Ebook: Fractals: Theory and Applications in Engineering

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 inEngineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

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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 inEngineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

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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 inEngineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.
Content:
Front Matter....Pages i-vii
Front Matter....Pages 1-1
From Self-Similarity to Local Self-Similarity: the Estimation Problem....Pages 3-16
Generalized Multifractional Brownian Motion: Definition and Preliminary Results....Pages 17-32
Elliptic Self Similar Stochastic Processes....Pages 33-45
Wavelets for Scaling Processes....Pages 47-64
Front Matter....Pages 65-65
Classification of Natural Texture Images from Shape Analysis of the Legendre Multifractal Spectrum....Pages 67-79
A Generalization of Multifractal Analysis Based on Polynomial Expansions of the Generating Function....Pages 81-91
Local Effective H?lder Exponent Estimation on the Wavelet Transform Maxima Tree....Pages 93-112
Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions....Pages 113-122
Front Matter....Pages 123-123
IFS-Type Operators on Integral Transforms....Pages 125-138
Comparison of Dimensions of a Self-Similar Attractor....Pages 139-151
Front Matter....Pages 153-153
Vector Analysis on Fractal Curves....Pages 155-170
Local Fractional Calculus: a Calculus for Fractal Space-Time....Pages 171-181
Front Matter....Pages 183-183
Conformal Multifractality of Random Walks, Polymers, and Percolation in Two Dimensions....Pages 185-206
Fractal Pores and Fractal Tunnels: Traps for “Particles” or “Sound Particles”....Pages 207-227
Fractal Pores and the Degradation of Shales....Pages 229-243
Continuous Wavelet Transform Analysis of Fractal Superlattices....Pages 245-259
Front Matter....Pages 261-261
Mixing in Laminar Chaotic Flows: Differentiable Structures and Multifractal Features....Pages 263-275
Adhesion AFM Applied to Lipid Monolayers. A Fractal Analysis....Pages 277-289
Front Matter....Pages 291-291
Faster Fractal Image Coding Using Similarity Search in a KL-transformed Feature Space....Pages 293-306
Can One Break the “Collage Barrier” in Fractal Image Coding?....Pages 307-323
Two Algorithms for Non-Separable Wavelet Transforms and Applications to Image Compression....Pages 325-345

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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 inEngineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.
Content:
Front Matter....Pages i-vii
Front Matter....Pages 1-1
From Self-Similarity to Local Self-Similarity: the Estimation Problem....Pages 3-16
Generalized Multifractional Brownian Motion: Definition and Preliminary Results....Pages 17-32
Elliptic Self Similar Stochastic Processes....Pages 33-45
Wavelets for Scaling Processes....Pages 47-64
Front Matter....Pages 65-65
Classification of Natural Texture Images from Shape Analysis of the Legendre Multifractal Spectrum....Pages 67-79
A Generalization of Multifractal Analysis Based on Polynomial Expansions of the Generating Function....Pages 81-91
Local Effective H?lder Exponent Estimation on the Wavelet Transform Maxima Tree....Pages 93-112
Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions....Pages 113-122
Front Matter....Pages 123-123
IFS-Type Operators on Integral Transforms....Pages 125-138
Comparison of Dimensions of a Self-Similar Attractor....Pages 139-151
Front Matter....Pages 153-153
Vector Analysis on Fractal Curves....Pages 155-170
Local Fractional Calculus: a Calculus for Fractal Space-Time....Pages 171-181
Front Matter....Pages 183-183
Conformal Multifractality of Random Walks, Polymers, and Percolation in Two Dimensions....Pages 185-206
Fractal Pores and Fractal Tunnels: Traps for “Particles” or “Sound Particles”....Pages 207-227
Fractal Pores and the Degradation of Shales....Pages 229-243
Continuous Wavelet Transform Analysis of Fractal Superlattices....Pages 245-259
Front Matter....Pages 261-261
Mixing in Laminar Chaotic Flows: Differentiable Structures and Multifractal Features....Pages 263-275
Adhesion AFM Applied to Lipid Monolayers. A Fractal Analysis....Pages 277-289
Front Matter....Pages 291-291
Faster Fractal Image Coding Using Similarity Search in a KL-transformed Feature Space....Pages 293-306
Can One Break the “Collage Barrier” in Fractal Image Coding?....Pages 307-323
Two Algorithms for Non-Separable Wavelet Transforms and Applications to Image Compression....Pages 325-345
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