On the Disclination Lines of Nematic Liquid Crystals (Communications in Computational Physics, 2018)
Defects in liquid crystals are of great practical importance and theoreticalinterest. Despite tremendous efforts, predicting the location and transition of defectsunder various topological constraint and external field remains to be a challenge.We investigate defect patterns of nematic liquid crystals confined in three-dimensionalspherical droplet and two-dimensional disk under different boundaryconditions, within the Landau-de Gennes model. We implement a spectral methodthat numerically solves the Landau-de Gennes model with high accuracy, which allowsus to study the detailed static structure of defects. We observe five types of defectstructures. Among them the 1/2-disclination lines are the most stable structure at lowtemperature. Inspired by numerical results, we obtain the profile of disclination linesanalytically. Moreover, the connection and difference between defect patterns underthe Landau-de Gennes model and the Oseen-Frank model are discussed. Finally, threeconjectures are made to summarize some important characteristics of defects in theLandau-de Gennes theory. This work is a continuing effort to deepen our understandingon defect patterns in nematic liquid crystals.