Dynamic Critical Phenomena in Channel Flow

TL;DR

This paper investigates the critical behavior of driven particle flow in a 2D random medium, revealing robust phase transition characteristics and divergence in convergence times near the threshold, with implications for vortex motion in superconductors.

Contribution

It introduces a simple model for channel flow in disordered media, demonstrating the robustness of critical behavior and analyzing divergence in convergence times at the threshold.

Findings

Flow concentrates on a sparse network of channels above threshold

Convergence time diverges with a larger exponent than current density

Critical behavior is independent of how the driving force is increased

Abstract

A simple model of the driven motion of interacting particles in a two dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state current. The critical behavior is found to be surprisingly robust, being independent of whether the driving force is increased suddenly or adiabatically. Just above threshold, the flow is concentrated on a sparse network of channels, but the time scale for convergence to this fixed network diverges with a larger exponent that that for convergence of the current density to its steady-state value. This is argued to be caused by the ``dangerous irrelevance'' of dynamic particle collisions at the critical point. Possible applications to vortex motion near to the critical current in dirty thin film superconductors are discussed briefly.