Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification
Alejandro B. Kolton 1, Pierre Le Doussal2, Kay Jörg Wiese2
1
Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET),
Universidad Nacional de Cuyo (UNCUYO), Av. E. Bustillo 9500,
R8402AGP San Carlos de Bariloche, Río Negro, Argentina.
2
Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France.
Abstract
We study several probability distributions relevant to the avalanche dynamics
of elastic interfaces driven on a random substrate: The distribution of size,
duration, lateral extension or area, as well as velocities. Results from the
functional renormalization group and scaling relations involving two
independent exponents, roughness $\zeta$, and dynamics $z$, are confronted to
high-precision numerical simulations of an elastic line with short-range
elasticity, i.e. of internal dimension $d=1$. The latter are based on a novel
stochastic algorithm which generates its disorder on the fly. Its precision
grows linearly in the time-discretization step, and it is parallelizable. Our
results show good agreement between theory and numerics, both for the critical
exponents as for the scaling functions. In particular, the prediction ${\sf a}
= 2 - \frac{2}{d+ \zeta- z}$ for the velocity exponent is confirmed with good
accuracy.
arXiv:1904.08657 [pdf]
EPL 127 (2019) 46001 [pdf]
Copyright (C)
by Kay Wiese. Last edited October 15, 2019.