Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
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用于表征向列向错线的拓扑、几何和运动的奇点识别
DOI：
10.1039/d1sm01584b
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发表时间：
2022
期刊：
影响因子：
3.4
通讯作者：
Viñals, Jorge
中科院分区：
文献类型：
--
作者：
Schimming, Cody D.;Viñals, Jorge
本文介绍了三维液晶向错线的一个表征，它是一个与绕向错线的旋转矢量有关的张量。这个量表示在方面的张量的序参数Q，并分解为一个二元涉及的切向量的向错线和旋转矢量。此外，我们通过将该张量与拓扑电荷密度联系起来，推导出向错线速度的运动学定律，就像矢量模型中缺陷的Halperin-Mazenko描述一样。使用这个框架，相互作用的线向错和自零向错环的速度的分析预测给出并通过数值计算确认。
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.