[PDF] Dynamics Of Condensation In Stochastic Particle Systems eBook

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Page : pages
File Size : 30,46 MB
Release : 2007
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Stochastic particle systems far from equilibrium show a great variety of critical phenomena already in one dimension. We concentrate on models where the number of particles is locally conserved. In the first part of the thesis we study boundary induced phase transitions, by characterizing stationary measures of the asymmetric simple exclusion process on a semi-infinite lattice with generalized boundary conditions. In the same context we establish the hydrodynamic limit for the multi species zero range process (ZRP) and solve the macroscopic system of hyperbolic conservation laws with open boundaries. In the second part we present a rigorous analysis of the condensation transition in the ZRP with periodic boundaries. We show the equivalence of ensembles and for a single species system we prove that the condensed phase typically concentrates on a single lattice site. Using random walk arguments supported by Monte Carlo simulations, we also derive a coarsening scaling law for the dynamics of the condensation, depending on the symmetry of the jump probabilities and on space dimension.

Author : Giambattista Giacomin
Publisher : Springer
Page : 649 pages
File Size : 14,17 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 : Weizhu Bao
Publisher : World Scientific
Page : 307 pages
File Size : 23,79 MB
Release : 2007
Category : Mathematics
ISBN : 9812770224

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The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on Nanoscale Material Interfaces: Experiment, Theory and Simulation'' from November 2004 to January 2005. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field. This invaluable volume collects the expanded lecture notes of four of those self-contained tutorials. The topics covered include dynamics in different models of domain coarsening and coagulation and their mathematical analysis in material sciences; a mathematical and computational study for quantized vortices in the celebrated GinzburgOCoLandau models of superconductivity and the mean field GrossOCoPitaevskii equations of superfluidity; the nonlinear SchrAdinger equation and applications in BoseOCoEinstein condensation and plasma physics as well as their efficient and accurate computation; and finally, an introduction to constitutive modeling of macromolecular fluids within the framework of the kinetic theory. This volume serves to inspire graduate students and researchers who will embark upon original research work in these fields."

Author : Patrícia Gonçalves
Publisher : Springer
Page : 395 pages
File Size : 31,23 MB
Release : 2015-04-04
Category : Mathematics
ISBN : 3319166379

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This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems. The purpose of the second meeting on Particle Systems and PDEs was to bring together renowned researchers working actively in the respective fields, to discuss their topics of expertise and to present recent scientific results in both areas. Further, the meeting was intended to present the subject of interacting particle systems, its roots in and impacts on the field of physics and its relation with PDEs to a vast and varied public, including young researchers. The book also includes the notes from two mini-courses presented at the conference, allowing readers who are less familiar with these areas of mathematics to more easily approach them. The contributions will be of interest to mathematicians, theoretical physicists and other researchers interested in interacting particle systems, partial differential equations, statistical mechanics, stochastic processes, kinetic theory, dynamical systems and mathematical modeling aspects.

Author : Andreas Schadschneider
Publisher : Elsevier
Page : 585 pages
File Size : 20,77 MB
Release : 2010-10-01
Category : Science
ISBN : 0080560520

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The first part of the book provides a pedagogical introduction to the physics of complex systems driven far from equilibrium. In this part we discuss the basic concepts and theoretical techniques which are commonly used to study classical stochastic transport in systems of interacting driven particles. The analytical techniques include mean-field theories, matrix product ansatz, renormalization group, etc. and the numerical methods are mostly based on computer simulations. In the second part of the book these concepts and techniques are applied not only to vehicular traffic but also to transport and traffic-like phenomena in living systems ranging from collective movements of social insects (for example, ants) on trails to intracellular molecular motor transport. These demonstrate the conceptual unity of the fundamental principles underlying the apparent diversity of the systems and the utility of the theoretical toolbox of non-equilibrium statistical mechanics in interdisciplinary research far beyond the traditional disciplinary boundaries of physics. Leading industry experts provide a broad overview of the interdisciplinary nature of physics Presents unified descriptions of intracellular, ant, and vehicular traffic from a physics point of view Applies theoretical methods in practical everyday situations Reference and guide for physicists, engineers and graduate students

Author : Lev. P. Pitaevskii
Publisher : Oxford University Press
Page : 392 pages
File Size : 45,2 MB
Release : 2003-04-03
Category : Science
ISBN : 9780198507192

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Bose-Einstein Condensation represents a new state of matter and is one of the cornerstones of quantum physics, resulting in the 2001 Nobel Prize. Providing a useful introduction to one of the most exciting field of physics today, this text will be of interest to a growing community of physicists, and is easily accessible to non-specialists alike.