Depinning as a coagulation process

¹ Boğaziçi University, Physics Department - Bebek 34342 Istanbul, Turkey
² Brown University, Division of Applied Mathematics - Providence, RI 02912, USA

^(a) melih.iseri@boun.edu.tr
^(b) david_kaspar@brown.edu
^(c) mmungan@boun.edu.tr

Received: 9 June 2016
Accepted: 8 September 2016

Abstract

We consider a one-dimensional model that describes the depinning of an elastic string of particles in a strongly pinning, phase-disordered periodic environment under a slowly increasing force. 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 and numerical simulations show that the evolution of the sizes of active regions is well described by a Smoluchowski coagulation equation, allowing us to predict correlation lengths and avalanche sizes in terms of certain moments of the size distribution.