[PDF] Out Of Equilibrium Dynamics Of Disordered And Stochastic Systems eBook

Author : Giambattista Giacomin
Publisher : Springer
Page : 649 pages
File Size : 31,61 MB
Release : 2019-06-30
Category : Mathematics
ISBN : 3030150968

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Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.

Author : Manuel Osvaldo Cáceres
Publisher : Springer
Page : 568 pages
File Size : 17,40 MB
Release : 2017-03-07
Category : Science
ISBN : 3319515535

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This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluctuations around metastable and unstable points are given. It also describes relaxation theory of non-stationary Markov periodic in time systems. The theory of finite and infinite transport in disordered networks, with a discussion of the issue of anomalous diffusion is introduced. Further, it provides the basis for establishing the relationship between quantum aspects of the theory of linear response and the calculation of diffusion coefficients in amorphous systems.

Author : Véronique Gayrard
Publisher : Springer Nature
Page : 279 pages
File Size : 11,62 MB
Release : 2019-09-15
Category : Mathematics
ISBN : 3030290778

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These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.

Author : Günter Radons
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 20,93 MB
Release : 2005-11-02
Category : Science
ISBN : 3540268693

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Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

Author : Wolfgang Kliemann
Publisher : CRC Press
Page : 397 pages
File Size : 19,28 MB
Release : 2018-05-04
Category : Mathematics
ISBN : 1351091956

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Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.

Author : Sacha Friedli
Publisher : Cambridge University Press
Page : 643 pages
File Size : 47,65 MB
Release : 2017-11-23
Category : Mathematics
ISBN : 1107184827

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A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Author : Uwe C. Täuber
Publisher : Cambridge University Press
Page : 529 pages
File Size : 45,81 MB
Release : 2014-03-06
Category : Science
ISBN : 0521842239

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A comprehensive and unified introduction to describing and understanding complex interacting systems.

Author : Christian Vaca
Publisher :
Page : 113 pages
File Size : 21,40 MB
Release : 2015
Category :
ISBN :

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We discuss some general methodology used to study stochastic systems outside of equilibrium, be it mechanical or thermal equilibrium via the use of the Master equation or Langevin-like methods. We apply these methods to the following problems in non-equilibrium statistical mechanics: The nonlinear dynamics of semiflexible filaments networks under load, the position-velocity distribution of an ion trapped in an RF-trap in the presence of two different buffer gasses at different temperatures, and the response function of two harmonically coupled particles near a mechanical phase transition interacting with a non-Gaussian and Gaussian, white noise source. We find that the movement of a tracer particle in semiflexible networks is governed by single filament crosslinker rupture events. For the ion trapped in the RF-trap, we find non-Maxwellian probability distributions for the system far from equilibrium but in a steady state. We find the response function for the two harmonically coupled particles shows new interactions with the dissipative background due to the introduction of non-Gaussian noise in a spatially asymmetric fashion to lowest order in perturbation theory. Finally we discuss extensions of the methods used to future work.

Author : G‚za Gy”rgyi
Publisher : World Scientific
Page : 608 pages
File Size : 29,15 MB
Release : 1992
Category : Science
ISBN : 9789810209384

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This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to P‚ter Sz‚pfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.