Behavior of Solutions to Time-Dependant and Inhomogenous Ginzburg-Landau Models

Indiana University, Bloomington IN

Investigators

Abstract

Behavior of Solutions to Time-dependent and Inhomogeneous Ginzburg-Landau Models Abstract of Proposed Research Peter J Sternberg This project is to conduct a rigorous investigation of some equations that have been proposed as models for superconductors. In particular, we shall study certain solutions of the time-dependent Ginzburg-Landau equations with applied currents and investigate the stability of certain steady states, the possible formation of "non-topological" vortices and the co-existence of normal and supercurrents. Superconductivity is an important topic whose mathematical modeling is poorly developed. Under this proposal, and in collaboration with some colleagues and students, we aim to further develop the mathematical analysis of some of the accepted equations and explain the observed phenomena.