Issue 11, 2022

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 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.

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

Article information

Article type
Paper
Submitted
05 Nov 2021
Accepted
24 Feb 2022
First published
24 Feb 2022

Soft Matter, 2022,18, 2234-2244

Author version available

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

C. D. Schimming and J. Viñals, Soft Matter, 2022, 18, 2234 DOI: 10.1039/D1SM01584B

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