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

VL - 109

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 10

M1 - 105702

ER -