Kamil S M, Sinha Sudeshna, Menon Gautam I
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 1):011706. doi: 10.1103/PhysRevE.78.011706. Epub 2008 Jul 18.
We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector, and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned, and coexistence states, accommodated in a phase diagram which closely resembles phase diagrams obtained using representations of the dynamics which are based on ordinary differential equations. We also study the behavior of the map under periodic perturbations of the shear rate. Such a map can serve as a building block for the construction of lattice models of the complex spatiotemporal states predicted for sheared nematics.
我们提出并研究了一种局部映射，它能够描述向列型液晶在稳定剪切流作用下所呈现的从规则到混沌的各种动力学状态。该映射是根据由向列型指向矢轴、次指向矢轴以及它们的公共法线所描述的局部坐标系旋转的四元数参数化来构建的，还有两个额外的标量描述有序强度。我们的模型产生了划动、摆动、翻滚、排列以及共存状态，这些状态容纳在一个相图中，该相图与使用基于常微分方程的动力学表示所获得的相图非常相似。我们还研究了剪切速率的周期性扰动下该映射的行为。这样的映射可以作为构建晶格模型的一个基本单元，用于描述预测的剪切向列型液晶的复杂时空状态。
