Nonlinear fluid flow in random media: Critical phenomena near threshold

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Abstract
A simple model for nonlinear collective transport in random media with strong disorder is presented and analyzed. It should apply to systems such as strongly pinned vortex lines in thin superconducting films or low-density fluid flow down a randomly rough inclined plane, in which the randomness is strong enough to break the flow into channels. The model exhibits a threshold force above which macroscopic flow exists. The critical behavior around this threshold is obtained analytically in mean-field theory, which should be valid in three dimensions and higher, and in one dimension. Analytical bounds and numerical simulations are used in the two-dimensional case. Correlation lengths above and below threshold scale differently. Multiple divergent length scales are seen above threshold. Possible modifications due to thermal fluctuations and other effects, and applications to physical systems, are discussed.