Statistical Mechanics And Fractals
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Statistical Mechanics And Fractals
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Author : Roland L. Dobrushin
language : en
Publisher: Springer
Release Date : 2006-11-15
Statistical Mechanics And Fractals written by Roland L. Dobrushin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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
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Author : Michel Laurent Lapidus
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Fractal Geometry And Applications A Jubilee Of Benoit Mandelbrot written by Michel Laurent Lapidus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
From Newton To Mandelbrot
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Author : Dietrich Stauffer
language : en
Publisher: Springer
Release Date : 2013-11-11
From Newton To Mandelbrot written by Dietrich Stauffer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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.
Analysis Probability And Mathematical Physics On Fractals
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Author : Patricia Alonso Ruiz
language : en
Publisher: World Scientific
Release Date : 2020-02-26
Analysis Probability And Mathematical Physics On Fractals written by Patricia Alonso Ruiz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii
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Author : David Carfi
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-24
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii written by David Carfi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-24 with Mathematics categories.
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
Fractals In Physics
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Author : L. Pietronero
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Fractals In Physics written by L. Pietronero and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
Fractals in Physics
From Newton To Mandelbrot
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Author : Dietrich Stauffer
language : en
Publisher: Springer Science & Business Media
Release Date : 1996
From Newton To Mandelbrot written by Dietrich Stauffer 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 1996 with Mathematics categories.
"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
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Author : Rainer Klages
language : en
Publisher: World Scientific
Release Date : 2007-06-15
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 2007-06-15 with Science 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.
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics
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Author : David Carfi
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-22
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Fractals In Pure Mathematics written by David Carfi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
Fractal Calculus And Its Applications F Calculus
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Author : Alireza Khalili Golmankhaneh
language : en
Publisher: World Scientific
Release Date : 2022-08-29
Fractal Calculus And Its Applications F Calculus written by Alireza Khalili Golmankhaneh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-29 with Mathematics categories.
Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.