Séminaire

14h: David Hewett "Homogenized boundary conditions and resonance effects in Faraday cages"

We consider two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). In the limit as the number of wires in the cage tends to infinity we use the asymptotic method of multiple scales to derive continuum models for the shielding, which involve homogenized boundary conditions on an idealised cage boundary. We investigate how the resulting models depend on the key cage parameters such as the size and shape of the wires, and in the electromagnetic case the frequency and polarisation of the incident field. We find in the electromagnetic case that there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying our continuum model we are able to calculate to high precision the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated membranes.

15h30: George Chkadua "Full Asymptotic Expansion of Solutions of Hypoelliptic Equations"