Pingwen Zhang

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  Defects of Liquid Crystals
  Pingwen Zhang

  Defects in liquid crystals (LCs) are of great practical and theoretical importance. Recently there is a growing interest in LCs materials under topological constrain and/or external force, but the defects pattern and dynamics are still poorly understood. We investigate three-dimensional spherical droplet within the Landau-de Gennes model under different boundary conditions. When the Q-tensor is uniaxial, the model degenerates to vector model (Oseen-Frank), but Q-tensor model is superior to vector model as the former allows biaxial in the order parameter. Using numerical simulation, a rich variety of defects pattern are found, and the results suggest that, line disclinations always involve biaxial, or equivalently, uniaxial only admits point defects. Then we believe that Q-tensor model is essential to include the disclinations line which is a common phenomena in LCs. The mathematical implication of this observation will be discussed in this talk.