Stochastic model for a vortex depinning in random media

A solvable model of interface depinning in random media

We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written directly for an infinite system. For a flat distribution of random local forces the value of the depinning threshold can be obtained exactly. In the case of ...

Depinning in a Random Medium

We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel features due to the breakdown of hyperscaling in a random system. There is a second-order transition between a localized and a delocalized phase of the polymer; we ...

Depinning of a metastable disordered vortex lattice.

We report on experiments investigating the depinning dynamics of a strongly pinned vortex lattice in 2H-NbSe2. We find that the depinning process starts at currents that are well below the critical current of the entire lattice and that it is governed by the formation of contiguous channels of mobile vortices connecting the sample edges. We obtain the formation time of the first channel by moni...

Depinning asymptotics in ergodic media

We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomog...

A Stochastic Optimization Model for Groundwater Management