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 Mathematical Methods for Hydrodynamic Limits written by Anna Demasi and published by . This book was released on 2014-09-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 From Divergent Power Series to Analytic Functions written by Werner Balser and published by Springer. This book was released on 1994-08-29 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
Download or read book Hydrodynamic Limits and Related Topics written by Shui Feng and published by American Mathematical Soc.. This book was released on with total page 164 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 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 Nonlinear Stochastic PDEs written by Tadahisa Funaki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.
Download or read book From Kinetic Models to Hydrodynamics written by Matteo Colangeli and published by Springer Science & Business Media. This book was released on 2013-03-25 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.
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 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 Nonequilibrium Problems in Many Particle Systems written by Carlo Cercignani and published by Springer. This book was released on 1993-08-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the text of four sets of lectures delivered at the third session of the Summer School organized by C.I.M.E. (Centro Internazionale Matematico Estivo). These texts are preceded by an introduction written by C. Cercignani and M. Pulvirenti which summarizes the present status in the area of Nonequilibrium Problems in Many-Particle Systems and tries to put the contents of the different sets of lectures in the right perspective, in order to orient the reader. The lectures deal with the global existence of weak solutions for kinetic models and related topics, the basic concepts of non-standard analysis and their application to gas kinetics, the kinetic equations for semiconductors and the entropy methods in the study of hydrodynamic limits. CONTENTS: C. Cercignani, M. Pulvirenti: Nonequilibrium Problems in Many-Particle Systems. An Introduction.- L. Arkeryd: Some Examples of NSA in Kinetic Theory.- P.L. Lions: Global Solutions of Kinetic Models and Related Problems.- P.A. Markowich: Kinetic Models for Semiconductors.- S.R.S. Varadhan: Entropy Methods in Hydrodynamic Scaling.
Download or read book An Introduction to the Theory of Hydrodynamic Limits written by Fritz József and published by . This book was released on 2001 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Problems and Methods of Hydrodynamic Weather Forecasting written by Vladimir Gordin and published by CRC Press. This book was released on 2000-09-20 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parame
Download or read book Hydrodynamic Instability written by American Mathematical Society and published by . This book was released on 1962 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The State of Matter written by Michael Aizenman and published by World Scientific. This book was released on 1994 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, a collection of works by leading figures in the field, provides a view of the current research in a broad area of mathematical physics.The collection celebrates Elliot H Lieb's sixtieth birthday and his imprint on the subject. The preface by W Thirring offers a glimpse into the life and work-style of Lieb and some of his contemporaries.
Download or read book Hydrodynamic Limits of the Boltzmann Equation written by Laure Saint-Raymond and published by Springer. This book was released on 2009-04-20 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.
Download or read book Free Boundary Problems in PDEs and Particle Systems written by Gioia Carinci and published by Springer. This book was released on 2016-06-22 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases.All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms.In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.
