Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
Soft Matter. 2017 Aug 16;13(32):5481-5490. doi: 10.1039/c7sm01195d.
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter, 2016, 12, 6490] pointed out that topological defects are not point-like objects but actually have orientational properties, which strongly affect the energetics and motion of the defects. That paper developed a mathematical formalism which describes the orientational properties as vectors. Here, we agree with the basic concept of defect orientation, but we suggest an alternative mathematical formalism. We represent the defect orientation by a tensor, with a rank that depends on the topological charge: rank 1 for a charge of +1/2, rank 3 for a charge of -1/2. Using this tensor formalism, we calculate the orientation-dependent interaction between defects, and we present numerical simulations of defect motion.
拓扑缺陷是所有液晶结构和动力学的重要组成部分，它们在活性液晶的实验和模拟中尤为重要。在最近的一篇论文中，Vromans 和 Giomi [Soft Matter, 2016, 12, 6490] 指出，拓扑缺陷不是点状物体，而是实际上具有取向性质，这强烈影响缺陷的能量和运动。该论文提出了一种数学形式主义，将取向性质描述为向量。在这里，我们同意缺陷取向的基本概念，但我们建议采用替代的数学形式主义。我们通过张量表示缺陷取向，其阶数取决于拓扑电荷：电荷为+1/2 时为 1 阶，电荷为-1/2 时为 3 阶。使用这个张量形式主义，我们计算了缺陷之间的取向相关相互作用，并展示了缺陷运动的数值模拟。
