Vortices and Dislocations

This talk will review the analogies and differences between macroscopic models for fluid and superconducting vortices and dislocations in crystals, each being regarded as a "free" line singularity of solutions of a partial differential equation. A systematic derivation will be given of the dynamics of the line singularity in each case as well as some of the implications for homogenised models in which many singularities are present. A difficulty arises with dislocations where it appears that the discrete structure of the core needs to be taken into account.