REU Site: Inverse Problems for Electrical Networks

电力网络逆问题只由电阻组成的电力网络对指定端子上施加的电压有明确的响应。如果已知网络的配置(拓扑)和电阻的电阻，则可以计算该响应。将研究的反问题是那些给出响应并且电阻和/或拓扑未知但需要的问题。将研究平面网络和非平面网络。此外，还将研究涉及散射理论和薛定谔方程的类似问题。我们将研究与连续反问题的关系。每个暑期有八名本科生要解决这些问题。

Inverse Problems For Electrical NetworksAn electrical network consisting only of resistors has a definite response to voltages applied at designated terminals. This response can be computed if the configuration (topology) of the network and resistances of the resistors are known. The inverse problems that will be studied are those in which the response is given and the resistances and/or topology are not known but desired. Planar and non-planar networks will be studied. In addition, similar problems involving scattering theory and the Schrodinger equation will be studied. Relations to continuous inverse problems will be investigated. Eight undergraduates per summer will work on these problems.