Volume 127, Number 4, August 2019
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||11 September 2019|
Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification
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 - 24 rue Lhomond, 75005 Paris, France
Received: 18 April 2019
Accepted: 16 August 2019
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 ζ, 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 for the velocity exponent is confirmed with good accuracy.
PACS: 64.60.av – Cracks, sandpiles, avalanches, and earthquakes / 68.35.Rh – Phase transitions and critical phenomena / 05.70.Jk – Critical point phenomena
© EPLA, 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.