Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms

• Main Authors: Emerson, David B, Farrell, Patrick E, Adler, James H, MacLachlan, Scott P, Atherton, Timothy J
• Format: Journal Article
• Language: English
• Published: 14.06.2017
• Subjects: Physics - Soft Condensed Matter
• DOI: 10.48550/arxiv.1706.04597

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.