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.
