Multifractals and 1/f Noise: Wild Self-Affinity in Physics (1963-1976)

Overview

This book is a major contribution to an understanding of wild variability and randomness along two wide open frontiers of physics. Specially written introductions provide a new synthesis and historical background, and organize the twenty-odd reprints of works that first appeared from 1962 to 1976.
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Paperback (Softcover reprint of the original 1st ed. 1999)
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Overview

This book is a major contribution to an understanding of wild variability and randomness along two wide open frontiers of physics. Specially written introductions provide a new synthesis and historical background, and organize the twenty-odd reprints of works that first appeared from 1962 to 1976.
Read More Show Less

Product Details

  • ISBN-13: 9781461274346
  • Publisher: Springer New York
  • Publication date: 4/30/2014
  • Edition description: Softcover reprint of the original 1st ed. 1999
  • Pages: 442

Table of Contents

Preface 1
I Introductions and Short Pieces 17
1 Panorama of grid-bound self-affine variability 18
2 Sketches of prehistory and history 62
3 Scaling, invariants and fixed points 100
4 Filtering and specifications of self-affinity 111
5 Short excerpts 117
II Unifractal Errors and Levy Dusts 131
6 New model for error clustering on telephone circuits 132
7 Self-similarity and conditional stationarity 166
III Intermittent 1/f Noises and Conditioned Random Processes 207
8 1/f noises and the infrared catastrophe 208
9 Co-indicator functions and related 1/f noises 215
10 Sporadic random functions and conditional spectra self-similar examples and limits 247
11 Random sets of multiplicity for trigonometric series 284
IV Turbulence and Multifractal Measures 289
12 Sporadic turbulence 290
13 Intermittent free turbulence 292
14 Lognormal hypothesis and distribution of energy dissipation in intermittent turbulence 294
15 Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier 317
16 Iterated random multiplications and invariance under randomly weighted averaging 358
17 "On certain martingales of Benoit Mandelbrot": Guest contribution 372
18 Intermittent turbulence and fractal dimension: the kurtosis and the spectral exponent 5/3 + B 389
19 Fractal dimension, dispersion, and singularities of fluid motion 416
Cumulative Bibliography 419
Index 432
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