论文标题
三维非欧亚人几何形状中的液晶导演场
Liquid crystal director fields in three-dimensional non-Euclidean geometries
论文作者
论文摘要
本文研究了三维弯曲空间中的nematic液体晶体，并确定哪种导致变形模式与每种可能的非欧盟几何类型兼容。 Sethna等人的先前工作。表明双重扭曲在平面$ r^3 $中被挫败，但可以完全适合Hypersphere $ S^3 $。在这里，我们将该工作扩展到所有四种变形模式（张开，扭曲，弯曲和双轴张布）和所有八个瑟斯顿几何形状。至少一种类型的几何形状，导演变形的每种纯模式都可以完美地填充空间。该分析显示了弯曲空间中每个变形模式的理想结构，这对平面空间的要求感到沮丧。
This paper investigates nematic liquid crystals in three-dimensional curved space, and determines which director deformation modes are compatible with each possible type of non-Euclidean geometry. Previous work by Sethna et al. showed that double twist is frustrated in flat space $R^3$, but can fit perfectly in the hypersphere $S^3$. Here, we extend that work to all four deformation modes (splay, twist, bend, and biaxial splay) and all eight Thurston geometries. Each pure mode of director deformation can fill space perfectly, for at least one type of geometry. This analysis shows the ideal structure of each deformation mode in curved space, which is frustrated by the requirements of flat space.
