Long-range interactions in the avalanches of elastic interfaces

TL;DR

This paper investigates how long-range interactions influence the dynamics and statistical properties of avalanches in elastic interfaces near the depinning transition, providing universal scaling forms and analytical insights.

Contribution

It derives universal scaling forms for correlation functions and analyzes the impact of long-range interactions on avalanche statistics and spatial structure.

Findings

Universal scaling form of local velocity correlation functions.

Long-range interactions affect avalanche cluster statistics.

Analytical insights into avalanche spatial structure within a mean-field model.

Abstract

Disordered systems submitted to a slowly increasing external stress often reacts with a jerky dynamics characterized by bursts of activity, called avalanches, which are the manifestation of an out-of-equilibrium phase transition. This thesis focuses on the dynamics of elastic interfaces near the depinning transition, and more specially on the effect of long-range interactions. I derive the universal scaling form of the correlation functions of the local velocity field. It allows to test the universality class of the transition as well as the range of the interactions. I also study the statistics of the clusters that form in presence of long-range interactions and show how it relates to the statistics of the global avalanches. Finally I present analytical advances towards the understanding of the spatial structure of avalanches within a mean-field model, the Brownian force model.