Fractals: Theory and Applications in Engineering 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 in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.

Locally Self Similar Processes.- From Self-Similarity to Local Self-Similarity: the Estimation Problem.- Generalized Multifractional Brownian Motion: Definition and Preliminary Results.- Elliptic Self Similar Stochastic Processes.- Wavelets for Scaling Processes.- Multifractal Analysis.- Classification of Natural Texture Images from Shape Analysis of the Legendre Multifractal Spectrum.- A Generalization of Multifractal Analysis Based on Polynomial Expansions of the Generating Function.- Local Effective Holder Exponent Estimation on the Wavelet Transform Maxima Tree.- Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions.- IFS.- IFS-Type Operators on Integral Transforms.- Comparison of Dimensions of a Self-Similar Attractor.- Fractional Calculus.- Vector Analysis on Fractal Curves.- Local Fractional Calculus: a Calculus for Fractal Space-Time.- Physical Sciences.- Conformal Multifractality of Random Walks, Polymers, and Percolation in Two Dimensions.- Fractal Pores and Fractal Tunnels: Traps for “Particles” or “Sound Particles”.- Fractal Pores and the Degradation of Shales.- Continuous Wavelet Transform Analysis of Fractal Superlattices.- Chemical Engineering.- Mixing in Laminar Chaotic Flows: Differentiate Structures and Multifractal Features.- Adhesion AFM Applied to Lipid Monolayers. A Fractal Analysis.- Image Compression.- Faster Fractal Image Coding Using Similarity Search in a KL-transformed Feature Space.- Can One Break the “Collage Barrier” in Fractal Image Coding?.- Two Algorithms for Non-Separable Wavelet Transforms and Applications to Image Compression.