Mathematics of Materials Science

Materials science is concerned with predicting the behaviour and properties of materials and with designing new materials with desired properties. Often the formation of a particular material will involve understanding phase transformations and the interaction of evolution of distinct phases within a material.

A celebrated example is a model of spinoidal decomposition, in which a binary mixture decomposes into two distinct phases and the two phases evolve and coarsen in scale. The Cahn-Hilliard equation

is a model for this process. There are many fascinating mathematical questions about the ε→0 limit of this equation and others like it.

Often the phenomena of interest are at very small scales, where interfaces and surfaces play an important or role when they interact with the bulk.

Crystal growth, alloy solidification, the behaviour of gas-liquid foams, 3-D printing, numerical methods for modelling microstructures and rigorous analysis of PDEs that arise in materials science are all areas in which the Continuum Mechanics group at Glasgow have research interests.