Fractals and Disordered SystemsArmin Bunde, Shlomo Havlin 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. |
Contents
| 1 | |
| 6 | |
Analogies with Thermodynamics and Multifractal Scaling | 43 |
Percolation I | 51 |
Percolation II | 97 |
Fractal Growth | 151 |
Fractures | 175 |
References | 204 |
References | 259 |
Jørgen K Kjems | 263 |
Risø National Laboratory | 295 |
Cellular Automata | 297 |
A Appendix | 308 |
References | 320 |
Benoit B Mandelbrot | 323 |
A Appendix | 340 |
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Common terms and phrases
aerogels aggregation Aharony B.B. Mandelbrot backbone behavior Bunde calculate Cayley tree cell cellular automata Chap characterized chemical distance configurations Coniglio connected consider constant correlation length crack critical concentration critical exponents crossover defined dendritic density dependence described diffusion discussed disorder distribution dmin dynamical elastic electrode Euclidean example experimental finite fluctuations fluid fractal dimension fractal geometry fractal structures fracton fracture frequency function growth probabilities growth sites H.E. Stanley H.J. Herrmann Havlin infinite cluster interface Ising model Laplace equation length scales Lett linear mass Meakin monomer multifractal nearest neighbor obtained parameter particles percolation cluster percolation system percolation threshold perimeter sites phase transition phenomena phonon Phys physical pores porous power law properties random walker randomly red bonds regime Sapoval Sect self-affine self-similar shown in Fig simulations spins square lattice Stauffer surface temperature values viscous fingering walk