Distribution of velocities in an avalanche

CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75005 Paris, France, EU

^a wiese@lpt.ens.fr

Received: 12 October 2011
Accepted: 18 January 2012

Abstract

For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d⩾d_uc, the n-times distribution of the center-of-mass velocity is equivalent to the prediction from the ABBM stochastic equation. Our method allows to compute space and time dependence from an instanton equation. We extend the calculation beyond mean field, to lowest order in ϵ=d_uc−d.