Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and ToolsSpringer Science & Business Media, 2003年12月2日 - 528 頁 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. |
內容
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 |
453 | |
17 Randomness | 457 |
477 | |
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applied asymptotic avalanche average behavior central limit theorem characterized cluster condition configuration control parameter convergence correlation corresponds critical exponents critical point cumulative decay defined density derivative described deviation diffusion directed percolation discussed in Chap disorder dynamics earthquakes elements energy equation estimation expression fault field finite fixed point fluctuations fractal dimension fractional function Gaussian law given global hierarchical infinite interactions Ising model larger lattice Lett Lévy laws log-periodic macroscopic magnetic mathematical mechanism multifractal noise observed obtained order parameter particle pdf's phase transitions Phys physics plates power law distribution probability problem properties quenched disorder random variables random walk regime renormalization group result rupture sandpile models scale invariance self-organized criticality self-similar Sornette spin statistical stochastic stress stretched exponential structure tail temperature theory thermodynamic threshold tion transform variance velocity Weibull Weibull distribution X₁ zero
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第 iv 頁 - Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences University of California Los Angeles...