ANALYSES, ALGORITHMS, AND COMPUTATIONS FOR MODELS OF HIGH-TEMPERATURE SUPERCONDUCTIVITY Qiang Du Department of Mathematics Michigan State University E. Lansing, MI 48824 Project Abstract During the past few years, the investigator and his colleagues have achieved significant progress in the modeling, analysis, and computation of superconducting phenomena. The proposed work of the investigator and his collaborators includes the further development and refinement of their previous work on mezoscale models (in particular, the Ginzburg-Landau model and its variants), as well as new computational and analytical explorations into the macroscale (homogenized) models. At the mezoscale level, the investigator continues the development and implementation of efficient algorithms for treating a variety of interesting phenomena involving the motion of vortices in type-II superconductors, especially the high critical temperature layered superconductors. At the macroscale, the investigator proposes to develop enhancements of existing models that can account for inhomogenieties and for applied currents and voltages and to develop and implement discretization and solution algorithms for determining approximate solutions for these models. The types of phenomena the investigator and his colleagues wish to simulate include vortex liquid and vortex glass structures, pinning by normal impurities and thickness variations, motion and de-pinning due to thermal fluctuations and applied currents and voltages, resistivity caused by motion, and critical currents. Superconductivity is one of the grand challenges identified as being crucial to future economic prosperity and scientific leadership. With the advent of modern computational technology, scientists, engineers, and mathematicians who wish to design superconducting devices and/or who wish to study the physics of superconductivity are in need robust and efficient algorithms and codes for the numerical simulation of superconduc ting phenomena. The investigator and his colleagues are aimed at meeting such a need. Useful tools will be developed not only for the use of physicists and material scientists interested in studying superconducting phenomena at the vortex level, but also for those involved in the design of superconducting devices.
