Vortex dynamics in mesoscopic superconducting square of variable surface

In this paper we apply the time dependent Ginzburg-Landau (TDGL) equations to the study of thin superconducting films of variable surfaces in the presence of an external applied magnetic field. We have made a systematic investigation of both the lower and upper critical fields as a function of the topological parameters which control the shape of the film surfaces. We also make a detailed investigation of the vortex dynamics as they nucleate into the sample.