Relaxation and gradient methods for molecular orientation in liquid crystals

Abstract

Relaxation and gradient methods have been developed during the past several years for the computation of molecular orientation in liquid crystals. These methods have contributed to the classification of stable defect structures and the description of some of the transitions that occur under the influence of electric and magnetic fields. The bulk energy of the liquid crystal depends on the orientation of the optic axis, and this gives the variational problem a nonconvex constraints. Further, minimum energy configurations can be discontinous and can have singularities. In this paper, new relaxation and gradient methods are proposed to handle this nonconvex constraint. The results of numerical experiments and error analysis are presented.