## Dynamics of line singularities

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A Carpio, S J Chapman, S D Howison
& J R Ockendon

The dynamics of line singularities in three different physical
systems are considered,
namely vortices in an inviscid fluid, vortices in a type-II
supercondctor, and dislocations in an elastic crystal.
When the core of the singularity can be regularised with a continuum
model, as 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 the case for
dislocations, where the derivation of a law of motion is still an open
problem in the mathematical sense.