Finite System-size Effects in Self-organized Criticality Systems

We explore upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems governed by self-organized criticality. We generalize the idealized straight power-law size distribution and Pareto distribution functions in order to accommodate incomplete sampling, limited instrumental sensitivity, finite system-size effects, and Black Swan and Dragon King extreme events. Our findings are as follows. (i) Solar flares show no finite system-size limits up to L less than or similar to 200 Mm, but solar flare durations reveal an upper flare duration limit of less than or similar to 6 hr. (ii) Stellar flares observed with Kepler exhibit inertial ranges of E 10(34)-10(37) erg, finite system-size ranges of E 10(37)-10(38) erg, and extreme events at E (1-5) x 10(38) erg. (iii) The maximum flare energies of different spectral type stars (M, K, G, F, A, giants) reveal a positive correlation with the stellar radius, which indicates a finite system-size limit imposed by the stellar surface area. Fitting our finite system-size models to terrestrial data sets (earthquakes, wildfires, city sizes, blackouts, terrorism, words, surnames, web links) yields evidence (in half of the cases) for finite system-size limits and extreme events, which can be modeled with dual power-law size distributions.

Automated summary

This study explores the upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems, broadening the existing size distribution functions to accommodate various factors. Findings reveal different system size limits for solar flares and stellar flares, as well as evidence of finite system-size limits and extreme events in terrestrial datasets.