Fractals’ Physical Origin and Properties

1. Front Matter

   Pages i-viii

   PDF

2. Multifractals and Turbulence

   1. Front Matter

      Pages 1-1

      PDF

   2. A Class of Multinomial Multifractal Measures with Negative (Latent) Values for the “Dimension” f(α)

      • Benoit B. Mandelbrot

      Pages 3-29

   3. Some Aspects of the Fractal Approach to the Fully Developed Turbulence

      • Angelo Vulpiani

      Pages 31-47

   4. Nonlinear Variability in Geophysics: Multifractal Simulations and Analysis

      • Daniel Schertzer, Shaun Lovejoy

      Pages 49-79

3. Fractal Properties of Critical Fluctuations and Polymers

   1. Front Matter

      Pages 81-81

      PDF

   2. Fractal Critical Phenomena in Two Dimensions and Conformal Invariance

      • Bertrand Duplantier

      Pages 83-121

   3. Fractal Structure of Ising and Potts Clusters: Static and Dynamic Approach

      • Antonio Coniglio

      Pages 123-133

4. Fractal Growth Models: General Features

   1. Front Matter

      Pages 135-135

      PDF

   2. Diffusion-Limited Aggregation: Recent Developments

      • Paul Meakin, Susan Tolman

      Pages 137-168

   3. New Theoretical Methods for Fractal Growth

      • L. Pietronero, A. Erzan, C. Evertsz

      Pages 169-191

   4. Continuum Description of Active Zones

      • Zoltán Rácz

      Pages 193-203

   5. Multifractality, Scaling, and Diffusive Growth

      • Thomas C. Halsey

      Pages 205-216

   6. Is There a Phase Transition in the Multifractal Spectrum of DLA?

      • Jysoo Lee, Preben Alstrøm, H. Eugene Stanley

      Pages 217-226

5. Application of Fractal Growth Models to Physical Phenomena

   1. Front Matter

      Pages 227-227

      PDF

   2. Fractals and Patterns in Electrodepostion

      • Leonard M. Sander, David G. Grier

      Pages 229-237

   3. On the Possible Application of Fractal Scaling Ideas in Dendritic Growth

      • R. C. Ball

      Pages 239-242

   4. Realistic Models of Dielectric Breakdown

      • H. J. Wiesmann

      Pages 243-257

   5. Cluster-Cluster Aggregation with Dipole-Dipole Interactions

      • R. Botet, G. Helgesen, A. T. Skjeltorp, P. M. Mors, R. Jullien

      Pages 259-267

   6. Shapes of Deterministic Cracks Obtained under Shear

      • H. J. Herrmann

      Pages 269-276

This volume contains the Proceedings of the Special Seminar on: FRAGTALS held from October 9-15, 1988 at the Ettore Majorana Centre for Scientific Culture, Erice (Trapani), Italy. The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of critical properites of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Seminar was to provide an overview of the recent developments in the field. Most of the contributions are theoretical, but some experimental work is also included. Du:cing the past few years two tendencies have emerged in this field: one is to realize that many phenomena can be naturally modelled by fractal structures. So one can use this concept to define simple modele and study their physical properties. The second point of view is more microscopic and tries to answer the question: why nature gives rise to fractal structures. This implies the formulation of fractal growth modele based on physical concepts and their theoretical understanding in the same sense as the Renormalization Group method has allowed to understand the critical properties of phase transitions.

• Area
• development
• field
• fractal
• fractal dimension
• fractal geometry
• geometry
• group
• Natural
• Self-similarity
• similarity
• Variance
• Volume

From Book News, Inc.
Proceedings of the Special Seminar on Fractals, held October 1988, in Erice, Italy. Most of the contributions are theoretical, but some experimental work is also included. They discuss multifractals and turbulence, fractal properties of critical fluctuations and polymers, general features of fractal growth models, the application of those models to physical phenomena, diffusion and vibrations on fractals, diffusion fronts and invasion percolation, random surfaces, and large scale distribution of matter in the universe.
Annotation copyright Book News, Inc. Portland, Or.

• University of Rome “La Sapienza”, Rome, Italy

  Luciano Pietronero

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