Self-Organized Criticality in Astrophysics (eBook)

The Statistics of Nonlinear Processes in the Universe

Markus Aschwanden (Autor)

eBook Download: PDF

2011 | 2011
XIV, 416 Seiten
Springer Berlin (Verlag)
978-3-642-15001-2 (ISBN)

Infos

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.

Inhalt

Self-Organized Criticality in Astrophysics 3
Contents 7
Preface 13
1. Self-Organized Criticality Phenomena 15
1.1 The Concept of Self-Organized Criticality 15
1.2 SOC Laboratory Experiments 19
1.3 SOC in Human Activities 21
1.4 SOC in Biophysics 26
1.5 SOC in Geophysics 28
1.6 SOC in Magnetospheric Physics 33
1.7 SOC in Planetary Physics 36
1.8 SOC in Solar Physics 37
1.9 SOC in Stellar Physics 42
1.10 SOC in Galaxies and Cosmology 46
1.11 Summary 48
1.12 Problems 49
2. Numerical SOC Models 50
2.1 SOC Simulations of Laboratory Experiments 51
2.1.1 Coupled Pendulums 51
2.1.2 The Bak-Tang-Wiesenfeld 1-D Sandpile Model 52
2.1.3 The Bak–Tang–Wiesenfeld 2-D Sandpile Model 54
2.1.4 The Lattice-Gas Model 57
2.2 SOC Simulations of Human Activities 59
2.2.1 Conway’s Game of Life Model 59
2.2.2 Traffic Jam Simulations 60
2.2.3 Financial Market Simulations 63
2.3 SOC Simulations in Biophysics 64
2.3.1 The Punctuated Equilibrium (Bak–Sneppen Model) 64
2.4 SOC Simulations in Geophysics 66
2.4.1 Slider-Block Spring Model 66
2.4.2 The Forest-Fire Model 67
2.5 SOC Simulations in Magnetospheric Physics 70
2.5.1 SOC Model with Finite System Size 70
2.5.2 Cellular Automaton Model with Discretized MHD 71
2.6 SOC Simulations in Solar Physics 76
2.6.1 Isotropic Cellular Automaton Models 76
2.6.2 Anisotropic Cellular Automaton Models 80
2.6.3 Discretized MHD Cellular Automaton Models 83
2.6.4 Divergence-Free Field Braiding Models 86
2.6.5 Branching Process Models 90
2.7 SOC Simulations in Astrophysics 90
2.7.1 Cellular Automaton Model of Accretion Disk Fluctuations 91
2.8 Summary 94
2.9 Problems 94
3. Analytical SOC Models 95
3.1 The Exponential-Growth Model 96
3.2 The Powerlaw-Growth Model 101
3.3 The Logistic-Growth Model 106
3.4 Analytical Fit to Numerical SOC Simulations 110
3.5 Inertial Range, Lower and Upper Cutoff 114
3.6 Continuum Limit of Cellular Automaton Model 117
3.7 Summary 121
3.8 Problems 121
4. Statistics of Random Processes 123
4.1 Binomial Distribution 124
4.2 Gaussian Distribution 127
4.3 Poisson Distribution 129
4.4 Exponential Distribution 131
4.5 Count Rate Statistics 134
4.6 White Noise 134
4.7 1/f Power Spectra Nomenclature 138
4.8 Shot Noise or Flicker Noise 141
4.8.1 Derivation of Schottky’s Theorem 141
4.8.2 Shot Noise Spectrum for Rectangular Pulses 143
4.8.3 Shot Noise Spectrum for Exponential-Decay Pulses 144
4.8.4 Shot Noise Spectrum and Distribution of Pulse Durations 145
4.9 Log-Normal Distribution 147
4.10 Summary 149
4.11 Problems 149
5. Waiting-Time Distributions 151
5.1 Waiting Times 152
5.2 NonstationaryWaiting-Time Statistics 154
5.3 Measurement of Waiting Times 158
5.4 Waiting-Time Statistics in Geophysics 161
5.5 Waiting-Time Statistics in Magnetospheric Physics 163
5.6 Waiting-Time Statistics in Solar Physics 165
5.6.1 Solar Flare Hard X-Rays 166
5.6.2 Solar Flare Soft X-Rays 171
5.6.3 Coronal Mass Ejections 174
5.6.4 Solar Radio Bursts 175
5.6.5 Solar Wind 175
5.7 Waiting-Time Statistics in Astrophysics 177
5.7.1 Flare Stars 177
5.7.2 Black Hole Accretion Disks 179
5.8 Summary 181
5.9 Problems 182
6. Event Detection Methods 183
6.1 Test Data for Event Detection 184
6.2 Threshold-Based Event Detection 186
6.3 Highpass-Filtered Event Detection 192
6.4 Peak-Based Event Detection 194
6.5 Fourier-Filtered Event Detection 194
6.6 Time Scale Statistics from Power Spectra 196
6.7 Wavelet-Based Time Scale Statistics 199
6.8 Principal Component Analysis 203
6.9 Image-Based Event Detection 205
6.10 Summary 210
6.11 Problems 212
7. Occurrence Frequency Distributions 213
7.1 Basics of Frequency Distribution Functions 214
7.1.1 Differential Frequency Distributions 214
7.1.2 Cumulative Frequency Distributions 215
7.1.3 Rank-Order Plots 218
7.1.4 Numerical Generation of Frequency Distributions 220
7.1.5 Integrals of Powerlaw Distributions 222
7.1.6 Powerlaw Scaling Laws and Correlations 223
7.1.7 Accuracy of Powerlaw Fits 224
7.2 Frequency Distributions in Magnetospheric Physics 226
7.3 Frequency Distributions in Solar Physics 229
7.3.1 Solar Flare Hard X-rays 229
7.3.2 Solar Flare Soft X-rays 236
7.3.3 Solar Flare Extreme Ultraviolet Emission 241
7.3.4 Solar Radio Emission 245
7.3.5 Solar Energetic Particle (SEP) Events 249
7.4 Frequency Distributions in Astrophysics 250
7.4.1 Stellar Flares 251
7.4.2 Pulsar Glitches 254
7.4.3 Soft Gamma-Ray Repeaters 256
7.4.4 Black Hole Objects 257
7.4.5 Blazars 258
7.5 Summary 259
7.6 Problems 260
8. Fractal Geometry 261
8.1 1-D Fractals 262
8.1.1 The Cantor Set and Koch Curve 262
8.1.2 Irregularity of Time Series 263
8.1.3 Variability of Solar Radio Emission 265
8.2 2-D Fractals 268
8.2.1 Hausdorff Dimension and Box-Counting Method 269
8.2.2 Solar Photosphere and Chromosphere 271
8.2.3 Solar Flares 274
8.3 3-D Fractals 279
8.3.1 Cellular Automaton Simulations 280
8.3.2 Solar Flares 282
8.4 Multifractal Analysis 285
8.5 Spatial Power Spectrum Analysis 287
8.6 Statistics of Spatial Scales 289
8.6.1 Solar Photosphere and Chromosphere 289
8.6.2 Solar Flares 291
8.6.3 Lunar Craters 292
8.6.4 Asteroid Belt 294
8.6.5 Saturn Ring 295
8.7 Summary 297
8.8 Problems 297
9. Physical SOC Models 299
9.1 A General (Physics-Free) Definition of SOC 300
9.2 Astrophysics 301
9.2.1 Galaxy Formation 301
9.2.2 Star Formation 302
9.2.3 Blazars 303
9.2.4 Neutron Star Physics 305
9.2.5 Blackhole Objects and Accretion Disks 307
9.2.6 Cosmic Rays 308
9.3 Solar and Stellar Physics 310
9.3.1 Maxwell’s Electrodynamics 310
9.3.2 The Solar Dynamo 311
9.3.3 Magnetic Field Braiding 313
9.3.4 Magnetic Reconnection in Solar/Stellar Flares 316
9.3.5 Thermal Energy of Flare Plasma 318
9.3.6 Nonthermal Energy of Flares 320
9.3.7 Particle Acceleration 323
9.3.8 Coherent Radio Emission 325
9.3.9 Master Equation 326
9.4 Magnetospheric Physics 327
9.4.1 Coronal Mass Ejections and Magnetospheric Storms 327
9.4.2 Heliospheric Field and Magnetospheric Substorms 328
9.5 Summary 331
9.6 Problems 332
10. SOC-Like Models 333
10.1 Hierarchical SOC Systems 334
10.2 Self-Organization without Criticality 336
10.3 Brownian Motion and Diffusion 338
10.4 MHD Turbulence 341
10.4.1 Solar Corona 341
10.4.2 Solar Wind 344
10.4.3 Magnetospheric Substorms 346
10.4.4 Interstellar Medium 347
10.5 Forced Criticality Models 349
10.5.1 Magnetospheric Physics 349
10.6 Percolation Models 350
10.6.1 Solar Active Regions 351
10.7 Nonlinear Chaotic Systems 352
10.7.1 Astrophysics 353
10.7.2 Solar Physics 354
10.8 Summary 356
10.9 Problems 357
Appendices 359
Appendix A: Physical Constants 359
Appendix B: Plasma Parameters 360
Notation 361
Physical Units Symbols 361
Latin Symbols 361
Greek Symbols 363
Acronyms 364
Image Credit: PublicWebsites 367
References 369
Index 401

Produkt-Details

• Erscheint lt. Verlag: 11.1.2011
• Reihe/Serie: Astronomy and Planetary Sciences
• Reihe/Serie: Astronomy and Planetary Sciences
• Reihe/Serie: Springer Praxis Books
• Reihe/Serie: Springer Praxis Books
• Zusatzinfo: XIV, 416 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Literatur
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Technik
• Schlagworte: Nonlinear Processes • Self-organization in Cosmology • self-organization in plasmas • self-organized criticality • Self-organized criticality in Accretion disks • solar flares • Stellar Flares
• ISBN-10: 3-642-15001-2 / 3642150012
• ISBN-13: 978-3-642-15001-2 / 9783642150012