Spatial clustering of depinning avalanches in presence of long-range interactions

TL;DR

This paper investigates how long-range interactions affect the spatial structure of avalanches in disordered elastic interfaces at depinning, revealing cluster scaling laws and a branching process description.

Contribution

It introduces a new analysis of avalanche clustering under long-range elasticity and links cluster statistics to the interface's roughness exponent.

Findings

Avalanches form disconnected clusters with specific scaling properties.

Cluster statistics follow a Bienaym{é}-Galton-Watson process.

Results are relevant for experimental avalanche analysis.

Abstract

Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. In this paper we determine the scaling properties of the clusters and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaym{\'e}-Galton-Watson process describing the statistics of the cluster number. Our work has a concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.