On a system of multi-component Ginzburg-Landau vortices

On compound vortices in a two-component Ginzburg-Landau functional

We study the structure of vortex solutions in a Ginzburg–Landau system for two complex valued order parameters. We consider the Dirichlet problem in the disk in R2 with symmetric, degree-one boundary condition, as well as the associated degree-one entire solutions in all of R2. Each problem has degree-one equivariant solutions with radially symmetric profile vanishing at the origin, of the same...

Dynamics of Ginzburg-Landau vortices

Some Dynamical Properties of Ginzburg-Landau Vortices

Here 0 is a two-dimensional, smooth, bounded domain, E is a positive parameter, u : R x R, R2, g : 8 R R2 is smooth, and Igl(x) = l , x E 80. Naturally we also assume the compatibility condition that u&) = g(x) on dfl. The system (l.lH1.3) can be viewed as a simplified evolutionary GinzburgLandau equation in the theory of superconductivity (141, [51, 1111, [18]). The same system also appears in...

Ginzburg-landau Vortices and Mandelstam Diagrams

Some years ago, in D’Hoker and Phong (1989) studied the functional determinants of Laplacian on Mandelstam diagrams. They considered some renormalizations of the functional determinants of Laplacian on Mandelstam diagrams and explored their applications in String Theory. Recently, on quite a different subject, in Qing (1997) studied the renormalized energy for Ginzburg-Landau vortices on closed...

Ginzburg-landau Vortices Driven by the Landau-lifshitz-gilbert Equation

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of GinzburgLandau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear...