Depinning as a coagulation process

TL;DR

This paper models the depinning transition of an elastic string in a disordered environment as a coagulation process, using a Smoluchowski equation to predict critical behaviors like correlation lengths and avalanche sizes.

Contribution

It introduces a novel approach by modeling depinning as a coagulation process and applies a Smoluchowski equation to analyze critical behavior in a one-dimensional sandpile model.

Findings

Active region sizes follow a Smoluchowski coagulation distribution.

Predicted correlation lengths match numerical simulations.

Avalanche sizes can be quantitatively described by the coagulation model.

Abstract

We consider a one-dimensional sandpile model which mimics an elastic string of particles driven through a strongly pinning periodic environment with phase disorder. The evolution towards depinning occurs by the triggering of avalanches in regions of activity which are at first isolated but later grow and merge. For large system sizes the dynamically critical behavior is dominated by the coagulation of these active regions. Our analysis of the evolution and numerical simulations show that the observed sizes of active regions is well-described by a Smoluchowski coagulation equation, allowing us to predict correlation lengths and avalanche sizes.