论文标题
良好的振动：分类域的包装规则
Good Fibrations: Packing Rules for Diabolic Domains
论文作者
论文摘要
我们描述了一种在液晶无弯曲纹理中填充倍重型“分生物”结构域的理论。这些域连续缝合在一起，提供了类似于近晶液晶中焦圆锥结构域的无弯纹理的menagerie。我们展示了不同的领域如何通过Lorentz的转换相互关联，并且此过程可能会降低系统的弹性能量。我们讨论了可能形成的许多阶段，包括蓝相的扭转类似物。我们还讨论了这些可分解的结构域如何受到“超硫酸升高”的影响，从而产生类似于冲击波的缺陷。我们探索了这些纹理的几何形状，证明了它们与HopF链接的Milnor纤维的关系。最后，我们展示了这些领域的理论如何在四维空间中统一。
We describe a theory of packing hyperboloid 'diabolic' domains in bend-free textures of liquid crystals. The domains sew together continuously, providing a menagerie of bend-free textures akin to the packing of focal conic domains in smectic liquid crystals. We show how distinct domains may be related to each other by Lorentz transformations, and that this process may lower the elastic energy of the system. We discuss a number of phases that may be formed as a result, including splay-twist analogues of blue phases. We also discuss how these diabolic domains may be subject to "superluminal boosts", yielding defects analogous to shocks waves. We explore the geometry of these textures, demonstrating their relation to Milnor fibrations of the Hopf link. Finally, we show how the theory of these domains is unified in four-dimensional space.
