Knot theory realizations in nematic colloids
Knot theory realizations in nematic colloids
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DOI：
10.1073/pnas.1417178112
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发表时间：
2015-02-10
影响因子：
11.1
通讯作者：
Zumer, Slobodan
中科院分区：
文献类型：
--
作者：
Copar, Simon;Tkalec, Uros;Zumer, Slobodan
向列编织物是由分散在液晶中的胶体颗粒缠绕在一起的向错环形成的可重构的结和链。我们专注于在薄的扭曲的双折射层稳定的二维阵列的胶体粒子，可以控制与激光镊子纠缠的双折射向错。我们采取实验组装的结构，并展示了结不变量，构造的图形，和表面与向错环的物理上可观察到的特征，具体到手头的几何形状的对应关系。介质的非线性性质给纽结理论的传统结果增加了额外的拓扑参数，这些参数与纽结拓扑相耦合，并在可能结构的相图中引入了有序性。晶体顺序允许琼斯多项式和中间图的简化构造，并且构造算法中的步骤在液晶的物理学中被镜像。
Nematic braids are reconfigurable knots and links formed by the disclination loops that entangle colloidal particles dispersed in a nematic liquid crystal. We focus on entangled nematic disclinations in thin twisted nematic layers stabilized by 2D arrays of colloidal particles that can be controlled with laser tweezers. We take the experimentally assembled structures and demonstrate the correspondence of the knot invariants, constructed graphs, and surfaces associated with the disclination loop to the physically observable features specific to the geometry at hand. The nematic nature of the medium adds additional topological parameters to the conventional results of knot theory, which couple with the knot topology and introduce order into the phase diagram of possible structures. The crystalline order allows the simplified construction of the Jones polynomial and medial graphs, and the steps in the construction algorithm are mirrored in the physics of liquid crystals.