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

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Teaching: Applied and Engineering Mathematics

• MATH2000 Calculus and Linear Algebra II
• MATH3401 Partial Differential Equations
• MATH4107 Asymptotic Methods