Colloquium: Paul Martin

Speaker: Paul Martin, Colorado School of Mines

Title: Acoustic and electric Faraday cages

Abstract: A Faraday cage is used for shielding from external fields. We consider simple two-dimensional mathematical models of cages, using many identical small circles to represent the cross-sections of many parallel wires. The main emphasis of the talk will be on periodic configurations of N small circles distributed evenly around a large circle (a ring). We calculate the fields around the wires due to an ambient (or incident) field, and then we investigate what happens when N gets large so that the gaps between the wires shrinks. We expect that, in the limit, the cage will behave as a ring (with no gaps), and this expectation is confirmed. However, we will see that the limiting problem is approached very slowly.

Faculty host: Junshan Lin

Brief Description of the Speaker’s Academic and Professional Achievements/Credentials:

Prof. Paul Martin works in applied mathematics that includes waves propagations, inverse problems, waves in anisotropic and inhomogeneous media, and has published over 130 papers in peer review journals. He is the Editor-in-Chief of SIAM Journal on Applied Mathematics and serves on the editorial board of Quarterly Journal of Mechanics and Applied Mathematics, Journal of Integral Equations and Applications, etc. He also published one book entitled Multiple Scattering: Interaction of Time-Harmonic Waves with NObstacles (Cambridge University Press, 2006).