DYNAMICS OF LINE SINGULARITIES

The dynamics of line singularities in three different physical systems are considered, namely vortices in an inviscid fluid, vortices in a t ype-II superconductor, and dislocations in an elastic crystal. When th e core of the singularity can be regularized with a continuum model, a s is the case for superconducting and fluid vortices, the dynamics can be derived systematically in the asymptotic limit as the core radius tends to zero. The asymptotic analysis is more difficult when the core of the singularity is so small as to demand an atomic model, as is th e case for dislocations, where the derivation of a law of motion is st ill an open problem in the mathematical sense.