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)∼vm-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.
ASJC Scopus subject areas
- Physics and Astronomy(all)