On The Dynamics Of Correlations In Scaling Limits Of Interacting Particle Systems
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Scaling Limits Of Interacting Particle Systems
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Author : Claude Kipnis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Scaling Limits Of Interacting Particle Systems written by Claude Kipnis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The idea of writing up a book on the hydrodynamic behavior of interacting particle systems was born after a series of lectures Claude Kipnis gave at the University of Paris 7 in the spring of 1988. At this time Claude wrote some notes in French that covered Chapters 1 and 4, parts of Chapters 2, 5 and Appendix 1 of this book. His intention was to prepare a text that was as self-contained as possible. lt would include, for instance, all tools from Markov process theory ( cf. Appendix 1, Chaps. 2 and 4) necessary to enable mathematicians and mathematical physicists with some knowledge of probability, at the Ievel of Chung (1974), to understand the techniques of the theory of hydrodynamic Iimits of interacting particle systems. In the fall of 1991 Claude invited me to complete his notes with him and transform them into a book that would present to a large audience the latest developments of the theory in a simple and accessible form. To concentrate on the main ideas and to avoid unnecessary technical difficulties, we decided to consider systems evolving in finite lattice spaces and for which the equilibrium states are product measures. To illustrate the techniques we chose two well-known particle systems, the generalized exclusion processes and the zero-range processes. We also conceived the book in such a manner that most chapters can be read independently of the others. Here are some comments that might help readers find their way.
On The Dynamics Of Correlations In Scaling Limits Of Interacting Particle Systems
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Author : Raphael Elias Winter
language : en
Publisher:
Release Date : 2018
On The Dynamics Of Correlations In Scaling Limits Of Interacting Particle Systems written by Raphael Elias Winter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Dynamics categories.
From Particle Systems To Partial Differential Equations
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Author : Cédric Bernardin
language : en
Publisher: Springer Nature
Release Date : 2021-05-30
From Particle Systems To Partial Differential Equations written by Cédric Bernardin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-30 with Mathematics categories.
This book includes the joint proceedings of the International Conference on Particle Systems and PDEs VI, VII and VIII. Particle Systems and PDEs VI was held in Nice, France, in November/December 2017, Particle Systems and PDEs VII was held in Palermo, Italy, in November 2018, and Particle Systems and PDEs VIII was held in Lisbon, Portugal, in December 2019. Most of the papers are dealing with mathematical problems motivated by different applications in physics, engineering, economics, chemistry and biology. They illustrate methods and topics in the study of particle systems and PDEs and their relation. The book is recommended to probabilists, analysts and to those mathematicians in general, whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to those physicists who work in statistical mechanics and kinetic theory.
Large Scale Dynamics Of Interacting Particles
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Author : Herbert Spohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Large Scale Dynamics Of Interacting Particles written by Herbert Spohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
From Particle Systems To Partial Differential Equations
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Author : Eric Carlen
language : en
Publisher: Springer Nature
Release Date : 2024-09-25
From Particle Systems To Partial Differential Equations written by Eric Carlen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-25 with Science categories.
This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations X, which was held at the University of Minho, Braga, Portugal, from 2022. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology.
Stochastic Partial Differential Equations And Applications
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Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2002-04-05
Stochastic Partial Differential Equations And Applications written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.
Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
Mathematical Methods For Hydrodynamic Limits
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Author : Anna DeMasi
language : en
Publisher: Springer
Release Date : 2006-11-14
Mathematical Methods For Hydrodynamic Limits written by Anna DeMasi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
From Particle Systems To Partial Differential Equations
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Author : Patrícia Gonçalves
language : en
Publisher: Springer
Release Date : 2018-12-29
From Particle Systems To Partial Differential Equations written by Patrícia Gonçalves and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-29 with Science categories.
This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations V, which was held at the University of Minho, Braga, Portugal, from the 28th to 30th November 2016. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book appeals to probabilists, analysts and also to mathematicians in general whose work focuses on topics in mathematical physics, stochastic processes and differential equations, as well as to physicists working in the area of statistical mechanics and kinetic theory.
Self Organized Criticality Three Decades Later
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Author : Subhrangshu Sekhar Manna
language : en
Publisher: Frontiers Media SA
Release Date : 2022-01-28
Self Organized Criticality Three Decades Later written by Subhrangshu Sekhar Manna and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-28 with Science categories.
A Non Equilibrium Statistical Mechanics
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Author : Tian-Quan Chen
language : en
Publisher: World Scientific
Release Date : 2003
A Non Equilibrium Statistical Mechanics written by Tian-Quan Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book presents the construction of an asymptotic technique for solving the Liouville equation, which is to some degree an analogue of the Enskog-Chapman technique for solving the Boltzmann equation. Because the assumption of molecular chaos has been given up at the outset, the macroscopic variables at a point, defined as arithmetic means of the corresponding microscopic variables inside a small neighborhood of the point, are random in general. They are the best candidates for the macroscopic variables for turbulent flows. The outcome of the asymptotic technique for the Liouville equation reveals some new terms showing the intricate interactions between the velocities and the internal energies of the turbulent fluid flows, which have been lost in the classical theory of BBGKY hierarchy.