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庞加莱的力学:阐明焦点圆锥域中隐藏的对称性

The power of Poincare: Elucidating the hidden symmetries in focal conic domains
课程网址: http://videolectures.net/clc2010_kamien_tpop/  
主讲教师: Randall D. Kamien
开课单位: 宾夕法尼亚大学
开课时间: 2010-08-05
课程语种: 英语
中文简介:
焦点锥形区通常是“吸烟枪”,通过它可以识别近晶液晶相。等间距近晶层的几何形状非常通用,但同时难以使用。在这次演讲中,我们开发了一种研究冥想中焦点集的方法,该方法利用隐藏的庞加莱对称性,仅通过将近晶层视为来自一个更高维的投影来揭示。我们使用这个视角来阐明几种经典的焦点圆锥纹理,包括Dupin的同心旋转,多边形纹理和倾斜晶粒边界。
课程简介: 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 talk we develop an approach to the study of focal sets in smectics which exploits a hidden Poincare 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.
关 键 词: 庞加莱力学; 液晶; 对称
课程来源: 视频讲座网
最后编审: 2019-01-21:chenxin
阅读次数: 84