Motion of Singularities in the Heat Flow of Harmonic Maps into a Sphere

Abstract

Numerical experiments are used to determine the motion of singularities in the heat flow of harmonic maps into a unit sphere. These singularities are closely related to point defects in a nematic liquid crystals. The motion of singularities is affected by initial positions and interaction between singularities and boundary conditions. In particular, it is shown that the motion of singularities is the same as the motion of point defects in nematic liquid crystals under Neumann boundary conditions. For Dirichlet boundary conditions, the results do not properly reflect the crystal defect motion due to the shortcoming of the model.