Poincaré的力量：阐明焦锥域中隐藏的对称性
The Power of Poincaré: Elucidating the Hidden Symmetries in Focal Conic Domains
摘要：
焦锥域通常是近晶液晶相的“吸烟枪”。等间距近晶层的几何形状是高度通用的，但同时难以处理。在这封信中，我们开发了一种方法来研究焦集smectics利用隐藏的庞加莱对称性揭示只有通过查看近晶层的投影从一个更高的维度。我们用这个角度来阐明几个经典的焦锥纹理，包括Dupin的同心圆，多边形纹理和倾斜晶界。
英文摘要：
Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures and tilt-grain boundaries.
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