Scattering by fractal screens

David Hewett (UCL)

Joint work with Simon Chandler-Wilde and Andrea Moiola (Reading)

The analysis of acoustic and electromagnetic scattering by planar screens is a classical topic in wave propagation. But previous works assume that the screen is a smooth (e.g. Lipschitz or smoother) open subset of the plane. In this talk I will present recent work on developing well-posed boundary value problem and boundary integral equation formulations for the case where the screen is an arbitrary subset of the plane. In particular, the screen could be fractal, or have fractal boundary. Such problems are of interest in the study of fractal antennas in electrical engineering, and of fractal models of snowflakes/ice crystals in atmospheric physics. The roughness of the screen presents interesting questions concerning how boundary conditions should be enforced, and the appropriate function space setting. One observes some surprising solution behaviours - for example, waves can penetrate a sound-hard screen from which a set of measure zero has been removed, provided the fractal dimension of the removed set is large enough.