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 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. |
Contents
1 | 19 |
Volatile Fractals | 43 |
References | 52 |
Introduction | 54 |
Percolation I | 59 |
A Simple Example | 62 |
5 | 83 |
Branched Polymers | 93 |
4 | 209 |
7 | 222 |
8 | 229 |
2 | 235 |
6 | 246 |
References | 253 |
By JeanFrançois Gouyet Michel Rosso and Bernard Sapoval | 263 |
Fractals and Experiments | 303 |
2 | 105 |
By Shlomo Havlin and Armin Bunde With 20 Figures | 115 |
3 | 127 |
5 | 137 |
6 | 143 |
7 | 152 |
References | 170 |
Fractal Growth | 177 |
4 | 186 |
5 | 192 |
References | 198 |
Hans J Herrmann | 201 |
References | 335 |
Risø National Laboratory | 336 |
The Kauffman Model | 339 |
5 | 351 |
References | 363 |
Institute of Physics University of Oslo Norway | 367 |
2 | 370 |
4 | 376 |
6 | 382 |
by B B Mandelbrot | 390 |
| 400 | |
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Common terms and phrases
admittance aerogels aggregation Aharony B.B. Mandelbrot backbone behavior bond percolation boundary conditions Bunde Cayley tree cell Chap Chem chemical distance Coniglio connected consider constant correlation length crack critical exponents crossover density depends described diffusion front discussed disorder distribution dmin dynamical elastic electrode example experimental finite fluctuations fluid fractal dimension fractal dimension df 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 Meakin membrane monomers multifractal nearest-neighbor neighboring obtained parameters particles percolation cluster percolation system percolation threshold perimeter sites phase transition phonon Phys physical polymer pores porous power-law properties random walker randomly reaction red bonds regime Sapoval Sect self-affine self-similar shown in Fig Sierpinski simulations square lattice studied surface values Vicsek viscous fingering voltage