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Statistical Mechanics and Fractals

Author: Roland L. Dobrushin

Publisher: Springer

Published: 2006-11-15

Total Pages: 103

ISBN-13: 3540482059

This book is composed of two texts, by R.L. Dobrushin and S. Kusuoka, each representing the content of a course of lectures given by the authors. They are pitched at graduate student level and are thus very accessible introductions to their respective subjects for students and non specialists. CONTENTS: R.L. Dobrushin: On the Way to the Mathematical Foundations of Statistical Mechanics.- S. Kusuoka: Diffusion Processes on Nested Fractals.

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Author: Michel Laurent Lapidus

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 592

ISBN-13: 0821836382

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This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics

Author: Rainer Klages

Publisher: World Scientific

Published: 2007

Total Pages: 458

ISBN-13: 9812771514

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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.

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Author: Michel Laurent Lapidus

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 534

ISBN-13: 0821836374

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Statistical Mechanics and Fractals

Author: Roland L. Dobrushin

Publisher: Springer

Published: 1993

Total Pages: 116

ISBN-13: 9783540575160

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Fractal Concepts in Condensed Matter Physics

Author: Tsuneyoshi Nakayama

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 216

ISBN-13: 3662051931

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Concisely and clearly written by two foremost scientists, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics. The authors’ unified description of different dynamic problems makes the book extremely accessible.

Critical Phenomena in Natural Sciences

Author: Didier Sornette

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 445

ISBN-13: 366204174X

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A modern up-to-date introduction for readers outside statistical physics. It puts emphasis on a clear understanding of concepts and methods and provides the tools that can be of immediate use in applications.

From Newton to Mandelbrot

Author: Dietrich Stauffer

Publisher: Springer

Published: 2013-11-11

Total Pages: 233

ISBN-13: 3642867804

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From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a diskette where a selection of executable programs exploring the fractal concept can be found.

From Newton to Mandelbrot

Author: Dietrich Stauffer

Publisher: Springer Science & Business Media

Published: 1996

Total Pages: 244

ISBN-13: 9783540565895

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"From Newton to Mandelbrot. A Primer in Theoretical Physics with Fractals for the Personal Computer" takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions and a MS-DOS diskette where a selection of executable programs exploring the fractal concept can be found. The Diskette The programs included on a 3 1/2" MS-DOS diskette runs on any IBM or compatible computer. System requirements: EGA or VGA graphics card, 16 colors and 1 MB RAM, MS-DOS 3.30 or higher; 386 processor or higher: - Fractal coastline - Gasket - Forest fire - Aggregation - Diffusion-limited aggregation

Microscopic Chaos, Fractals And Transport In Nonequilibrium Statistical Mechanics

Author: Rainer Klages

Publisher: World Scientific

Published: 2007-06-15

Total Pages: 458

ISBN-13: 9814479314

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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.