A tensor model for liquid crystals on a spherical surface

Rod-like molecules confned on a spherical surface can organize themselves into nematic liquid crystal phases.This can give rise to novel textures displayed on the surface,which has been observed in experiments.An important theoretical question is how to fnd and predict these textures.Mathematically,a stable confguration of the nematic fluid corresponds to a local minimum in the free energy landscape.By applying Taylor expansion and Bingham approximation to a general molecular model,we obtain a closed-form tensor model,which gives a free energy form that is diferent from the classic Landau-de Gennes model.Based on the tensor model,we implement an efcient numerical algorithm to locate the local minimum of the free energy.Our model successfully predicts the splay,tennis-ball and rectangle textures.Among them,the tennis-ball confguration has the lowest free energy.