Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes (Q1953023)

This work presents a mathematical model of Ginzburg-Landau vortices pinned by many small holes in a superconductor, in the presence of an external magnetic field. ``A scaling relation between sizes of holes and the magnitude of the external magnetic field'' is derived ``when a family of nested subdomains with pinned vortices of increasing multiplicity appears''. The purpose of this study is to obtain a homogenized vorticity density. It is proved that for weak magnetic fields there is zero vorticity; for moderate magnetic fields simple vortices are obtained, while stronger magnetic fields lead to multiple vortices.