"Boundary vortices in thin magnetic films",

Abstract:

We analyze a model for thin ferromagnetic films that leads to the 
formation of vortices at the boundary. The energy asymptotically splits 
into a singular part depending only on the number of vortices and a 
finite part depending on their position. This finite part, the 
renormalized energy that can be calculated rather easily, describes the 
energy landscape quite well, and is shown to also control the gradient 
flow motion associated to the boundary vortex functional. The results 
and proofs are similar to the theory for Ginzburg-Landau vortices by 
Bethuel-Brezis-Helein for the static and Sandier-Serfaty for the dynamic 
case.