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

@article{Berlyand2013HomogenizedDO,
  title={Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes},
  author={Leonid Berlyand and Volodymyr Rybalko},
  journal={NHM},
  year={2013},
  volume={8},
  pages={115-130}
}
We consider a homogenization problem for the magnetic GinzburgLandau functional in domains with a large number of small holes. We establish a scaling relation between sizes of holes and the magnitude of the external magnetic field when the multiple vortices pinned by holes appear in nested subdomains and their homogenized density is described by a hierarchy of variational problems. This stands in sharp contrast with homogeneous superconductors, where all vortices are known to be simple. The… CONTINUE READING