Nonequilibrium Phase Transitions in Lattice Models
Nonequilibrium Phase Transitions in Lattice Models

Author: Joaquin Marro

Publisher: Cambridge University Press

Published: 1999-05-06

Total Pages: 345

ISBN-13: 0521480620

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This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena and examine simulation results in detail. Several possible theoretical approaches to the driven lattice gas are presented. In the next two chapters, absorbing-state transitions are discussed in detail. The later chapters examine a variety of systems subject to dynamic disorder before returning to look at the more surprising effects of multiparticle rules, nonunique absorbing-states and conservation laws. Examples are given throughout the book, the emphasis being on using simple representations of nature to describe ordering in real systems. The use of methods such as mean-field theory, Monte Carlo simulation, and the concept of universality to study and interpret these models is described. Detailed references are included.

Non-Equilibrium Phase Transitions
Non-Equilibrium Phase Transitions

Author: Malte Henkel

Publisher: Springer Science & Business Media

Published: 2008-11-27

Total Pages: 385

ISBN-13: 1402087659

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This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

Statistical Mechanics of Lattice Systems
Statistical Mechanics of Lattice Systems

Author: Sacha Friedli

Publisher: Cambridge University Press

Published: 2017-11-23

Total Pages: 643

ISBN-13: 1107184827

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

Universality in Nonequilibrium Lattice Systems
Universality in Nonequilibrium Lattice Systems

Author: G‚za ?dor

Publisher: World Scientific

Published: 2008

Total Pages: 297

ISBN-13: 981281227X

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"Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically." "The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results."--BOOK JACKET.

Directions In Condensed Matter Physics: Memorial Volume In Honor Of Shang-keng Ma
Directions In Condensed Matter Physics: Memorial Volume In Honor Of Shang-keng Ma

Author: Geoffrey Grinstein

Publisher: World Scientific

Published: 1986-08-01

Total Pages: 270

ISBN-13: 9814513601

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This volume collects several in-depth articles giving lucid discussions on new developments in statistical and condensed matter physics. Many, though not all, contributors had been in touch with the late S-K Ma. Written by some of the world's experts and originators of new ideas in the field, this book is a must for all researchers in theoretical physics. Most of the articles should be accessible to diligent graduate students and experienced readers will gain from the wealth of materials contained herein.

Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter
Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter

Author: Alessandro Manacorda

Publisher: Springer

Published: 2018-07-28

Total Pages: 211

ISBN-13: 3319950800

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This book investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The book guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system.

Nonequilibrium Statistical Physics
Nonequilibrium Statistical Physics

Author: Roberto Livi

Publisher: Cambridge University Press

Published: 2017-10-05

Total Pages: 439

ISBN-13: 1107049547

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A comprehensive and pedagogical text on nonequilibrium statistical physics, covering topics from random walks to pattern formation.

Phase Transitions
Phase Transitions

Author: Ricard V. Solé

Publisher: Princeton University Press

Published: 2011-08-14

Total Pages: 238

ISBN-13: 0691150753

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Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, Phase Transitions examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur. Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Solé shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies. Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.

Self-Organization in Complex Ecosystems. (MPB-42)
Self-Organization in Complex Ecosystems. (MPB-42)

Author: Ricard Solé

Publisher: Princeton University Press

Published: 2012-01-06

Total Pages: 384

ISBN-13: 140084293X

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Can physics be an appropriate framework for the understanding of ecological science? Most ecologists would probably agree that there is little relation between the complexity of natural ecosystems and the simplicity of any example derived from Newtonian physics. Though ecologists have long been interested in concepts originally developed by statistical physicists and later applied to explain everything from why stock markets crash to why rivers develop particular branching patterns, applying such concepts to ecosystems has remained a challenge. Self-Organization in Complex Ecosystems is the first book to clearly synthesize what we have learned about the usefulness of tools from statistical physics in ecology. Ricard Solé and Jordi Bascompte provide a comprehensive introduction to complex systems theory, and ask: do universal laws shape the structure of ecosystems, at least at some scales? They offer the most compelling array of theoretical evidence to date of the potential of nonlinear ecological interactions to generate nonrandom, self-organized patterns at all levels. Tackling classic ecological questions--from population dynamics to biodiversity to macroevolution--the book's novel presentation of theories and data shows the power of statistical physics and complexity in ecology. Self-Organization in Complex Ecosystems will be a staple resource for years to come for ecologists interested in complex systems theory as well as mathematicians and physicists interested in ecology.