The growth of the super conducting phase in the presence of a magnetic field can be described through a diffusion equation for the field with appropriate boundary conditions on the super conductor-normal interface. This problem is equivalent to diffusion of heat into a under cooled melt. In simulations of the time-dependent Ginzburg-Landau equations for the super conductor the occurance of complex structures such as the flux lattice in type-II super conductors (corresponding to negative surface tension) has been observed.
Holger Frahm, Salman Ullah and Alan T. Dorsey
Flux dynamics and growth of the superconducting phase
(Phys. Rev. Lett. 66 (1991) 3067-3070)