Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA.
Phys Rev Lett. 2010 Jun 25;104(25):257802. doi: 10.1103/PhysRevLett.104.257802. Epub 2010 Jun 24.
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.
焦锥域通常是鉴定向列相液晶的“确凿证据”。各向同性的近晶层的几何形状具有高度的一般性，但同时也很难处理。在这封信中，我们开发了一种研究向列相焦锥域的方法，该方法利用了一种隐藏的庞加莱对称性，只有通过将近晶层视为从一维高维的投影才能揭示这种对称性。我们利用这种视角来阐明几种经典的焦锥纹理，包括杜宾的同心环面、多边形纹理和倾斜晶粒边界。
