Inverse Problems for Electrical Networks -REU Site

仅由电阻组成的电网对施加在指定端子上的电压有确定的电流响应。一旦施加电压，就可以测量这些指定端子上的电流响应。将要研究的反问题是那些响应已知，而网络的电阻和/或拓扑未知但需要的问题。平面和非平面网络将被研究。此外，还将研究涉及有向网络和薛定谔方程的类似问题。与连续反问题和无限网络的关系将被研究。每年夏天将有8名本科生研究这些问题。

An electrical network consisting only of resistors has a definite current response to voltages applied at designated terminals. The current response at these designated terminals can be measured once the voltages are applied. The inverse problems that will be studied are those in which the response is known and the resistances and/or topology of the network are not known but desired. Planar and non-planar networks will be studied. In addition, similar problems involving directed networks and the Schrodinger equation will be studied. Relations to continuous inverse problems and infinite networks will be investigated. Eight undergraduates per summer will work on these problems.