Phase changes and dislocations

On a macroscopic scale, liquid/solid phase changes are modelled by the famous "Stefan" model which is the simplest procedure for representing latent heat mathematically. Unfortunately this model is ill-posed whenever superheating or supercooling is present, i.e. whenever the solid is at a temperature above the melting temperature or the temperature of the liquid is below the melting temperature. This presents many interesting mathematical and computational challenges.

At the other extreme, phase changes can occur within a solid: steel can, over long times, changes its internal structure from a safe, "ductile" phase to an unsafe "brittle" phase. Here the modelling challenge is to faithfully represent the volumetric redistribution of material rather than the interfacial realignment that occurs in solidification/melting.

In metals this means that dislocations in the atomic lattice must be modelled mathematically on a variety of length scales, and such a study will hopefully lead eventually to new theories of placticity on the macroscopic scale.

People working in this area within OCIAM are

• Dr John Ockendon

• Prof. Jon Chapman

• Dr Sam Howison

• Dr R. Voskoboynikov