Mathematical Sciences: REU - "Inverse Problems for Electrical Networks

这个REU网站奖将带八名本科生到华盛顿大学研究反问题。电网络的反问题是，当网络对边界电压的响应已知时，确定网络中每个电阻的电导率。阻抗层析成像的反问题是通过测量边界上的电位和电流来确定整个导电体内部的电导率。学生将研究电网的响应矩阵与网络中的导体之间的关系。他们还将研究这些离散问题在导电体逆问题中的应用。该项目将持续八周。在第一周将有讲座描述已知的结果，开放的问题，和数值方法。然后，学生将开始自己选择的项目，使用可用的计算设施，如果合适的话。学生可以自己动手，也可以两三人一组。在剩下的几周内，他们将继续定期会面。最后，学生们要就他们的项目写论文。

9531487 Morrow This REU site award will bring eight undergraduates to the University of Washington to work on inverse problems. The inverse problem for an electrical network is to determine the conductivity of each of the resistors in the network when the response of the network to boundary voltages is known. The inverse problem in impedance tomography is to determine the conductivity throughout the interior of a conducting body from measurements of potentials and currents on the boundary. Students will investigate relations between the response matrix of an electrical network and the conductors in the network. They will also work on applications of these discrete problems to inverse problems for conducting bodies. The program will run for eight weeks. During the first week there will be lectures describing known results, open problems, and numerical approaches. Students will then begin working on projects of their own choosing, using the available computing facilities, if appropriate. Students can work on their own or in teams of two or three. They will continue to meet at regularly scheduled times for the remaining weeks. At the end the students will write papers on their projects.