Aschwanden Self-Organized Criticality in Astrophysics

The Statistics of Nonlinear Processes in the Universe
1. Auflage 2011
ISBN: 978-3-642-15001-2
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 416 Seiten

Markus Aschwanden introduces the concept of self-organized criticality (SOC) and shows that due to its universality and ubiquity it is a law of nature for which he derives the theoretical framework and specific physical models in this book. He begins by providing an overview of the many diverse phenomena in nature which may be attributed to SOC behaviour. The author then introduces the classic lattice-based SOC models that may be explored using numerical computer simulations. These simulations require an in-depth knowledge of a wide range of mathematical techniques which the author introduces and describes in subsequent chapters. These include the statistics of random processes, time series analysis, time scale distributions, and waiting time distributions. Such mathematical techniques are needed to model and understand the power-law-like occurrence frequency distributions of SOC phenomena. Finally, the author discusses fractal geometry and scaling laws before looking at a range of physical SOC models which may be applicable in various aspects of astrophysics. Problems, solutions and a glossary will enhance the pedagogical usefulness of the book. SOC has been receiving growing attention in the astrophysical and solar physics community. This book will be welcomed by students and researchers studying complex critical phenomena.

Autoren/Hrsg.

Aschwanden, Markus

Inhaltsverzeichnis

1;Self-Organized Criticality in Astrophysics;3
1.1;Contents;7
1.2;Preface;13
1.3;1. Self-Organized Criticality Phenomena;15
1.3.1;1.1 The Concept of Self-Organized Criticality;15
1.3.2;1.2 SOC Laboratory Experiments;19
1.3.3;1.3 SOC in Human Activities;21
1.3.4;1.4 SOC in Biophysics;26
1.3.5;1.5 SOC in Geophysics;28
1.3.6;1.6 SOC in Magnetospheric Physics;33
1.3.7;1.7 SOC in Planetary Physics;36
1.3.8;1.8 SOC in Solar Physics;37
1.3.9;1.9 SOC in Stellar Physics;42
1.3.10;1.10 SOC in Galaxies and Cosmology;46
1.3.11;1.11 Summary;48
1.3.12;1.12 Problems;49
1.4;2. Numerical SOC Models;50
1.4.1;2.1 SOC Simulations of Laboratory Experiments;51
1.4.1.1;2.1.1 Coupled Pendulums;51
1.4.1.2;2.1.2 The Bak-Tang-Wiesenfeld 1-D Sandpile Model;52
1.4.1.3;2.1.3 The Bak–Tang–Wiesenfeld 2-D Sandpile Model;54
1.4.1.4;2.1.4 The Lattice-Gas Model;57
1.4.2;2.2 SOC Simulations of Human Activities;59
1.4.2.1;2.2.1 Conway’s Game of Life Model;59
1.4.2.2;2.2.2 Traffic Jam Simulations;60
1.4.2.3;2.2.3 Financial Market Simulations;63
1.4.3;2.3 SOC Simulations in Biophysics;64
1.4.3.1;2.3.1 The Punctuated Equilibrium (Bak–Sneppen Model);64
1.4.4;2.4 SOC Simulations in Geophysics;66
1.4.4.1;2.4.1 Slider-Block Spring Model;66
1.4.4.2;2.4.2 The Forest-Fire Model;67
1.4.5;2.5 SOC Simulations in Magnetospheric Physics;70
1.4.5.1;2.5.1 SOC Model with Finite System Size;70
1.4.5.2;2.5.2 Cellular Automaton Model with Discretized MHD;71
1.4.6;2.6 SOC Simulations in Solar Physics;76
1.4.6.1;2.6.1 Isotropic Cellular Automaton Models;76
1.4.6.2;2.6.2 Anisotropic Cellular Automaton Models;80
1.4.6.3;2.6.3 Discretized MHD Cellular Automaton Models;83
1.4.6.4;2.6.4 Divergence-Free Field Braiding Models;86
1.4.6.5;2.6.5 Branching Process Models;90
1.4.7;2.7 SOC Simulations in Astrophysics;90
1.4.7.1;2.7.1 Cellular Automaton Model of Accretion Disk Fluctuations;91
1.4.8;2.8 Summary;94
1.4.9;2.9 Problems;94
1.5;3. Analytical SOC Models;95
1.5.1;3.1 The Exponential-Growth Model;96
1.5.2;3.2 The Powerlaw-Growth Model;101
1.5.3;3.3 The Logistic-Growth Model;106
1.5.4;3.4 Analytical Fit to Numerical SOC Simulations;110
1.5.5;3.5 Inertial Range, Lower and Upper Cutoff;114
1.5.6;3.6 Continuum Limit of Cellular Automaton Model;117
1.5.7;3.7 Summary;121
1.5.8;3.8 Problems;121
1.6;4. Statistics of Random Processes;123
1.6.1;4.1 Binomial Distribution;124
1.6.2;4.2 Gaussian Distribution;127
1.6.3;4.3 Poisson Distribution;129
1.6.4;4.4 Exponential Distribution;131
1.6.5;4.5 Count Rate Statistics;134
1.6.6;4.6 White Noise;134
1.6.7;4.7 1/f Power Spectra Nomenclature;138
1.6.8;4.8 Shot Noise or Flicker Noise;141
1.6.8.1;4.8.1 Derivation of Schottky’s Theorem;141
1.6.8.2;4.8.2 Shot Noise Spectrum for Rectangular Pulses;143
1.6.8.3;4.8.3 Shot Noise Spectrum for Exponential-Decay Pulses;144
1.6.8.4;4.8.4 Shot Noise Spectrum and Distribution of Pulse Durations;145
1.6.9;4.9 Log-Normal Distribution;147
1.6.10;4.10 Summary;149
1.6.11;4.11 Problems;149
1.7;5. Waiting-Time Distributions;151
1.7.1;5.1 Waiting Times;152
1.7.2;5.2 NonstationaryWaiting-Time Statistics;154
1.7.3;5.3 Measurement of Waiting Times;158
1.7.4;5.4 Waiting-Time Statistics in Geophysics;161
1.7.5;5.5 Waiting-Time Statistics in Magnetospheric Physics;163
1.7.6;5.6 Waiting-Time Statistics in Solar Physics;165
1.7.6.1;5.6.1 Solar Flare Hard X-Rays;166
1.7.6.2;5.6.2 Solar Flare Soft X-Rays;171
1.7.6.3;5.6.3 Coronal Mass Ejections;174
1.7.6.4;5.6.4 Solar Radio Bursts;175
1.7.6.5;5.6.5 Solar Wind;175
1.7.7;5.7 Waiting-Time Statistics in Astrophysics;177
1.7.7.1;5.7.1 Flare Stars;177
1.7.7.2;5.7.2 Black Hole Accretion Disks;179
1.7.8;5.8 Summary;181
1.7.9;5.9 Problems;182
1.8;6. Event Detection Methods;183
1.8.1;6.1 Test Data for Event Detection;184
1.8.2;6.2 Threshold-Based Event Detection;186
1.8.3;6.3 Highpass-Filtered Event Detection;192
1.8.4;6.4 Peak-Based Event Detection;194
1.8.5;6.5 Fourier-Filtered Event Detection;194
1.8.6;6.6 Time Scale Statistics from Power Spectra;196
1.8.7;6.7 Wavelet-Based Time Scale Statistics;199
1.8.8;6.8 Principal Component Analysis;203
1.8.9;6.9 Image-Based Event Detection;205
1.8.10;6.10 Summary;210
1.8.11;6.11 Problems;212
1.9;7. Occurrence Frequency Distributions;213
1.9.1;7.1 Basics of Frequency Distribution Functions;214
1.9.1.1;7.1.1 Differential Frequency Distributions;214
1.9.1.2;7.1.2 Cumulative Frequency Distributions;215
1.9.1.3;7.1.3 Rank-Order Plots;218
1.9.1.4;7.1.4 Numerical Generation of Frequency Distributions;220
1.9.1.5;7.1.5 Integrals of Powerlaw Distributions;222
1.9.1.6;7.1.6 Powerlaw Scaling Laws and Correlations;223
1.9.1.7;7.1.7 Accuracy of Powerlaw Fits;224
1.9.2;7.2 Frequency Distributions in Magnetospheric Physics;226
1.9.3;7.3 Frequency Distributions in Solar Physics;229
1.9.3.1;7.3.1 Solar Flare Hard X-rays;229
1.9.3.2;7.3.2 Solar Flare Soft X-rays;236
1.9.3.3;7.3.3 Solar Flare Extreme Ultraviolet Emission;241
1.9.3.4;7.3.4 Solar Radio Emission;245
1.9.3.5;7.3.5 Solar Energetic Particle (SEP) Events;249
1.9.4;7.4 Frequency Distributions in Astrophysics;250
1.9.4.1;7.4.1 Stellar Flares;251
1.9.4.2;7.4.2 Pulsar Glitches;254
1.9.4.3;7.4.3 Soft Gamma-Ray Repeaters;256
1.9.4.4;7.4.4 Black Hole Objects;257
1.9.4.5;7.4.5 Blazars;258
1.9.5;7.5 Summary;259
1.9.6;7.6 Problems;260
1.10;8. Fractal Geometry;261
1.10.1;8.1 1-D Fractals;262
1.10.1.1;8.1.1 The Cantor Set and Koch Curve;262
1.10.1.2;8.1.2 Irregularity of Time Series;263
1.10.1.3;8.1.3 Variability of Solar Radio Emission;265
1.10.2;8.2 2-D Fractals;268
1.10.2.1;8.2.1 Hausdorff Dimension and Box-Counting Method;269
1.10.2.2;8.2.2 Solar Photosphere and Chromosphere;271
1.10.2.3;8.2.3 Solar Flares;274
1.10.3;8.3 3-D Fractals;279
1.10.3.1;8.3.1 Cellular Automaton Simulations;280
1.10.3.2;8.3.2 Solar Flares;282
1.10.4;8.4 Multifractal Analysis;285
1.10.5;8.5 Spatial Power Spectrum Analysis;287
1.10.6;8.6 Statistics of Spatial Scales;289
1.10.6.1;8.6.1 Solar Photosphere and Chromosphere;289
1.10.6.2;8.6.2 Solar Flares;291
1.10.6.3;8.6.3 Lunar Craters;292
1.10.6.4;8.6.4 Asteroid Belt;294
1.10.6.5;8.6.5 Saturn Ring;295
1.10.7;8.7 Summary;297
1.10.8;8.8 Problems;297
1.11;9. Physical SOC Models;299
1.11.1;9.1 A General (Physics-Free) Definition of SOC;300
1.11.2;9.2 Astrophysics;301
1.11.2.1;9.2.1 Galaxy Formation;301
1.11.2.2;9.2.2 Star Formation;302
1.11.2.3;9.2.3 Blazars;303
1.11.2.4;9.2.4 Neutron Star Physics;305
1.11.2.5;9.2.5 Blackhole Objects and Accretion Disks;307
1.11.2.6;9.2.6 Cosmic Rays;308
1.11.3;9.3 Solar and Stellar Physics;310
1.11.3.1;9.3.1 Maxwell’s Electrodynamics;310
1.11.3.2;9.3.2 The Solar Dynamo;311
1.11.3.3;9.3.3 Magnetic Field Braiding;313
1.11.3.4;9.3.4 Magnetic Reconnection in Solar/Stellar Flares;316
1.11.3.5;9.3.5 Thermal Energy of Flare Plasma;318
1.11.3.6;9.3.6 Nonthermal Energy of Flares;320
1.11.3.7;9.3.7 Particle Acceleration;323
1.11.3.8;9.3.8 Coherent Radio Emission;325
1.11.3.9;9.3.9 Master Equation;326
1.11.4;9.4 Magnetospheric Physics;327
1.11.4.1;9.4.1 Coronal Mass Ejections and Magnetospheric Storms;327
1.11.4.2;9.4.2 Heliospheric Field and Magnetospheric Substorms;328
1.11.5;9.5 Summary;331
1.11.6;9.6 Problems;332
1.12;10. SOC-Like Models;333
1.12.1;10.1 Hierarchical SOC Systems;334
1.12.2;10.2 Self-Organization without Criticality;336
1.12.3;10.3 Brownian Motion and Diffusion;338
1.12.4;10.4 MHD Turbulence;341
1.12.4.1;10.4.1 Solar Corona;341
1.12.4.2;10.4.2 Solar Wind;344
1.12.4.3;10.4.3 Magnetospheric Substorms;346
1.12.4.4;10.4.4 Interstellar Medium;347
1.12.5;10.5 Forced Criticality Models;349
1.12.5.1;10.5.1 Magnetospheric Physics;349
1.12.6;10.6 Percolation Models;350
1.12.6.1;10.6.1 Solar Active Regions;351
1.12.7;10.7 Nonlinear Chaotic Systems;352
1.12.7.1;10.7.1 Astrophysics;353
1.12.7.2;10.7.2 Solar Physics;354
1.12.8;10.8 Summary;356
1.12.9;10.9 Problems;357
1.13;Appendices;359
1.13.1;Appendix A: Physical Constants;359
1.13.2;Appendix B: Plasma Parameters;360
1.14;Notation;361
1.14.1;Physical Units Symbols;361
1.14.2;Latin Symbols;361
1.14.3;Greek Symbols;363
1.15;Acronyms;364
1.16;Image Credit: PublicWebsites;367
1.17;References;369
1.18;Index;401