Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools

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Springer Science & Business Media, Dec 2, 2003 - Science - 528 pages
Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena. This is the first textbook written by a well-known expert that provides a modern up-to-date introduction for workers outside statistical physics. The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to post-docs in geophysics and meteorology.
 

Contents

1 Useful Notions of Probability Theory
1
2 Sums of Random Variables Random Walks
33
2 Sums of Random Variables Random Walks
41
3 Large Deviations
59
Îx Nẞ can be written in the form
65
Êx Nẞ can be written in the form
65
4 Power Law Distributions
93
5 Fractals and Multifractals
123
10 Transitions Bifurcations and Precursors
255
11 The Renormalization Group
267
12 The Percolation Model
293
a square lattice on
305
a square lattice on
305
a square lattice on
305
13 Rupture Models
313
14 Mechanisms for Power Laws
345

start
128
VI
131
N
132
J
136
6 RankOrdering Statistics and Heavy Tails
163
Probabilistic Point
199
1
217
8 LongRange Correlations
223
Critical Phenomena
241
Critical Phenomena
249
10 Transitions Bifurcations and Precursors
253
14 Mechanisms for Power Laws
347
15 SelfOrganized Criticality
395
15 SelfOrganized Criticality
397
16 Introduction to the Physics
417
17 Randomness
433
16 Introduction to the Physics
441
References
453
17 Randomness
457
References
477
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