Michael LeBlanc, Luiza Angheluta, Karin Dahmen, Nigel Goldenfeld
We report exact predictions for universal scaling exponents and scaling functions associated with the distribution of the maximum collective avalanche propagation velocities $v_m$ in the mean field theory of the interface depinning transition. We derive the extreme value distribution $P(v_m|T)$ for the maximum velocities in avalanches of fixed duration $T$, and verify the results by numerical simulation near the critical point. We find that the tail of the distribution of maximum velocity for an arbitrary avalanche duration, $v_m$, scales as $P(v_m)\sim v_m^{-2}$ for large $v_m$. These results account for the observed power-law distribution of the maximum amplitudes in acoustic emission experiments of crystal plasticity, and are also broadly applicable to other systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.
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http://arxiv.org/abs/1303.1783
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