Mentor: Daniel Onofrei
Fall 2009 project description:
During this summer, I participated in an individual REU project with Professor Daniel Onofrei in which we studied cloaking theory. After gaining an understanding of cloaking, we discussed future research projects that we intend to pursue over the course of the fall semester, ultimately culminating in a thesis to assist in the completion of a mathematics departmental honors degree. The research projects are described below.
In the transformation-based approximate cloaking scheme, it is necessary to surround the target object (that which is to be cloaked) with a conducting layer. Presently only one, relatively thick conducting layer has been considered. On avenue I am planning on pursuing consists of analyzing the scenario when a very thin conducting layer is placed around the target in place of the original, thicker layer. One would like to determine how the "estimate" is affected by this change from a thicker layer to a thinner one, where the "estimate" is a measure of how close the approximate cloak is to a perfect cloak. The second project we plan to work on related to the conducting layer is the addition of multiple conducting layers with another analysis of the effect on the "estimate." In addition, the original cloak did not have any dissipation. I plan on making the model more realistic by considering a cloak with some dissipation, since all materials dissipate waves to some degree. Finally, it would be beneficial to consider the plausibility of broadband cloaking (i.e. cloaking for multiple frequencies at once).