New mathematics

The goal of this theme is the development of new analytical and computational techniques for the study of direct and inverse problems for multiscale media with periodic or random microstructure. Both wave propagation and diffusion phenomena are being addressed. Wave propagation and diffusion in composite materials are described by partial differential equations with rapidly oscillating coefficients in space, either periodic or random. Such can be studied using the well developed theory of homogenisation for PDEs. Standard homogenisation theory is however not applicable to the study of Metamaterials, since it is necessary to consider wave phenomena at high frequencies where the wavelength and microstructure dimension  are of similar orders.

This theme is split into the following sub topics:

1: Development of new Homogenisation Theories

2: Reiterated homogenisation and high-contrast materials