Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines

Abstract

We introduce a characterization of disclination lines in three dimensional nematic liquid crystals as a tensor quantity related to the so called rotation vector around the line. This quantity is expressed in terms of the nematic tensor order parameter $\mathbf{Q}$, and shown to decompose as a dyad involving the tangent vector to the disclination line and the rotation vector. Further, we derive a kinematic law for the velocity of disclination lines by connecting this tensor to a topological charge density as in the Halperin-Mazenko description of defects in vector models. Using this framework, analytical predictions for the velocity of interacting line disclinations and of self-annihilating disclination loops are given and confirmed through numerical computation.

11 pages, 7 figures

References in corpus (6)

• Active matter
• Introduction to Q-tensor theory
• Biphasic, Lyotropic, Active Nematics
• Orientation of topological defects in 2D nematic liquid crystals
• Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal
• Anisotropic disclination cores in nematic liquid crystals modelled by a self consistent molecular field theory