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A key result of solar flare statistics is the continuity of size distributions over nine orders of magnitude, consisting of nanoflares, microflares, and large flares, covering a range of ~1024–1033 ergs in energy. The FD-SOC model predicts power law distribution functions with a slope of when the energy of flare events are derived from the flare event 2-D area , but a flatter slope of , if the flare energies are derived from the volume-integrated total flux of the 3-D flare volume. These predictions match the observations of EUV nanoflares and microflares. These scaling laws imply more energy is distributed at large flare sizes , and thus, makes nanoflares less important for coronal heating. Such scaling laws are numerically simulated with cellular automaton codes and are applied to the time evolution of coronal loops, magnetic field line breading, and magnetic reconnection processes.
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