Mesoscopic plasticity and the vortex density model of superconductivity

Local mismatches in the atomic structure of a crystalline material are known as dislocations, and may be modelled as line sources of stress. Dislocations move around in a material in response to stress(each confined to a particular plane known as the slip plane), and may become tangled. Under cyclic loading of a material such as copper it is observed that a ``microstructure'' forms in which dislocations separate into regions of high dislocation density and regions of near pristine material. Mathematically similar line singularities occur in the theory of superconductivity, where they are known as flux tubes, or superconducting vortices. These vortices move in response to an electric current in the same way that dislocations move in response to stress.Superconducting vortices exhibit an instability in which a single straight line vortex may develop a helical structure. The goal of this project is to analyse the analogous problem in dislocation dynamics, to determine whether the corresponding instability has a role to play in the formation of the dislocation microscructure.