Mean field limits of the Gross-Pitaevskii and parabolic Ginzburg-Landau equations Page 1
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 30, Number 3, July 2017 …

We consider the time-dependent Ginzburg–Landau model of superconductivity in the
presence of an electric current flowing through a two-dimensional wire. We show that when …

We consider the time-dependent 2D Ginzburg–Landau equation in the whole plane with
terms modeling impurities and applied currents. The Ginzburg–Landau vortices are then …

We study the Landau–Lifshitz–Gilbert equation for the dynamics of a magnetic vortex
system. We include the spin-torque effects of an applied spin current, and we rigorously …

We study a mixed heat and Schrödinger Ginzburg–Landau evolution equation on a
bounded two-dimensional domain with an electric current applied on the boundary and a …

Abstract Using a Ginzburg–Landau model, we study the vortex behavior of a rectangular thin
film superconductor subjected to an applied current fed into a portion of the sides and an …

This thesis is devoted to the mathematical study of effects of disorder in various physical
systems. We start with three stochastic homogenization problems in connection with static …

Abstract We study the Ginzburg–Landau equations in the presence of large electric currents
that are smaller than the critical current where the normal state loses its stability. For steady …

We investigate a version of the time-dependent Ginzburg–Landau system that models a thin
superconducting wire subjected to an applied voltage. Using a mixture of rigorous analysis …

We establish the existence of a global solution for a new family of fluid-like equations, which
are obtained in certain regimes in [24] as the mean-field evolution of the supercurrent …