Branched Microstructures in the Ginzburg--Landau Model of Type-I Superconductors

摘要: We consider the Ginzburg--Landau energy for a type-I superconductor in shape of an infinite three-dimensional slab, with two-dimensional periodicity, applied magnetic field which is uniform and perpendicular to slab. determine optimal scaling law minimal terms parameters problem when sufficiently small sample thick. This proven via ansatz-free lower bounds explicit branching construction refines further as one approaches surface sample. Two different regimes appear, exponents. In first regime, leads almost pattern on boundary; second inhomogeneity survives up boundary.