论文标题
拓扑，几何形状和列表披露线运动表征的奇异性识别
Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines
论文作者
论文摘要
我们引入了三维列液晶中的披露线的表征，作为与该线周围所谓的旋转载体有关的张量。该数量是根据列张量顺序参数$ \ mathbf {q} $表示的，并显示为将切线向量与披露线和旋转矢量涉及切线向量分解。此外，我们通过将此张量与拓扑电荷密度连接到矢量模型中缺陷的Halperin-Mazenko描述中，从而得出了披露线速度的运动学定律。使用此框架，通过数值计算给出并确认了相互作用线脱节速度和自我宣传循环速度的分析预测。
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.
