Statistical Mechanics And Fractals
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Statistical Mechanics and Fractals
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
language: en
Publisher: American Mathematical Soc.
Release Date: 2004
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.
Analysis, Probability And Mathematical Physics On Fractals
Author: Patricia Alonso Ruiz
language: en
Publisher: World Scientific
Release Date: 2020-02-26
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.