用收缩算法计算椭圆通道中胆甾相液晶的平衡态
Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms
摘要：
研究了胆甾相液晶受限于椭圆形通道的问题。该系统在几何上是不理想的，这是因为螺旋体倾向于采用均匀的扭转变形率，但椭圆域排除了这一点。通过层的变形或引入缺陷来解决挫折，从而产生特别丰富的平衡构型家族。为了确定的解决方案集，我们适应和应用一个新的家庭的算法，被称为通货紧缩的方法，迭代修改的自由能extremisation问题，删除以前已知的解决方案。第二个算法，放气延续，用于跟踪解决方案分支的功能的纵横比的椭圆和首选间距的椭圆。
英文摘要：
We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform rate of twist deformation, but the elliptical domain precludes this. The frustration is resolved by deformation of the layers or introduction of defects, leading to a particularly rich family of equilibrium configurations. To identify the solution set, we adapt and apply a new family of algorithms, known as deflation methods, that iteratively modify the free energy extremisation problem by removing previously known solutions. A second algorithm, deflated continuation, is used to track solution branches as a function of the aspect ratio of the ellipse and preferred pitch of the cholesteric.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
