2 research outputs found
First critical field of highly anisotropic three-dimensional superconductors via a vortex density model
We analyze a mean field model for d anisotropic superconductors with a
layered structure, in the presence of a strong magnetic field. The mean field
model arises as the -limit of the Lawrence-Doniach energy in certain
regimes. A reformulation of the problem based on convex duality allows us to
characterize the first critical field of the layered superconductor,
up to leading order. In previous work, Alama-Bronsard-Sandier \cite{ABS} have
derived the asymptotic value of for configurations satisfying
periodic boundary conditions; in that setting describing minimizers of the
Lawrence-Doniach energy reduces to a d problem. In this work, we treat the
physical case without any periodicity assumptions, and are thus led to studying
a delicate and essentially d non-local obstacle problem first derived by
Baldo-Jerrard-Orlandi-Soner \cite{BJOS2} for the isotropic Ginzburg-Landau
energy. We obtain a characterization of using the special anisotropic
structure of the mean field model