Finite System-Size Effects in Self-Organized Criticality Systems. (arXiv:2101.03124v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Aschwanden_M/0/1/0/all/0/1">Markus J. Aschwanden</a>
We explore upper limits for the largest avalanches or catastrophes in
nonlinear energy dissipation systems governed by self-organized criticality
(SOC). We generalize the idealized “straight” power low size distribution and
Pareto distribution functions in order to accomodate for incomplete sampling,
limited instrumental sensitivity, finite system-size effects, “Black-Swan” and
“Dragon-King” extreme events. Our findings are: (i) Solar flares show no finite
system-size limits up to L < 200 Mm, but solar flare durations reveal an upper
flare duration limit of < 6 hrs; (ii) Stellar flares observed with KEPLER
exhibit inertial ranges of $E approx 10^{34}-10^{37}$ erg, finite system-size
ranges at $E approx 10^{37}-10^{38}$ erg, and extreme events at $E =(1-5)
times 10^{38}$ erg; (iii) The maximum flare energy 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
(Earth quakes, 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.
We explore upper limits for the largest avalanches or catastrophes in
nonlinear energy dissipation systems governed by self-organized criticality
(SOC). We generalize the idealized “straight” power low size distribution and
Pareto distribution functions in order to accomodate for incomplete sampling,
limited instrumental sensitivity, finite system-size effects, “Black-Swan” and
“Dragon-King” extreme events. Our findings are: (i) Solar flares show no finite
system-size limits up to L < 200 Mm, but solar flare durations reveal an upper
flare duration limit of < 6 hrs; (ii) Stellar flares observed with KEPLER
exhibit inertial ranges of $E approx 10^{34}-10^{37}$ erg, finite system-size
ranges at $E approx 10^{37}-10^{38}$ erg, and extreme events at $E =(1-5)
times 10^{38}$ erg; (iii) The maximum flare energy 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
(Earth quakes, 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.
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