Collective Particle Flow through Random Media

TL;DR

This paper introduces a simple model for the nonlinear collective transport of interacting particles in a strongly disordered random medium, analyzing the threshold-driven transition between no flow and steady flow regimes.

Contribution

It presents a new model capturing the threshold behavior and critical phenomena of particle flow in disordered media, with analytic insights into the moving phase statistics.

Findings

Existence of a finite threshold for particle flow

Flow occurs on a sparse network near threshold

Critical behavior analyzed via mean field theory

Abstract

A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized by the presence or absence of a steady-state particle current. Below this threshold, transient motion is found in response to an increase in the force, while above threshold the flow approaches a steady state with motion only on a network of channels which is sparse near threshold. Some of the critical behavior near threshold is analyzed via mean field theory, and analytic results on the statistics of the moving phase are derived. Many of the results should apply, at least qualitatively, to the motion of magnetic bubble arrays and to the driven motion of vortices in thin film superconductors when the randomness is strong enough to destroy the tendencies to lattice order even on short length scales. Various history dependent phenomena are also discussed.