The properties of many important natural and manufactured materials are
linked to their internal microstructure. The
study of how these microstructural details influence macroscopic properties leads to
fascinating scientific and mathematical questions. The results show how manufactured materials
can be optimised.

Topology Optimization: Design of artificial bone implants

Models of random structures: Gaussian random fields, 3D Poisson models, percolation models, diffusion limited aggregation, fractal networks and trees

Material Properties: conductivity/resistivity, diffusion coeffcients, anomalous diffusion, elastic properties, fluid flow, random walker probabilities

Analysis of experimental techniques: Statistical reconstruction of 3D models from 2D images; Small angle neutron and x-ray scattering