QE33.2.M3 H47 2002
550/.1/51
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Hergarten, Stefan, 1964-
Self organized criticality in earth systems / Stefan Hergarten.
— Berlin ; New York : Springer, c2002. ix, 272 p. : il. ; 25 cm.
Incluye referencias bibliográficas (p. [259]-268) e índices.
Machine generated contents note: 1. Fractals and Fractal Distributions 1 — 1.1 The Fractal Dimension3 — 1.2 Determining Fractal Dimensions8 — 1.3 Fractal Distributions13 — 1.4 Fractals or Fractal Distributions? 17 — 1.5 Are Fractals Useful?19 — 1.6 Where do Fractals Come From? 21 — 2. Recognizing Power-Law Distributions25 — 2.1 Maximum Likelihood, Least Squares, and Linear Regression 26 — 2.2 Do Cumulative Size Distributions Tell the Truth?28 — 2.3 Binning31 — 2.4 Censoring37 — 3. Self-Affine Time Series41 — 3.1 Brownian Motion42 — 3.2 White Noise44 — 3.3 Fourier Transforms46 — 3.4 Fractional Brownian Motion48 — 3.5 Generating FBM51 — 3.6 Scaling Properties of FBM52 — 3.7 Self-Affine Scale Invariance and Fractal Dimensions55 — 3.8 Recognizing FBM56 — 3.9 The Variogram Analysis59 — 3.10 Predictability64 — 4. Deterministic Chaos67 — 4.1 The Lorenz Equations68 — 4.2 The Physics Behind the Lorenz Equations69 — 4.3 Phase Space, Attractors, and Bifurcations74 — 4.4 Limit Cycles and Strange Attractors77 — 4.5 The Lyapunov Exponent78 — 4.6 Does it Matter whether God Plays Dice?84 — 4.7 Deterministic Chaos and Self-Affine Fractals85 — 5. Self-Organized Criticality87 — 5.1 Critical-Point Phenomena88 — 5.2 The Bak-Tang-Wiesenfeld Model90 — 5.3 The Critical State98 — 5.4 What is SOC?99 — 5.5 Sandpile Dynamics and the BTW Model102 — 6. The Forest-Fire Model - Tuning and Universality109 — 6.1 The Forest-Fire Model109 — 6.2 Universality119 — 6.3 Non-Equilibrium States in SOC Systems122 — 7. Earthquakes and Stick-Slip Motion125 — 7.1 The Fractal Character of Earthquakes127 — 7.2 The Burridge-Knopoff Model130 — 7.3 Separation of Time Scales133 — 7.4 Cellular Automata135 — 7.5 The Olami-Feder-Christensen Model138 — 7.6 Boundary Conditions in the OFC Model142 — 7.7 Efficient Simulation of the OFC Model143 — 7.8 Is the OFC Model Self-Organized Critical?145 — 7.9 Rupture Area and Seismic Moment149 — 7.10 The Temporal Fingerprint of the OFC Model152 — 7.11 How Complex is the OFC Model?161 — 8. Landslides163 — 8.1 Fractal Properties of Landslides164 — 8.2 Are Landslides like Sandpile Avalanches?167 — 8.3 Data, Models, and Reality173 — 8.4 The Role of Time-Dependent Weakening175 — 8.5 On Predicting Slope Stability184 — 8.6 Are SOC and Universality Important in Landform Evolution? 187 — 9. Drainage Networks189 — 9.1 Fractal Properties of Drainage Networks189 — 9.2 Discharge, Drainage Areas, and Water Balance196 — 9.3 Peano's Basin198 — 9.4 Random-Walk Approaches200 — 9.5 Drainage Networks and Landform Evolution201 — 9.6 Optimal Channel Networks216 — 9.7 Drainage Networks and Self-Organized Criticality220 — 9.8 Optimization by Permanent Reorganization?233 — 10. SOC and Nothing Else?235 — 10.1 Ensembles of SOC systems236 — 10.2 SOC in Pre-Structured Systems240 — 10.3 Highly Optimized Tolerance245 — 11. Where do we Stand?253 — A. Numerics of Ordinary Differential Equations255.
ISBN 3540434526 (alk. paper)
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