Microscopic Chaos Fractals And Transport In Nonequilibrium Statistical Mechanics

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Microscopic Chaos Fractals And Transport In Nonequilibrium Statistical Mechanics

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Author : Rainer Klages
language : en
Publisher: World Scientific
Release Date : 2007

Microscopic Chaos Fractals And Transport In Nonequilibrium Statistical Mechanics written by Rainer Klages and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory. Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity. Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors. The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

Microscopic Chaos Fractals And Transport In Nonequilibrium Steady States Die Ver Ffentlichung Einer Erg Nzten Und Berarbeiteten Version Bei World Scientific Publishing Ist F R 2005 06 Geplant

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Author :
language : en
Publisher:
Release Date : 2004

Microscopic Chaos Fractals And Transport In Nonequilibrium Steady States Die Ver Ffentlichung Einer Erg Nzten Und Berarbeiteten Version Bei World Scientific Publishing Ist F R 2005 06 Geplant written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this thesis we summarize recent theoretical advances along these lines. We focus on two different approaches to nonequilibrium transport: One considers Hamiltonian dynamical systems under nonequilibrium boundary conditions, another one suggests a non-Hamiltonian approach to nonequilibrium situations created by external electric fields and by temperature or velocity gradients. A surprising result related to the former approach is that in simple low-dimensional periodic models the deterministic transport coefficients are typically fractal functions of control parameters. These fractal transport coefficients yield the first central theme of this thesis. We exemplify this phenomenon by deterministic diffusion in a simple chaotic map. We then construct an arsenal of analytical and numerical methods for computing further transport coefficients such as electrical conductivities andchemical reaction rates. These methods are applied to hierarchies of chaotic dynamical systems that are successively getting more complex, starting from abstract one-dimensional maps generalizing a simple random walk on the line up to particle billiards that should be directly accessible in experiments. In all cases, the resulting transport coefficients turn out to be either strictly fractal, or at least to be profoundly irregular. The impact of random perturbations on these quantities is also investigated. We furthermore provide some access roads towards a physical understanding of these fractalities. The second central theme is formed by a critical assessment of the non-Hamiltonian approach to nonequilibrium transport. Here we consider situations where the nonequilibrium constraints pump energy into a system, hence there must be some thermal reservoir that prevents the system from heating up. For this purpose a deterministic and t.

Microscopic Chaos Fractals And Transport In Nonequilibrium Steady States

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Author : Rainer Klages
language : en
Publisher:
Release Date : 2003

Microscopic Chaos Fractals And Transport In Nonequilibrium Steady States written by Rainer Klages and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.

Nonequilibrium Statistical Physics Of Small Systems

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Author : Rainer Klages
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-15

Nonequilibrium Statistical Physics Of Small Systems written by Rainer Klages and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-15 with Science categories.

This book offers a comprehensive picture of nonequilibrium phenomena in nanoscale systems. Written by internationally recognized experts in the field, this book strikes a balance between theory and experiment, and includes in-depth introductions to nonequilibrium fluctuation relations, nonlinear dynamics and transport, single molecule experiments, and molecular diffusion in nanopores. The authors explore the application of these concepts to nano- and biosystems by cross-linking key methods and ideas from nonequilibrium statistical physics, thermodynamics, stochastic theory, and dynamical systems. By providing an up-to-date survey of small systems physics, the text serves as both a valuable reference for experienced researchers and as an ideal starting point for graduate-level students entering this newly emerging research field.

Time Reversability Computer Simulation Algorithms Chaos

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Author : William Graham Hoover
language : en
Publisher: World Scientific
Release Date : 2012

Time Reversability Computer Simulation Algorithms Chaos written by William Graham Hoover and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach. Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers.

Time Reversibility Computer Simulation Algorithms Chaos

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Author : William Graham Hoover
language : en
Publisher: World Scientific
Release Date : 2012

Time Reversibility Computer Simulation Algorithms Chaos written by William Graham Hoover and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach. Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers.

Reviews Of Nonlinear Dynamics And Complexity

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Author : Heinz Georg Schuster
language : en
Publisher: John Wiley & Sons
Release Date : 2010-07-06

Reviews Of Nonlinear Dynamics And Complexity written by Heinz Georg Schuster and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-06 with Science categories.

Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new developments. This third volume contains new topics ranging from chaotic computing, via random dice tossing and stochastic limit-cycle oscillators, to a number theoretic example of self-organized criticality, wave localization in complex networks and anomalous diffusion. A first-class board of international scientists advises the editor, such that the carefully selected and invited contributions represent the latest and most relevant findings.

From Hamiltonian Chaos To Complex Systems

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Author : Xavier Leoncini
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-14

From Hamiltonian Chaos To Complex Systems written by Xavier Leoncini 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 2013-07-14 with Technology & Engineering categories.

From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems.

Chaotic Dynamics

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Author : Tamás Tél
language : en
Publisher: Cambridge University Press
Release Date : 2006-08-24

Chaotic Dynamics written by Tamás Tél and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-24 with Mathematics categories.

A clear introduction to chaotic phenomena for undergraduate students in science, engineering, and mathematics.

Thermodynamics And Statistical Mechanics Of Small Systems

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Author : Andrea Puglisi
language : en
Publisher: MDPI
Release Date : 2018-09-04

Thermodynamics And Statistical Mechanics Of Small Systems written by Andrea Puglisi and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-04 with categories.

This book is a printed edition of the Special Issue "Thermodynamics and Statistical Mechanics of Small Systems" that was published in Entropy