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Nonlinear dissipative systems in the state of self-organized criticalityrelease energy sporadically in avalanches of all sizes, such as in earthquakes,auroral substorms, solar and stellar flares, soft gamma-ray repeaters, andpulsar glitches. The statistical occurrence frequency distributions of eventenergies $E$ generally exhibit a powerlaw-like function $N(E)\proptoE^{-\alpha_E}$ with a powerlaw slope of $\alpha_E \approx 1.5$. The powerlawslope $\alpha_E$ of energies can be related to the fractal dimension $D$ of thespatial energy dissipation domain by $D=3/\alpha_E$, which predicts a powerlawslope $\alpha_E=1.5$ for area-rupturing or area-spreading processes with $D=2$.For solar and stellar flares, 2-D area-spreading dissipation domains arenaturally provided in current sheets or separatrix surfaces in a magneticreconnection region. Thus, this universal scaling law provides a useful newdiagnostic on the topology of the spatial energy dissipation domain ingeophysical and astrophysical observations.

A Universal Scaling Law for the Fractal Energy Dissipation Domain in Self-Organized Criticality Systems