25 Years of Self-Organized Criticality: Numerical Detection Methods

The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines - the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.Comment: Space Science Review series on SO

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper {\sl "Self-Organized Criticality: An explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in {\sl "Avalanches and the Distribution of Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized Criticality and Turbulence" (2012, 2013, Bern, Switzerland

Integrated flare model

This dissertation highlights the applicability of the SOC approach to the transient energy release events in the solar corona. Concerning the variability of the probability distribution functions’ exponents of the solar flares’ parameters related with the Rieger periodicity we develop an enhanced detection method based on the Scargle-Lomb periodogram and the Weighted Z wavelet transform, which shows that the Rieger periodicity is detectable also in weak flares without any privileged wavnumber in the propagation of the Rossby waves, which are assumed to be the cause for such periodicities. Regarding the fractality of solar flares, we investigate the correlation between the photospheric and the coronal structures through a non-linear force-free extrapolation of the magnetic field and the box-counting method, without finding any correlation due to the highly non-linear phenomena taking place in the low corona. Finally, we develop the static and the dynamic Integrated Flare Model based on cellular automata with driving and diffusion rules, which lead the simulated active regions to reach the state of the Self-Organized Criticality. Through this process we reproduce all the statistical properties of the solar flares, which are derived from the so far known observational studies.Αυτή η διατριβή επικεντρώνεται στην ανάδειξη της καταλληλότητας εφαρμογής της έννοιας της Κρίσιμης Αυτο-οργάνωσης στην περιγραφή των παροδικών γεγονότων έκλυσης ενέργειας στο ηλιακό στέμμα. Σχετικά με τη μεταβλητότητα των εκθετικών δεικτών των συναρτήσεων κατανομών των ηλιακών εκλάμψεων σε σχέση με την περιοδικότητα Rieger αναπτύσσεται μία εξελιγμένη μέθοδος ανίχνευσής της βασισμένη στο περιοδόγραμμα Scargle-Lomb και το Ζυγιμένο Μετασχηματισμό Κυματιδίου Ζ, που καταδεικνύει ότι η περιοδικότητα Rieger εμφανίζεται ακόμη και σε ασθενείς εκλάμψεις χωρίς προνομιακούς κυματάριθμους κατά τη διάδοση κυμάτων Rossby που πιθανώς αποτελούν την αιτία εμφάνισής της. Σε σχέση με τις φρακταλικές ιδιότητες εξετάζεται η συσχέτιση των δομών σε φωτοσφαιρικό και στεμματικό επίπεδο μέσω μη γραμμικής παρέκτασης του μαγνητικού πεδίου υπό την απουσία δυνάμεων και της μεθόδου απαρίθμησης κουτιών, χωρίς να προκύπτει καμία συσχέτιση λόγω των ισχυρά μη γραμμικών φαινομένων που συμβαίνουν σε χαμηλά στεμματικά ύψη. Τέλος αναπτύσσονται το στατικό και το δυναμικό Ολοκληρωμένο Μοντέλο Προσομοίωσης Εκλάμψεων, που βασίζονται σε κυψελικά αυτόματα με κανόνες οδήγησης και διάχυσης που οδηγούν τις προσομοιούμενες ενεργές περιοχές σε κατάσταση Κρίσιμης Αυτό-οργάνωσης. Μέσα από αυτήν τη διαδικασία αναπαράγονται όλες οι γνωστές στατιστικές ιδιότητες των εκλάμψεων από έως τώρα παρατηρήσεις

Enhanced Rieger type periodicities' detection in X-ray solar flares and statistical validation of Rossby waves' existence

The known Rieger Periodicity (ranging in literature from 150 up to 160 days) is obvious in numerous solar indices. Many sub-harmonic periodicities have also been observed (128-, 102-, 78-, and 51- days) in flare, sunspot, radio bursts, neutrino flux and flow data, coined as Rieger Type Periodicities (RTPs). Several attempts are focused to the discovery of their source, as well as the explanation of some intrinsic attributes that they present, such as their connection to extremely active flares, their temporal intermittency as well as their tendency to occur near solar maxima. In this paper, we link the X-ray flare observations made on Geosynchronous Operational Environmental Satellites (GOES) to an existing theoretical model (Lou 2000), suggesting that the mechanism behind the Rieger Type Periodicities is the Rossby Type Waves. The enhanced data analysis methods used in this article (Scargle-Lomb periodogram and Weighted Wavelet Z-Transform) provide the proper resolution needed to argue that. RTPs are present also in less energetic flares, contrary to what has been inferred from observations so far

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper “Self-Organized Criticality: An explanation of 1/fnoise” by Bak et al. (1987), the idea has been applied to solar physics, in “Avalanches and the Distribution of Solar Flares” by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.Fil: Aschwanden, Markus J.. Lockheed Martin Corporation; Estados UnidosFil: Crosby, Norma B.. Belgian Institute For Space Aeronomy; BélgicaFil: Dimitropoulou, Michaila. University Of Athens; GreciaFil: Georgoulis, Manolis K.. Academy Of Athens; GreciaFil: Hergarten, Stefan. Universitat Freiburg Im Breisgau; AlemaniaFil: McAteer, James. University Of New Mexico; Estados UnidosFil: Milovanov, Alexander V.. Max Planck Institute For The Physics Of Complex Systems; Alemania. Russian Academy Of Sciences. Space Research Institute; Rusia. Enea Centro Ricerche Frascati; ItaliaFil: Mineshige, Shin. Kyoto University; JapónFil: Morales, Laura Fernanda. Canadian Space Agency; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nishizuka, Naoto. Japan National Institute Of Information And Communications Technology; JapónFil: Pruessner, Gunnar. Imperial College London; Reino UnidoFil: Sanchez, Raul. Universidad Carlos Iii de Madrid. Instituto de Salud; EspañaFil: Sharma, A. Surja. University Of Maryland; Estados UnidosFil: Strugarek, Antoine. University Of Montreal; CanadáFil: Uritsky, Vadim. Nasa Goddard Space Flight Center; Estados Unido