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, 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. Front Matter....Pages I-XIV Fractals and Multifractals: The Interplay of Physics and Geometry....Pages 1-50 Percolation I....Pages 51-96 Percolation II....Pages 97-150 Fractal Growth....Pages 151-174 Fractures....Pages 175-206 Fractal Electrodes, Fractal Membranes, and Fractal Catalysts....Pages 207-228 Fractal Surfaces and Interfaces....Pages 229-262 Fractals and Experiments....Pages 263-296 Cellular Automata....Pages 297-322 Exactly Self-Similar Left-Sided Multifractals....Pages 323-344 Back Matter....Pages 345-350