Spatial shape of avalanches in the Brownian force model
Thimothée Thiery, Pierre Le Doussal, Kay Jörg Wiese
CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France.
Abstract
We study the Brownian force model (BFM), a solvable model of avalanche statistics
for an interface, in a general discrete setting. The BFM describes the overdamped
motion of elastically coupled particles driven by a parabolic well in independent
Brownian force landscapes. Avalanches are defined as the collective jump of the
particles in response to an arbitrary monotonous change in the well position
(i.e. in the applied force). We derive an exact formula for the joint probability
distribution of these jumps. From it we obtain the joint density of local avalanche
sizes for stationary driving in the quasi-static limit near the depinning threshold.
A saddle-point analysis predicts the spatial shape of avalanches in the limit of
large aspect ratios for the continuum version of the model. We then study fluctuations
around this saddle point, and obtain the leading corrections to the mean shape, the
fluctuations around the mean shape and the shape asymmetry, for finite aspect ratios.
Our results are finally confronted to numerical simulations.
arXiv:1504.05342 [pdf]
J. Stat. Mech. (2015) P08019 [pdf]
[MR report]
Copyright (C)
by Kay Wiese. Last edited April 24, 2015.