%0 Journal Article
%T Function spaces for liquid crystals
%A S. J. Bedford
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s00205-015-0913-7
%X We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function space choices for the order parameters $s$, ${\bf n}$, and ${\bf Q}$, we establish connections between the variational formulations of these theories. We use these results to derive a version of the Oseen-Frank theory using special functions of bounded variation. This proposed model can describe both orientable and non-orientable defects. Finally we study a number of frustrated nematic and cholesteric liquid crystal systems and show that the model predicts the existence of point and surface discontinuities in the director.
%U http://arxiv.org/abs/1411.5297v2