http://arxiv.org/abs/2203.12484
The statistics of nonlinear processes in avalanching systems, based on the {\sl 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 {\sl 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.
M. Aschwanden
Thu, 24 Mar 22
12/56
Comments: 51 pages, 6 Figures, 16 Tables
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