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摘要翻译：
我们提出并研究了一个局域映射，它能够描述向列相液晶在定常剪切流作用下所获得的从规则到混沌的各种动力学状态。该映射是用局部框架旋转的四元数参数化表示的，局部框架旋转由向列指向矢、子指向矢和与它们垂直的关节的轴描述，另外两个标量描述有序强度。我们的模型给出了皮划艇、摇摆、翻滚、对齐和共存状态，与以前基于耦合常微分方程的公式一致。这样的地图可以作为构造复杂时空状态的晶格模型的一个构件，为剪切向列学预测。
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英文标题：
《Regular and Chaotic States in a Local Map Description of Sheared Nematic
Liquid Crystals》
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作者：
S.M. Kamil, Sudeshna Sinha and Gautam I. Menon (IMSc, Chennai)
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
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, in agreement with previous formulations based on coupled ordinary differential equations. Such a map can serve as a building block for the construction of lattice models of the complex spatio-temporal states predicted for sheared nematics.
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PDF链接：
https://arxiv.org/pdf/801.3876
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