The reduction of the excited noise of transportation, especially in gas turbines of airplanes and ships or mufflers of cars, is currently of major public and industrial interest. We aim to describe the effective absorption properties of sound absorbing resonator structures and perforated walls. As the governing equations and structures possess several scales, we study the problems asymptotically. In this project we derive and study approximative boundary and transmission conditions, that take into account the physical phenomena on the small scales inside the holes of the perforated absorber and the boundary layers in their neighbourhood.
Photonic crystal wave-guides are devices that allow for exceptional tailoring of the properties of light propagation. Currently, the prediction of the properties relies mainly on models for infinite, perfect photonic crystal wave-guides. For photonic crystal circuits scattering matrix approaches have been proposed. In this project we study imperfect photonic crystal wave-guides and circuits of finite lengths with techniques of asymptotic expansion.