Singularities and Avalanches in Interface Growth with Quenched Disorder

TL;DR

This paper introduces a model for interface growth in disordered media, revealing a transition between universality classes and showing how slope constraints lead to avalanches near the depinning transition, explaining observed singularities.

Contribution

It presents a simple model demonstrating the transition between universality classes and the emergence of avalanches due to slope constraints in interface growth.

Findings

Avalanches of growth occur near the depinning transition.

Constraints on local slopes induce singular behavior.

The model explains observed singularities in interface motion.

Abstract

A simple model for an interface moving in a disordered medium is presented. The model exhibits a transition between the two universality classes of interface growth phenomena. Using this model, it is shown that the application of constraints to the local slopes of the interface produces avalanches of growth, that become relevant in the vicinity of the depinning transition. The study of these avalanches reveals a singular behavior that explains a recently observed singularity in the equation of motion of the interface.