The Fractality and Size Distributions of Astrophysical Self-Organized Criticality Systems |
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Markus J Aschwanden Submitted: 2022-03-22 14:57
The statistics of nonlinear processes in avalanching systems,
based on the self-organized criticality (SOC) concept
of Bak et al. (1987), predicts power law-like size (or
occurrence frequency) distribution functions. Following up
on previous work we define a standard SOC model in terms
of six assumptions: (i) multi-fractality; (ii) the
length-area-volume relationship of Mandelbrot (1977);
(iii) the flux-volume relationship, (iv) classical
diffusion, (v) the Euclidean volume limit at the event peak time,
and (vi) the spatio-temporal fluence or energy of an
avalanche event. We gather data of the fractal dimension
and power law slopes from 162 publications and assemble
them in 28 groups (e.g., solar and stellar flare energies),
from which we find that 75% of the groups
are consistent with the standard SOC model.
Alternative SOC models (Levy-flight, flat-world, non-fractal)
are slightly less correlated with the data. The remaining
discrepancies are attributed to outliers caused by
small-number statistics, background subtraction problems,
inadequate fitting ranges, and deviations from ideal power laws.
Authors: Markus J. Aschwanden
Projects: SDO-AIA
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Publication Status: submitted. 2022-03-22
Last Modified: 2022-03-23 13:12
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