Models, Algorithms, and Computations for Superconductivity

Prof. Qiang Du

Department of Mathematics, Michigan State University and the University of Science and Technology of Hongkong

Superconductivity has become of subject of renewed interest since the recent discovery of materials that retain superconductive properties at temperatures above the boiling point of nitrogen. In the last few years, we have been working on the development of numerical algorithms and computer codes for simulating various physical phenomena in superconductors. Our work ranges from the study of microscopic BCS models in the form of integral equations to the study of macroscopic homogenized models given by variational inequalities and nonlinear conservation laws. The center of attention in our research, however, has been focused on the study the mezoscale Ginzburg-Landau type models and their variations that account for properties of high-Tc materials. In this talk, numerical algorithms for the approximate solution of the model equations will be discussed along with some interesting simulations.