Mathematics – Analysis of PDEs
Scientific paper
2009-07-06
Mathematics
Analysis of PDEs
45 pages; v2: generalized BCs, streamlined presentation
Scientific paper
In this paper we study the time-dependent Ginzburg-Landau equations on a smooth, bounded domain $\Omega \subset \Rn{2}$, 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.
No associations
LandOfFree
Ginzburg-Landau vortex dynamics driven by an applied boundary current does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Ginzburg-Landau vortex dynamics driven by an applied boundary current, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ginzburg-Landau vortex dynamics driven by an applied boundary current will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-27875