Related papers: Finite System-Size Effects in Self-Organized Criti…
Power law size distributions are the hallmarks of nonlinear energy dissipation processes governed by self-organized criticality. Here we analyze 75 data sets of stellar flare size distributions, mostly obtained from the {\sl Extreme…
The observed size distributions of solar and stellar flares is found to be consistent with the predictions of the fractal-diffusive self-organized criticality (FD-SOC) model, which predicts power law slopes with universal constants of…
We search for outliers in extreme events of statistical size distributions of astrophysical data sets, motivated by the {\sl Dragon-King hypothesis} of Sornette (2009), which suggests that the most extreme events in a statistical…
We investigate the relevance of {\sl self-organized criticality (SOC)} models in previously published empirical datasets, which includes statistical observations in astrophysics, geophysics, biophysics, sociophysics, and informatics. We…
We extend a previous statistical solar flare study of 155 GOES M- and X-class flares observed with AIA/SDO (Aschwanden 2012) to all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 \ang) to test the wavelength-dependence of scaling…
We suggest a generalized definition of self-organized criticality (SOC) systems: SOC is a critical state of a nonlinear energy dissipation system that is slowly and continuously driven towards a critical value of a system-wide instability…
Solar flares and CMEs have a broad range of magnitudes. This review discusses the possibility of "extreme events," defined as those with magnitudes greater than have been seen in the existing historical record. For most quantitative…
Nonlinear dissipative systems in the state of self-organized criticality release energy sporadically in avalanches of all sizes, such as in earthquakes, auroral substorms, solar and stellar flares, soft gamma-ray repeaters, and pulsar…
In this study we are testing whether the power law slopes ($\alpha_F$, $\alpha_E$) of fluxes $(F)$, fluences or energies $(E)$ are universal in their size distributions, $N(F) \propto F^{-\alpha_F}$ and $N(E) \propto E^{-\alpha_E}$, in…
The observed powerlaw distributions of solar flare parameters can be interpreted in terms of a nonlinear dissipative system in the state of self-organized criticality (SOC). We present a universal analytical model of a SOC process that is…
We analyze the occurrence frequency distributions of peak fluxes $P$, total fluxes $E$, and durations $T$ of solar flares over the last three solar cycles (during 1980--2010) from hard X-ray data of HXRBS/SMM, BATSE/CGRO, and RHESSI. From…
The original concept of self-organized criticality (Bak et al.~1987), applied to solar flare statistics (Lu and Hamilton 1991), assumed a slow-driven and stationary flaring rate, which warrants time scale separation (between flare durations…
Scaling laws in astrophysical systems that involve the energy, the geometry, and the spatio-temporal evolution, provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard…
Self-organized criticality describes a class of dynamical systems that maintain themselves in an attractor state with no intrinsic length or time scale. Fundamentally, this theoretical construct requires a mechanism for instability that may…
We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in…
Solar flares strongly affect the Sun's atmosphere as well as the Earth's environment. Quantifying the maximum possible energy of solar flares of the present-day Sun, if any, is thus a key question in heliophysics. The largest solar flares…
We analyzed the soft X-ray light curves from the {\sl Geostationary Operational Environmental Satellites (GOES)} over the last 37 years (1975-2011) and measured with an automated flare detection algorithm over 300,000 solar flare events…
We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it…
In order to discuss the potential impact of solar 'superflares' on space weather, we investigated statistical relations among energetic proton peak flux with energy higher than $ 10 \rm MeV$ ($F_p$), CME speed near the Sun ($V_{CME}$)…
We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of…