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self-organized criticality in astrophysics the statistics of nonlinear processes in the universe[close]
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markus j aschwanden self-organized criticality in astrophysics the statistics of nonlinear processes in the universe praxis publishing chichester uk published in association with[close]
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professor dr markus aschwanden lockheed martin advanced technology center solar and astrophysics laboratory palo alto california usa cover images courtesy of nasa detailed image credits are given under figures 1.4a 1.12b 1.16 and 8.22 in appendix on image credit public websites springer±praxis books in astronomy and planetary sciences subject advisory editors philippe blondel c.geol f.g.s ph.d m.sc f.i.o.a senior scientist department of physics university of bath uk john mason m.b.e b.sc m.sc ph.d isbn 978-3-642-15000-5 doi 10.1007/978-3-642-15001-2 springer heidelberg dordrecht london new york springer-verlag berlin heidelberg 2011 this work is subject to copyright all rights are reserved whether the whole or part of the material is concerned speci®cally the rights of translation reprinting reuse of illustrations recitation broadcasting reproduction on micro®lm or in any other way and storage in data banks duplication of this publication or parts thereof is permitted only under the provisions of the german copyright law of september 9 1965 in its current version and permission for use must always be obtained from springer violations are liable to prosecution under the german copyright law the use of general descriptive names registered names trademarks etc in this publication does not imply even in the absence of a speci®c statement that such names are exempt from the relevant protective laws and regulations and therefore free for general use cover design jim wilkie project copy editor mike shardlow author-generated latex processed by edv-beratung herweg germany printed on acid-free paper springer is part of springer science business media www.springer.com[close]
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contents preface xiii 1 self-organized criticality phenomena 1.1 the concept of self-organized criticality 1.2 soc laboratory experiments 1.3 soc in human activities 1.4 soc in biophysics 1.5 soc in geophysics 1.6 soc in magnetospheric physics 1.7 soc in planetary physics 1.8 soc in solar physics 1.9 soc in stellar physics 1.10 soc in galaxies and cosmology 1.11 summary 1.12 problems numerical soc models 2.1 soc simulations of laboratory experiments 2.1.1 coupled pendulums 2.1.2 the bak-tang-wiesenfeld 1-d sandpile model 2.1.3 the baktangwiesenfeld 2-d sandpile model 2.1.4 the lattice-gas model 2.2 soc simulations of human activities 2.2.1 conway s game of life model 2.2.2 traffic jam simulations 2.2.3 financial market simulations 2.3 soc simulations in biophysics 2.3.1 the punctuated equilibrium baksneppen model 2.4 soc simulations in geophysics 2.4.1 slider-block spring model 2.4.2 the forest-fire model 1 1 5 7 12 14 19 22 23 28 32 34 35 37 38 38 39 41 44 46 46 47 50 51 51 53 53 54 2.[close]
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viii contents 2.5 soc simulations in magnetospheric physics 2.5.1 soc model with finite system size 2.5.2 cellular automaton model with discretized mhd 2.6 soc simulations in solar physics 2.6.1 isotropic cellular automaton models 2.6.2 anisotropic cellular automaton models 2.6.3 discretized mhd cellular automaton models 2.6.4 divergence-free field braiding models 2.6.5 branching process models 2.7 soc simulations in astrophysics 2.7.1 cellular automaton model of accretion disk fluctuations 2.8 summary 2.9 problems 3 analytical soc models 3.1 the exponential-growth model 3.2 the powerlaw-growth model 3.3 the logistic-growth model 3.4 analytical fit to numerical soc simulations 3.5 inertial range lower and upper cutoff 3.6 continuum limit of cellular automaton model 3.7 summary 3.8 problems statistics of random processes 4.1 binomial distribution 4.2 gaussian distribution 4.3 poisson distribution 4.4 exponential distribution 4.5 count rate statistics 4.6 white noise 4.7 1/f power spectra nomenclature 4.8 shot noise or flicker noise 4.8.1 derivation of schottky s theorem 4.8.2 shot noise spectrum for rectangular pulses 4.8.3 shot noise spectrum for exponential-decay pulses 4.8.4 shot noise spectrum and distribution of pulse durations 4.9 log-normal distribution 4.10 summary 4.11 problems waiting-time distributions 5.1 waiting times 5.2 nonstationary waiting-time statistics 5.3 measurement of waiting times 57 57 58 63 63 67 70 73 77 77 78 81 81 83 84 89 94 98 102 105 109 109 111 112 115 117 119 122 122 126 129 129 131 132 133 135 137 137 139 140 142 146 4 5.[close]
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contents ix 5.4 waiting-time statistics in geophysics 5.5 waiting-time statistics in magnetospheric physics 5.6 waiting-time statistics in solar physics 5.6.1 solar flare hard x-rays 5.6.2 solar flare soft x-rays 5.6.3 coronal mass ejections 5.6.4 solar radio bursts 5.6.5 solar wind 5.7 waiting-time statistics in astrophysics 5.7.1 flare stars 5.7.2 black hole accretion disks 5.8 summary 5.9 problems 6 event detection methods 6.1 test data for event detection 6.2 threshold-based event detection 6.3 highpass-filtered event detection 6.4 peak-based event detection 6.5 fourier-filtered event detection 6.6 time scale statistics from power spectra 6.7 wavelet-based time scale statistics 6.8 principal component analysis 6.9 image-based event detection 6.10 summary 6.11 problems occurrence frequency distributions 7.1 basics of frequency distribution functions 7.1.1 differential frequency distributions 7.1.2 cumulative frequency distributions 7.1.3 rank-order plots 7.1.4 numerical generation of frequency distributions 7.1.5 integrals of powerlaw distributions 7.1.6 powerlaw scaling laws and correlations 7.1.7 accuracy of powerlaw fits 7.2 frequency distributions in magnetospheric physics 7.3 frequency distributions in solar physics 7.3.1 solar flare hard x-rays 7.3.2 solar flare soft x-rays 7.3.3 solar flare extreme ultraviolet emission 7.3.4 solar radio emission 7.3.5 solar energetic particle sep events 7.4 frequency distributions in astrophysics 7.4.1 stellar flares 149 151 153 154 159 162 163 163 165 165 167 169 170 171 172 174 180 182 182 184 187 191 193 198 200 201 202 202 203 206 208 210 211 212 214 217 217 224 229 233 237 238 239 7.[close]
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x contents 7.5 7.6 8 7.4.2 pulsar glitches 7.4.3 soft gamma-ray repeaters 7.4.4 black hole objects 7.4.5 blazars summary problems 242 244 245 246 247 248 249 250 250 251 253 256 257 259 262 267 268 270 273 275 277 277 279 280 282 283 285 285 287 288 289 289 290 291 293 295 296 298 298 299 301 304 306 fractal geometry 8.1 1-d fractals 8.1.1 the cantor set and koch curve 8.1.2 irregularity of time series 8.1.3 variability of solar radio emission 8.2 2-d fractals 8.2.1 hausdorff dimension and box-counting method 8.2.2 solar photosphere and chromosphere 8.2.3 solar flares 8.3 3-d fractals 8.3.1 cellular automaton simulations 8.3.2 solar flares 8.4 multifractal analysis 8.5 spatial power spectrum analysis 8.6 statistics of spatial scales 8.6.1 solar photosphere and chromosphere 8.6.2 solar flares 8.6.3 lunar craters 8.6.4 asteroid belt 8.6.5 saturn ring 8.7 summary 8.8 problems physical soc models 9.1 a general physics-free definition of soc 9.2 astrophysics 9.2.1 galaxy formation 9.2.2 star formation 9.2.3 blazars 9.2.4 neutron star physics 9.2.5 blackhole objects and accretion disks 9.2.6 cosmic rays 9.3 solar and stellar physics 9.3.1 maxwell s electrodynamics 9.3.2 the solar dynamo 9.3.3 magnetic field braiding 9.3.4 magnetic reconnection in solar/stellar flares 9.3.5 thermal energy of flare plasma 9.[close]
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contents xi 9.3.6 nonthermal energy of flares 9.3.7 particle acceleration 9.3.8 coherent radio emission 9.3.9 master equation 9.4 magnetospheric physics 9.4.1 coronal mass ejections and magnetospheric storms 9.4.2 heliospheric field and magnetospheric substorms 9.5 summary 9.6 problems 10 soc-like models 10.1 hierarchical soc systems 10.2 self-organization without criticality 10.3 brownian motion and diffusion 10.4 mhd turbulence 10.4.1 solar corona 10.4.2 solar wind 10.4.3 magnetospheric substorms 10.4.4 interstellar medium 10.5 forced criticality models 10.5.1 magnetospheric physics 10.6 percolation models 10.6.1 solar active regions 10.7 nonlinear chaotic systems 10.7.1 astrophysics 10.7.2 solar physics 10.8 summary 10.9 problems 308 311 313 314 315 315 316 319 320 321 322 324 326 329 329 332 334 335 337 337 338 339 340 341 342 344 345 appendices 347 appendix a physical constants 347 appendix b plasma parameters 348 notation physical units symbols latin symbols greek symbols 349 349 349 351 acronyms 353 image credit public websites 357 references 359 index 391[close]
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preface how did this book come about in 1985 brian dennis published a review on solar flares and presented a stunning figure that showed a perfect powerlaw distribution in the occurrence of solar flares that extended over almost 4 orders of magnitude with a slope of -1.8 for which no explanation could be found just two years later in 1987 per bak the father of self-organized criticality soc published his landmark paper on the interpretation of the ubiquitous powerlaw distributions observed also in sandpile avalanches and earthquakes the so-called gutenbergrichter law by relating the scale-free behavior to the 1 f -flicker noise a few years later per bak gave a colloquium at the nasa goddard space flight center gsfc where he met brian dennis and heard about solar flare statistics but he admitted in his book how nature works that he did not really understand how solar flares work intuitively there was the notion that the intricate details of the underlying physical processes could not provide the answer to the fundamental understanding of the observed powerlaws in 1991 the two students ed lu and russ hamilton at stanford university wrote the first paper where self-organized criticality was applied to solar flare statistics which was interpreted and modeled with a cellular automaton model this approach offered an explanation of the observed powerlaws in terms of statistics of next-neighbor interactions of complex dissipative systems in a critical state this universal aspect fascinated me more and more and i gave a number of colloquia on self-organized criticality applied to solar flares at the eth zurich nasa gsfc and the university of maryland in 19911993 since powerlaw distributions were also observed for stellar flares pulsar glitches lunar craters and asteroid sizes i speculated that these may all be dissipative systems with self-organized criticality during one of the seminars at the university of maryland i remember that lucy mcfadden an expert in solar system small bodies commented that this was the most fascinating model she had ever heard of and asked whether it applied also to the powerlaw distributions of asteroids and saturn rings i did not know the answer at this time but an answer is given in this book a textbook that explains the fundamental aspects of self-organized criticality in terms of the statistics of nonlinear events has never been written in astrophysics which motivated me to undertake such an endeavor one of the major aims of this book is to convey a deeper understanding of the statistics of nonlinear processes that is common to solar flares sandpile avalanches and earthquakes although the underlying physics is completely different.[close]
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xiv preface this textbook is intended to be an introduction to the relatively new subject of selforganized criticality soc suitable for students and post-docs as well as for researchers who want to know all the relevant literature references the main applications are astrophysical phenomena although we include also a few other phenomena from geophysics or social sciences that provided important basic models later applied to astrophysical phenomena in chapter 1 we give an introductory broad overview of soc phenomena observed in the entire universe wherever publications with soc interpretations were found in the scientific literature the theoretical modeling of soc phenomena can be pursued in 3 different approaches by numerical mostly cellular automaton simulations chapter 2 by analytical modeling of statistical distributions chapter 3 or by physical modeling chapter 9 the temporal aspects of soc statistics includes random statistics chapter 4 waiting-time statistics chapter 5 and event-detection methods chapter 6 using these basic prerequisites we can then model and understand the occurrence frequency distributions of soc events which reveal the ubiquitous powerlaws that are the hallmark of soc chapter 7 the spatial aspects of soc events entail the geometry of fractal structures chapter 8 finally we arrive at a general physics-free definition of soc phenomena section 9.1 individual physical processes for astrophysical soc phenomena are summarized in table 9.1 and discussed case by case in the remainder of chapter 9 qualitatively for astrophysical observations and somewhat more quantitatively for solar physics applications alternatives to soc processes are discussed in chapter 10 which may also exhibit powerlaw distributions but can be discriminated from pure soc processes using the criteria of our physics-free soc definition table 10.1 do we understand soc completely now although we hope to have established a deeper understanding of soc phenomena in this book there are still a lot of open questions that can only be answered by large statistics of observations and by more detailed modeling for instance how does the statistics of next-neighbor interactions result in the exponential growth characteristics of soc avalanches what determines the powerlaw slopes how much is the powerlaw slope determined by mathematical statistics and how much by physical scaling laws the relatively new scientific discipline of self-organized criticality is a very interdisciplinary field and we hope that this book stimulates a crossfertilization in the data analysis and development of methods among the disciplines of astrophysics geophysics biophysics and social sciences the author is most indebted to invaluable discussions with comments from and reviewing by colleagues and friends who are listed in alphabetical order eric buchlin anne cristina cadavid sandra chapman paul charbonneau norma crosby pablo dmitruk manuel g¨ del henrik jeldtoft jensen debbie leddon yuri litvinenko william liu u nadege meunier laura morales jeff scargle virginia trimble astrid veronig nicolas watkins and mike wheatland the author wishes to acknowledge the efficient and most helpful support provided by springer/praxis especially by the publishers clive horwood praxis and ramon khanna springer who encouraged and supported the publication of this book extensive usage of scientific literature was enabled by the nasa astrophysics data system ads operated by the smithsonian astrophysical observatory sao as well as by numerous wikipedia and google searches special thanks go also to my family to my children pascal dominique and alexander julian and particularly to my wife carol j kersten for their enthusiastic support of this project palo alto california july 2010 markus j aschwanden[close]
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