Fractal growth phenomena /
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| Author / Creator: | Vicsek, Tamás |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | Singapore ; New Jersey : World Scientific, c1992. |
| Description: | xix, 488 p., 18 p. of plates : ill. (some col.) ; 26 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1461953 |
Table of Contents:
- 1. Introduction
- Pt. I. Fractals. 2. Fractal Geometry. 2.1. Fractals as mathematical and physical objects. 2.2. Definitions. 2.3. Types of fractals. 3. Fractal Measures. 3.1. Multifractality. 3.2. Relations among the exponents. 3.3. Fractal measures constructed by recursion. 3.4. Geometrical multifractality. 4. Methods for Determining Fractal Dimensions. 4.1. Measuring fractal dimensions in experiments. 4.2. Evaluation of numerical data. 4.3. Renormalization group
- Pt. II. Cluster Growth Models. 5. Local Growth Models. 5.1. Spreading percolation. 5.2. Invasion percolation. 5.3. Kinetic gelation. 5.4. Random walks. 6. Diffusion-limited Growth. 6.1. Diffusion-limited aggregation (DLA). 6.2. Diffusion-limited deposition. 6.3. Dielectric breakdown model. 6.4. Other non-local particle-cluster growth models. 7. Growing Self-affine Surfaces. 7.1. Eden model. 7.2. Ballistic aggregation. 7.3. Ballistic deposition. 7.4. Theoretical results. 8. Cluster-cluster Aggregation (CCA). 8.1. Structure. 8.2. Dynamic scaling for the cluster size distribution. 8.3. Experiments
- III. Fractal Pattern Formation. 9. Computer Simulations. 9.1. Equations. 9.2. Models related to diffusion-limited aggregation. 9.3. Generalizations of the dielectric breakdown model. 9.4. Boundary integral methods. 10. Experiments on Laplacian Growth. 10.1. Viscous fingering. 10.2. Crystallization. 10.3. Electrochemical deposition. 10.4. Other related experiments
- IV. Recent Developments. 11. Cluster Models of Self-similar Growth. 11.1. Diffusion-limited aggregation. 11.2. Fracture. 11.3. Other models. 11.4. Theoretical approaches. 12. Dynamics of Self-affine Surfaces. 12.1. Dynamic scaling. 12.2. Aggregation models. 12.3. Continuum equation approach. 12.4. Phase transition. 12.5. Rare events dominated kinetic roughening. 12.6. Multiaffinity. 13. Experiments. 13.1. Self-similar growth. 13.2. Self-affine growth. App. A. Algorithm for generating diffusion-limited aggregates
- App. B. Construction of a simple Hele-Shaw cell
- App. C. Basic concepts underlying multifractal measures.