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arXiv · 0907.1000

Ginzburg-Landau vortex dynamics driven by an applied boundary current

Ian Tice
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Abstract

In this paper we study the time-dependent Ginzburg-Landau equations on a smooth, bounded domain $Ω\subset \Rn{2}$, subject to an electrical current applied on the boundary. The dynamics with an applied current are non-dissipative, but via the identification of a special structure in an interaction energy, we are able to derive a precise upper bound for the energy growth. We then turn to the study of the dynamics of the vortices of the solutions in the limit $\ep \to 0$. We first consider the original time scale, in which the vortices do not move and the solutions undergo a "phase relaxation." Then we study an accelerated time scale in which the vortices move according to a derived dynamical law. In the dynamical law, we identify a novel Lorentz force term induced by the applied boundary current.

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Ian Tice. 2010-03-24. Ginzburg-Landau vortex dynamics driven by an applied boundary current. https://arxiv.org/abs/0907.1000

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