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

TL;DR

This paper introduces a tensor-based method to characterize and analyze the topology, geometry, and motion of disclination lines in three-dimensional nematic liquid crystals, combining theoretical derivations with numerical validation.

Contribution

It presents a novel tensor quantity derived from the nematic order parameter to identify disclination lines and establishes a kinematic law for their velocity, linking topology and motion.

Findings

Analytical predictions for disclination velocities

Confirmation of predictions through numerical simulations

Framework applicable to interacting and self-annihilating disclination loops

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.