REU 2011: Inverse Problems for Electrical Networks

REU 2011：电力网络的反问题

• 批准号: 1062253
• 负责人: James Morrow
• 金额: $ 24.37万
• 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: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2015-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1062253&HistoricalAwards=false
• 关键词: REU; 2011; Inverse; Problems; Electrical

The REU Program on Inverse Problems for Electrical Networks will bring eight undergraduates to the University of Washington in each of the summers 2011-13 to work on discrete inverse problems. The inverse problem for an electrical network is the problem of finding the conductivity of resistors in an electrical network when the boundary current response to boundary voltages (response matrix) is known. Resistances may be specified by directed or undirected edge functions or vertex functions. Students will investigate the relation between the response matrix and the geometry of the network. The best way to imagine the problem is to think of a box that has leads sticking out with an electrical ciruit inside: the problem is to determine the circuit without opening the box. Students will study the relation to other discrete equations such as the Helmholtz equation and will also study permutations, graphs, and knots--problems with similar features to electrical network problems.The program will run for eight weeks. During the first week there will be lectures on foundational material, known results, and open problems. Students will then begin work on projects of their own choosing, using the available human, library, and computer resources. Students will work on their own or in teams of two. They will meet with an advisor daily for the remaining weeks. Students will present intermediate and final oral and written reports.

REU电气网络逆问题项目将在2011-13年的每个夏天为华盛顿大学带来8名本科生，从事离散逆问题的研究。电网络的逆问题是在已知边界电流响应于边界电压（响应矩阵）的情况下求出电网络中电阻的电导率的问题。电阻可以由有向或无向边函数或顶点函数指定。学生将研究响应矩阵和网络几何之间的关系。想象这个问题的最好方法是想象一个盒子，里面有一个电路：问题是在不打开盒子的情况下确定电路。学生将学习与其他离散方程的关系，如亥姆霍兹方程，还将学习排列，图形和结-与电气网络问题具有相似特征的问题。该程序将运行八周。在第一周将有讲座的基础材料，已知的结果，和开放的问题。然后，学生将开始自己选择的项目工作，利用现有的人力，图书馆和计算机资源。学生将自己或两人一组工作。在接下来的几周里，他们将每天与顾问会面。学生将提交中期和最终的口头和书面报告。