields established the Fields Medal, an international prize for outstanding research, which soon became the highest award in mathematics. J.C. Fields intended it to be an international medal, and a glance at the varying backgrounds of the fifty-two Fields medallists shows it to be so. Who was Fields? What carried him from Hamilton, Canada West, where he was born in 1863, into the middle of this turbulent era of international scientific politics? A modest mathematician, he was an unassuming man. This biography outlines Fields' life and times and the difficult circumstances in which he created the Fields Medal. It is the first such published study.

Author: S. Friedlander
Publisher: Elsevier
ISBN: 0080532926
Category : Science
Languages : en
Pages : 829

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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.

Author: Giacomo Albi
Publisher: Springer Nature
ISBN: 3030671046
Category : Science
Languages : en
Pages : 251

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In 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: Roberto Monaco
Publisher: World Scientific
ISBN: 981448329X
Category : Science
Languages : en
Pages : 590

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Book Description
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences