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.