Distribution of velocities in an avalanche

TL;DR

This paper derives the velocity distribution in avalanches for driven elastic objects near depinning, connecting mean-field predictions with extended calculations beyond mean field using instanton equations.

Contribution

It provides a first-principles derivation of velocity distributions and extends the analysis beyond mean field to include lowest-order epsilon corrections.

Findings

Velocity distribution matches ABBM model predictions above the upper critical dimension.

Method allows computation of space and time dependence of velocities.

Extends understanding of avalanche dynamics beyond mean-field approximation.

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 epsilon=d_uc-d.