Fractals and Disordered Systems

Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. In each chapter, the connection between theory and experiment is emphasized, and a special chapter on "Fractals and Experiment" presents experimental studies of fractal systems. This second edition has been substantially revised and updates the literature in this important field. It is pedagogically written and so will be useful for students, teachers, and scientists who want to become familiar with this facinating subject. Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses, and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, including E. Stanley and B. Mandelbrot, the reader is introduced to basic concepts and techniques in disordered systems and is lead to the forefront of current research. In each chapter the connection between theory and experiment is emphasized, and a special chapter entitled "Fractals and Experiments" presents experimental studies of fractal systems in the laboratory. The book is written pedagogically. It can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field. Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field. Front Matter....Pages I-XXII Fractals and Multifractals: The Interplay of Physics and Geometry....Pages 1-58 Percolation I....Pages 59-114 Percolation II....Pages 115-176 Fractal Growth....Pages 177-200 Fractures....Pages 201-232 Transport Across Irregular Interfaces: Fractal Electrodes, Membranes and Catalysts....Pages 233-262 Fractal Surfaces and Interfaces....Pages 263-302 Fractals and Experiments....Pages 303-338 Cellular Automata....Pages 339-366 Exactly Self-similar Left-sided Multifractals....Pages 367-399 Back Matter....Pages 401-408