Mathematical Sciences: Projects in Inverse Conductivity

数学科学：逆电导率项目

• 批准号: 9000687
• 负责人: Edward Curtis
• 金额: $ 7.2万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-04-01 至 1992-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000687&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Projects; Inverse; Conductivity

Eight undergraduate students will be supported by this Research Experiences for Undergraduates award. They will work under the direction of two faculty advisors on mathematical problems concerned with inverse conductivity. The prototype of such problems is that of finding electrical conductivity of a body knowing only the surface voltages and currents. The discrete (and very difficult) analogue of this problem occurs when one replaces the conducting medium with a network of resistors. If the boundary current is known, then an algorithm exists which determines the resistances. One of the problems the students will work on is that of determining the boundary current from the potential. With that, they will go on to consider questions such as determining the size of the largest network for which the algorithm works, the detection of resistors of zero or infinite conductivity. In addition, work will be done in an effort to determine the shape of the region from surface currents, in estimating the degree of approximation one gets by replacing continuous media by a discrete network. Many other related problems will arise naturally which will provide realistic challenges to the students while assisting the senior investigators with their on-going research programs.

八名本科生将获得此支持 本科生研究经验奖。 他们将工作 在两位数学顾问的指导下， 与逆电导率有关的问题。 的原型 这样的问题是，找到导电性的， 身体只知道表面电压和电流。 的 这个问题的离散（和非常困难的）类似出现 当人们用一个网络代替导电介质时， 电阻器. 如果边界电流是已知的，则算法 它决定了阻力。 学生们要解决的问题之一是 从所述电势确定所述边界电流。 有了这个， 他们将继续考虑诸如确定 算法适用的最大网络的大小， 检测零或无限大电导率的电阻器。 在 此外，还将努力确定 从表面电流中估计该地区的程度 近似一个得到通过替换连续介质由 离散网络 许多其他相关的问题也会出现 这自然会给学生们带来现实的挑战 同时协助高级调查员进行 研究项目。