Nucleation of vortices with a temperature and time-dependent Ginzburg-Landau model of superconductivity

The standard scales that are used to non-dimensionalize the temperature- and time-dependent Ginzburg-Landau (TTDGL) model developed by Schmid [27], eliminate temperature-dependent parameters, and thus do not allow for superconducting phenomena due to variations in temperature. In this study, a set of new scales is presented to non-dimensionalize the TTDGL model so that the resulting dimensionless system depends upon a temperature parameter as well. Moreover, some properties of solutions to TTDGL system as a function of temperature are explored. Numerical experiments illustrating the temperature-dependency of vortex nucleation in type-II superconductors as well as the transition to the Meissner state in type-I superconductors are presented.