Nonlilnear Partial Differential Equations in Heterogeneous Superconducting Systems and High Critical Temperature Cuprate Compounds

New Mexico State University, Las Cruces NM

Investigators

Abstract

Giorgi DMS-0604843 The investigator analyzes mathematical models of heterogeneous superconducting systems and of high-critical-temperature copper oxides that show superconducting properties. Topics considered in heterogeneous superconducting systems include the effect of surface cold working or of contact with semiconductors on the critical parameters (such as transition temperature) that describe superconductivity in mesoscopic samples, the effect of interactions of mesoscopic magnetic textures with superconductors on transition temperatures and vortex pinning, and surface nucleation in superconductors surrounded by normal materials. In high-temperature superconductivity, the investigator extends mathematical techniques developed for low-temperature systems to the SO(5) model of high-temperature copper compounds. Superconductors are materials that show zero or almost zero resistance to the flow of electrical current. Usually this happens at extremely low temperatures. Some materials that are superconductors at higher temperatures are known, including some copper compounds of recent interest. But the theory that would describe their behavior is incomplete. The investigator studies mathematical models of composite superconducting materials and of superconductors based on copper compounds. A large body of experimental data are available, but definitive models for cuprate compounds do not exist. They are of special interest because materials based on these compounds show superconducting properties at desirably high temperatures. Superconductors are of commercial interest for building electronic sensing devices, energy storage devices, magnets, and quantum computers. Progress in nanotechnologies has raised the possibility of industrial applications of mesoscopic heterogeneous magnetic and superconducting systems.