  We discuss a dynamical theory for nematic liquid crystals describing the
stage of evolution in which the hydrodynamic fluid motion has already
equilibrated and the subsequent evolution proceeds via diffusive motion of the
orientational degrees of freedom. This diffusion induces a slow motion of
singularities of the order parameter field. Using asymptotic methods for
gradient flows, we establish a relation between the Doi-Smoluchowski kinetic
equation and vortex dynamics in two-dimensional systems. We also discuss moment
closures for the kinetic equation and Landau-de Gennes-type free energy
dissipation.
