Nonlinear dissipative systems in the state of self-organized criticality release energy sporadically in avalanches of all sizes , such as in earthquakes , auroral substorms , solar and stellar flares , soft gamma-ray repeaters , and pulsar glitches .
The statistical occurrence frequency distributions of event energies E generally exhibit a powerlaw-like function N ( E ) \propto E ^ { - \alpha _ { E } } with a powerlaw slope of \alpha _ { E } \approx 1.5 .
The powerlaw slope \alpha _ { E } of energies can be related to the fractal dimension D of the spatial energy dissipation domain by D = 3 / \alpha _ { E } , which predicts a powerlaw slope \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 are naturally provided in current sheets or separatrix surfaces in a magnetic reconnection region .
Thus , this universal scaling law provides a useful new diagnostic on the topology of the spatial energy dissipation domain in geophysical and astrophysical observations .