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

Abstract

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.