Statistical Dynamics: Matter Out Of Equilibrium
Statistical Dynamics: Matter Out Of Equilibrium

Author: Radu Balescu

Publisher: World Scientific

Published: 1997-04-19

Total Pages: 340

ISBN-13: 1783262613

DOWNLOAD EBOOK

In the first part of this book, classical nonequilibrium statistical mechanics is developed. Starting from the Hamiltonian dynamics of the molecules, it leads through the irreversible kinetic equations to the level of fluid mechanics. For simple systems, all the transport coefficients are determined by the molecular properties.The second part of the book treats complex systems that require a more extensive use of statistical concepts. Such problems, which are at the forefront of research, include: continuous time random walks, non-Markovian diffusion processes, percolation and related critical phenomena, transport on fractal structures, transport and deterministic chaos. These “strange transport processes” differ significantly from the usual (diffusive) transport. Their inclusion in a general treatise on statistical mechanics is a special feature of this invaluable book./a

A Concise Introduction to the Statistical Physics of Complex Systems
A Concise Introduction to the Statistical Physics of Complex Systems

Author: Eric Bertin

Publisher: Springer Science & Business Media

Published: 2011-09-28

Total Pages: 85

ISBN-13: 3642239234

DOWNLOAD EBOOK

This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting ‘entities’, and on the other to predict the macroscopic (or collective) behavior of the system considered from the microscopic laws ruling the dynamics of the individual ‘entities’. These two goals are, to some extent, also shared by what is nowadays called ‘complex systems science’ and for these reasons, systems studied in the framework of statistical physics may be considered as among the simplest examples of complex systems—allowing in addition a rather well developed mathematical treatment.

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

Author: Marco Pettini

Publisher: Springer Science & Business Media

Published: 2007-06-14

Total Pages: 460

ISBN-13: 0387499571

DOWNLOAD EBOOK

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.

Chaos
Chaos

Author: Angelo Vulpiani

Publisher: World Scientific

Published: 2010

Total Pages: 482

ISBN-13: 9814277665

DOWNLOAD EBOOK

Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.

Statistical Mechanics of Nonequilibrium Liquids
Statistical Mechanics of Nonequilibrium Liquids

Author: Denis J. Evans

Publisher: ANU E Press

Published: 2007-08-01

Total Pages: 318

ISBN-13: 1921313234

DOWNLOAD EBOOK

"There is a symbiotic relationship between theoretical nonequilibrium statistical mechanics on the one hand and the theory and practice of computer simulation on the other. Sometimes, the initiative for progress has been with the pragmatic requirements of computer simulation and at other times, the initiative has been with the fundamental theory of nonequilibrium processes. This book summarises progress in this field up to 1990"--Publisher's description.

Dynamics and Bifurcations
Dynamics and Bifurcations

Author: Jack K. Hale

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 577

ISBN-13: 1461244269

DOWNLOAD EBOOK

In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.

Dynamical Systems and Statistical Mechanics
Dynamical Systems and Statistical Mechanics

Author: I͡Akov Grigorʹevich Sinaĭ

Publisher: American Mathematical Soc.

Published: 1991

Total Pages: 266

ISBN-13: 9780821841020

DOWNLOAD EBOOK

Dynamical systems and statistical mechanics have been developing in close interaction during the past decade, and the papers in this book attest to the productiveness of this interaction. The first paper in the collection contains a new result in the theory of quantum chaos, a burgeoning line of inquiry which combines mathematics and physics and which is likely in time to produce many new connections and applications. Another paper, related to the renormalization group method for the study of maps of the circle with singularities due to a jump in the derivative, demonstrates that the fixed point of the renormgroup can in this case be sufficiently described. In certain situations, the renormgroup methods work better than the traditional KAM method. Other topics covered include: thermodynamic formalism for certain infinite-dimensional dynamical systems, numerical simulation of dynamical systems with hyperbolic behaviour, periodic points of holomorphic maps, the theory of random media, statistical properties of the leading eigenvalue in matrix ensembles of large dimension, spectral properties of the one-dimensional Schrodinger operator. This volume will appeal to many readers, as it covers a broad range of topics and presents a view of some of the frontier research in the Soviet Union today.