Multifractals and 1/f Noise: Wild Self-Affinity in Physics

Multifractals and 1/f Noise: Wild Self-Affinity in Physics

Paperback(Softcover reprint of the original 1st ed. 1999)

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Multifractals and 1/f Noise: Wild Self-Affinity in Physics by Benoit B. Mandelbrot

Mandelbrot is a world renowned scientist, known for his pioneering research in fractal geometry and chaos theory. In this volume, Mandelbrot defends the view that multifractals are intimately interrelated through the two fractal themes of "wildness" and "self-affinity". This link involves a powerful collection of technical tools, which are of use to diverse scientific communities. Among the topics covered are: 1/f noise, fractal dimension and turbulence, sporadic random functions, and a new model for error clustering on telephone circuits.

Product Details

ISBN-13: 9781461274346
Publisher: Springer New York
Publication date: 01/03/2014
Edition description: Softcover reprint of the original 1st ed. 1999
Pages: 442
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Preface.- Panorama of grid-bound self affine variablity.- Sketches of prehistory and history.- Scaling, invariants and fixed points.- Filtering and specifications of self-affinity.- Short pieces.- New model for error clustering on telephone circuits.- Additional tests on clustering.- Self-similarity and conditional stationarity.- 1/f noises and the infrared catastrophe.- Co-indicator functions and related 1/f noises.- Sporadic random functions and conditional spectra: Self-similar examples and limits.- Random sets of multiplicity for trigonometric series.- Sporadic turbulence.- Intermittent free turbulence.- Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence.- Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier.- Iterated random multiplications and invariance under randomly weighted averaging.- 'On certain martingales of Benoit Mandelbrot'.- Intermittent turbulence and fractal dimension: the kurtosis and the spectral exponent 5 3 + B.- Fractal dimension, dispersion, and singularities of fluid motion.- Elementary fractals and multifractals.- Bibliography.- Index.

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