Fractals: Theory and Applications in Engineering

1. Front Matter

   Pages i-vii

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2. Locally Self Similar Processes

   1. Front Matter

      Pages 1-1

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   2. From Self-Similarity to Local Self-Similarity: the Estimation Problem

      • Serge Cohen

      Pages 3-16

   3. Generalized Multifractional Brownian Motion: Definition and Preliminary Results

      • Antoine Ayache, Jacques Lévy Véhel

      Pages 17-32

   4. Elliptic Self Similar Stochastic Processes

      • Albert Benassi, Daniel Roux

      Pages 33-45

   5. Wavelets for Scaling Processes

      • Patrick Flandrin, Patrice Abry

      Pages 47-64

3. Multifractal Analysis

   1. Front Matter

      Pages 65-65

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   2. Classification of Natural Texture Images from Shape Analysis of the Legendre Multifractal Spectrum

      • Piotr Stanczyk, Peter Sharpe

      Pages 67-79

   3. A Generalization of Multifractal Analysis Based on Polynomial Expansions of the Generating Function

      • Antoine Saucier, Jiri Muller

      Pages 81-91

   4. Local Effective Hölder Exponent Estimation on the Wavelet Transform Maxima Tree

      • Zbigniew R. Struzik

      Pages 93-112

   5. Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions

      • Marc-Olivier Coppens, Benoit B. Mandelbrot

      Pages 113-122

4. IFS

   1. Front Matter

      Pages 123-123

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   2. IFS-Type Operators on Integral Transforms

      • Bruno Forte, Franklin Mendivil, Edward R. Vrscay

      Pages 125-138

   3. Comparison of Dimensions of a Self-Similar Attractor

      • Serge Dubuc, Jun Li

      Pages 139-151

5. Fractional Calculus

   1. Front Matter

      Pages 153-153

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   2. Vector Analysis on Fractal Curves

      • Massimiliano Giona

      Pages 155-170

   3. Local Fractional Calculus: a Calculus for Fractal Space-Time

      • Kiran M. Kolwankar, Anil D. Gangal

      Pages 171-181

6. Physical Sciences

   1. Front Matter

      Pages 183-183

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   2. Conformal Multifractality of Random Walks, Polymers, and Percolation in Two Dimensions

      • Bertrand Duplantier

      Pages 185-206

   3. Fractal Pores and Fractal Tunnels: Traps for “Particles” or “Sound Particles”

      • Jérôme Dorignac, Bernard Sapoval

      Pages 207-227

Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

• Wavelet
• algorithm
• algorithms
• calculus
• chemical engineering
• differential equation
• maximum
• operator
• polymer
• scaling
• wavelets

• Faculty of Technical Mathematics aus SC, Delft University of Technology, Delft, The Netherlands

  Michel Dekking

• INRIA, Le Chesnay Cedex, France

  Jacques Lévy Véhel, Evelyne Lutton

• Université Blaise Pascal, Département Mathématiques, Aubière Cedex, France

  Claude Tricot

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