Download or read book Hydrodynamic Limits of the Boltzmann Equation written by Laure Saint-Raymond and published by Springer Science & Business Media. This book was released on 2009-03-26 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Scaling Limits of Interacting Particle Systems written by Claude Kipnis and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.
Download or read book Introduction to Hydrodynamic Stability written by P. G. Drazin and published by Cambridge University Press. This book was released on 2002-09-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
Download or read book Mathematical Methods for Hydrodynamic Limits written by Anna DeMasi and published by Springer. This book was released on 2006-11-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.
Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2005-10-05 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
Download or read book Theory and Computation in Hydrodynamic Stability written by W. O. Criminale and published by Cambridge University Press. This book was released on 2019 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers modern and numerical techniques for the stability of fluid flow with illustrations, an extensive bibliography, and exercises with solutions.
Download or read book Lectures on Probability Theory and Statistics written by Amir Dembo and published by Springer Science & Business Media. This book was released on 2005-11-03 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.
Download or read book An Introduction to Magnetohydrodynamics written by P. A. Davidson and published by Cambridge University Press. This book was released on 2001-03-05 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids.
Download or read book The Theory And Practice Of Hydrodynamics And Vibration written by Subrata Kumar Chakrabarti and published by World Scientific Publishing Company. This book was released on 2002-11-05 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the basics of the hydrodynamics and vibration of structures subjected to environmental loads. It describes the interaction of hydrodynamics with the associated vibration of structures, giving simple explanations. Emphasis is placed on the applications of the theory to practical problems. Several case studies are provided to show how the theory outlined in the book is applied in the design of structures. Background material needed for understanding fluid-induced vibrations of structures is given to make the book reasonably self-sufficient. Examples are taken mainly from the novel structures that are of interest today, including ocean and offshore structures and components.Besides being a text for undergraduates, this book can serve as a handy reference for design engineers and consultants involved in the design of structures subjected to dynamics and vibration.
Download or read book Hydrodynamic Limits and Related Topics written by Shui Feng and published by American Mathematical Soc.. This book was released on 2000 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in nongradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced graduate course in hydrodynamic limits and interacting particle systems.
Download or read book Kinetic Equations written by Alexander V. Bobylev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.
Download or read book Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics written by Errico Presutti and published by Springer Science & Business Media. This book was released on 2008-11-01 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.
Download or read book Large Scale Dynamics of Interacting Particles written by Herbert Spohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the explanation of large-scale dynamics (evolution differential equations) from models of a very large number of interacting particles. This book addresses both researchers and students. Much of the material presented has never been published in book-form before.
Download or read book Hydrodynamic Instabilities written by François Charru and published by Cambridge University Press. This book was released on 2011-06-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The instability of fluid flows is a key topic in classical fluid mechanics because it has huge repercussions for applied disciplines such as chemical engineering, hydraulics, aeronautics, and geophysics. This modern introduction is written for any student, researcher, or practitioner working in the area, for whom an understanding of hydrodynamic instabilities is essential. Based on a decade's experience of teaching postgraduate students in fluid dynamics, this book brings the subject to life by emphasizing the physical mechanisms involved. The theory of dynamical systems provides the basic structure of the exposition, together with asymptotic methods. Wherever possible, Charru discusses the phenomena in terms of characteristic scales and dimensional analysis. The book includes numerous experimental studies, with references to videos and multimedia material, as well as over 150 exercises which introduce the reader to new problems.
Download or read book Lecture Notes on the Mathematical Theory of the Boltzmann Equation written by N. Bellomo and published by World Scientific. This book was released on 1995 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elasto Hydrodynamic Lubrication written by D. Dowson and published by Elsevier. This book was released on 2014-07-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elasto-Hydrodynamic Lubrication deals with the mechanism of elasto-hydrodynamic lubrication, that is, the lubrication regime in operation over the small areas where machine components are in nominal point or line contact. The lubrication of rigid contacts is discussed, along with the effects of high pressure on the lubricant and bounding solids. The governing equations for the solution of elasto-hydrodynamic problems are presented. Comprised of 13 chapters, this volume begins with an overview of elasto-hydrodynamic lubrication and representation of contacts by cylinders, followed by a discussion on equations relevant to lubrication, including the Reynolds equation. The reader is then introduced to lubrication of rigid cylinders; the importance of film thickness in highly loaded rigid contacts; the elasticity of solids in contact; and the theory of elasto-hydrodynamic lubrication. Subsequent chapters focus on apparatus and measurements of film thickness and film shape; friction and viscosity; and lubrication of gears and roller bearings. This book will be of interest to tribologists.
Download or read book Encyclopedia of Mathematical Physics written by Jean-Pierre Françoise and published by Academic Press. This book was released on 2006 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, France Gregory L. Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy.
