2022/01/01 by Cody D. Schimming, Jorge Viñals
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Classical mechanics #Condensed matter physics #Disclination #Exact solutions in general relativity #Geometry #Line (geometry) #Liquid Crystal Research Advancements #Liquid crystal #Mathematics #Micro and Nano Robotics #Physics #Quantum mechanics #Singularity #Tangent #Tangent vector #Tensor (intrinsic definition) #Tensor field #Topological defect #Topology (electrical circuits) #cond-mat.soft
paper · pdf · doi:10.1039/d1sm01584b
11 pages, 7 figures
openalex publication_date 2022/01/01 · arxiv created 2022/02/01 · arxiv updated 2022/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.