Universal fluctuations and extreme statistics of avalanches near the depinning transtition

TL;DR

This paper provides exact predictions for the universal scaling behavior of maximum velocities in avalanches near the depinning transition, explaining experimental observations across various physical systems.

Contribution

It derives exact universal scaling exponents and functions for avalanche maximum velocities within mean field theory, applicable to multiple physical systems.

Findings

Identification of a robust power-law regime in maximum event statistics

Explanation of peak amplitude distributions in acoustic emission experiments

Universal applicability across different systems in the depinning universality class

Abstract

We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.