Stochastic Dynamics And Boltzmann Hierarchy

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Stochastic Dynamics And Boltzmann Hierarchy

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Author : Dmitriĭ I︠A︡kovlevich Petrina
language : en
Publisher: Walter de Gruyter
Release Date : 2009

Stochastic Dynamics And Boltzmann Hierarchy written by Dmitriĭ I︠A︡kovlevich Petrina and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

"This book starts with a survey of results concerning existence of solutions of the BBGKY hierarchy for a system of hard spheres. It is followed (a) by a justification of the Boltzmann-Grad limit, (b) a derivation of the stochastic dynamics from the Hamiltonian dynamics of hard spheres in the Boltzmann-Grad limit, and (c) a derivation of the Ito-Liouville equation. In the next chapter, the stochastic Boltzmann hierarchy with boundary conditions is derived from the stochastic dynamics of point particles. Subsequently the existence of solutions of the stochastic Boltzmann hierarchy is proved and the property of chaos is established, and these results are used to deduce the Boltzmann equation." --Book Jacket.

Stochasty Na Dynamika Ta Ijerarchija Bol Cmana

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Author : D. Ya Petrina
language : en
Publisher:
Release Date : 2008

Stochasty Na Dynamika Ta Ijerarchija Bol Cmana written by D. Ya Petrina and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Stochastic Dynamics And Boltzmann Hierarchy

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Author : Dmitri Ya. Petrina
language : en
Publisher: Walter de Gruyter
Release Date : 2009-07-14

Stochastic Dynamics And Boltzmann Hierarchy written by Dmitri Ya. Petrina and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-14 with Mathematics categories.

The monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics. The book systematizes rigorous results obtained in this field in recent years, and it presents contemporary methods for the investigation of evolution equations of infinite-particle systems. The book is intended for experts in statistical physics, mathematical physics, and probability theory and for students of universities specialized in mathematics and physics.

Stochastic Dynamics And Boltzmann Hierarchy

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Author : Dmitrij Âkovlevič Petrina
language : en
Publisher:
Release Date : 2008

Stochastic Dynamics And Boltzmann Hierarchy written by Dmitrij Âkovlevič Petrina and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Many Particle Dynamics And Kinetic Equations

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Author : C. Cercignani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Many Particle Dynamics And Kinetic Equations written by C. Cercignani 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.

As our title suggests, there are two aspects in the subject of this book. The first is the mathematical investigation of the dynamics of infinite systems of in teracting particles and the description of the time evolution of their states. The second is the rigorous derivation of kinetic equations starting from the results of the aforementioned investigation. As is well known, statistical mechanics started in the last century with some papers written by Maxwell and Boltzmann. Although some of their statements seemed statistically obvious, we must prove that they do not contradict what me chanics predicts. In some cases, in particular for equilibrium states, it turns out that mechanics easily provides the required justification. However things are not so easy, if we take a step forward and consider a gas is not in equilibrium, as is, e.g., the case for air around a flying vehicle. Questions of this kind have been asked since the dawn of the kinetic theory of gases, especially when certain results appeared to lead to paradoxical conclu sions. Today this matter is rather well understood and a rigorous kinetic theory is emerging. The importance of these developments stems not only from the need of providing a careful foundation of such a basic physical theory, but also to exhibit a prototype of a mathematical construct central to the theory of non-equilibrium phenomena of macroscopic size.

Statistical Mechanics And The Physics Of Many Particle Model Systems

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Author : Alexander Leonidovich Kuzemsky
language : en
Publisher: World Scientific
Release Date : 2017-02-24

Statistical Mechanics And The Physics Of Many Particle Model Systems written by Alexander Leonidovich Kuzemsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-24 with Science categories.

The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models.This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography.The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.

Mystery Of Time The Asymmetry Of Time And Irreversibility In The Natural Processes

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Author : Alexander Leonidovich Kuzemsky
language : en
Publisher: World Scientific
Release Date : 2022-10-14

Mystery Of Time The Asymmetry Of Time And Irreversibility In The Natural Processes written by Alexander Leonidovich Kuzemsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-14 with Science categories.

The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time.The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.

Mathematical Foundations Of Classical Statistical Mechanics

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Author : D.Ya. Petrina
language : en
Publisher: CRC Press
Release Date : 2002-04-11

Mathematical Foundations Of Classical Statistical Mechanics written by D.Ya. Petrina and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-11 with Mathematics categories.

This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov

Stability Analysis Of Impulsive Functional Differential Equations

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Author : Ivanka Stamova
language : en
Publisher: Walter de Gruyter
Release Date : 2009-10-16

Stability Analysis Of Impulsive Functional Differential Equations written by Ivanka Stamova and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-16 with Mathematics categories.

This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.

Hierarchical Methods For Dynamics In Complex Molecular Systems

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Author : Johannes Grotendorst
language : en
Publisher: Forschungszentrum Jülich
Release Date : 2012

Hierarchical Methods For Dynamics In Complex Molecular Systems written by Johannes Grotendorst and has been published by Forschungszentrum Jülich this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.