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

非均质超导系统和高临界温度铜酸盐化合物中的非线性偏微分方程

• 批准号: 0604843
• 负责人: Tiziana Giorgi
• 金额: $ 12.2万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-15 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604843&HistoricalAwards=false
• 关键词: Nonlilnear; Partial; Differential; Equations; Heterogeneous

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.

GiorgiDMS-0604843 研究人员分析了数学模型的异质超导系统和高临界温度的铜氧化物，显示超导性能。 在异质超导系统中考虑的主题包括表面冷加工或与半导体接触对描述介观样品中超导性的临界参数（如收缩温度）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旋钉扎的影响，以及被正常材料包围的超导体的表面成核。 在高温超导方面，研究者将低温系统的超导技术扩展到高温铜化合物的SO（5）模型。 超导体是一种对电流的电阻为零或几乎为零的材料。 通常在极低的温度下发生。 一些材料在高温下是超导体是已知的，包括一些最近感兴趣的铜化合物。 但是描述它们行为的理论是不完整的。 研究人员研究复合超导材料和基于铜化合物的超导体的数学模型。 大量的实验数据是可用的，但铜酸盐化合物的确定性模型不存在。 它们特别令人感兴趣，因为基于这些化合物的材料在理想的高温下显示出超导特性。 超导体在建造电子传感设备、能量存储设备、磁体和量子计算机方面具有商业利益。 纳米技术的发展提高了介观异质磁性和超导系统的工业应用的可能性。