TY - JOUR
T1 - Distribution of maximum velocities in avalanches near the depinning transition
AU - Leblanc, Michael
AU - Angheluta, Luiza
AU - Dahmen, Karin
AU - Goldenfeld, Nigel
PY - 2012/9/4
Y1 - 2012/9/4
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.109.105702
DO - 10.1103/PhysRevLett.109.105702
M3 - Article
AN - SCOPUS:84865708749
SN - 0031-9007
VL - 109
JO - Physical review letters
JF - Physical review letters
IS - 10
M1 - 105702
ER -