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

GiorgiDMS-0604843研究人员分析了非均相超导系统和表现出超导特性的高临界温度铜氧化物的数学模型。在非均相超导体系统中考虑的问题包括表面冷加工或与半导体接触对描述介观样品超导电性的临界参数(如星化温度)的影响，介观磁性织构与超导体的相互作用对转变温度和涡钉扎的影响，以及正常材料包围的超导体中的表面成核。在高温超导中，研究人员将为低温系统开发的数学技术扩展到高温铜化合物的SO(5)模型。超导体是对电流的流动表现出零电阻或几乎零电阻的材料。通常情况下，这种情况发生在极低的温度下。一些在较高温度下成为超导体的材料是已知的，包括一些最近感兴趣的铜化合物。但能够描述它们行为的理论是不完整的。研究人员研究了复合超导材料和基于铜化合物的超导体的数学模型。有大量的实验数据可用，但铜酸盐化合物的确切模型还不存在。它们特别令人感兴趣，因为以这些化合物为基础的材料在理想的高温下表现出超导性。超导体在建造电子传感设备、储能设备、磁体和量子计算机方面具有商业价值。纳米技术的进展提高了介观非均相磁性和超导系统的工业应用的可能性。

GiorgiDMS-0604843 The investigator analyzes mathematical models ofheterogeneous superconducting systems and ofhigh-critical-temperature copper oxides that show superconductingproperties. Topics considered in heterogeneous superconductingsystems include the effect of surface cold working or of contactwith semiconductors on the critical parameters (such astransition temperature) that describe superconductivity inmesoscopic samples, the effect of interactions of mesoscopicmagnetic textures with superconductors on transition temperaturesand vortex pinning, and surface nucleation in superconductorssurrounded by normal materials. In high-temperaturesuperconductivity, the investigator extends mathematicaltechniques developed for low-temperature systems to the SO(5)model of high-temperature copper compounds. Superconductors are materials that show zero or almost zeroresistance to the flow of electrical current. Usually thishappens at extremely low temperatures. Some materials that aresuperconductors at higher temperatures are known, including somecopper compounds of recent interest. But the theory that woulddescribe their behavior is incomplete. The investigator studiesmathematical models of composite superconducting materials and ofsuperconductors based on copper compounds. A large body ofexperimental data are available, but definitive models forcuprate compounds do not exist. They are of special interestbecause materials based on these compounds show superconductingproperties at desirably high temperatures. Superconductors areof commercial interest for building electronic sensing devices,energy storage devices, magnets, and quantum computers. Progressin nanotechnologies has raised the possibility of industrialapplications of mesoscopic heterogeneous magnetic andsuperconducting systems.