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We study the problem of a cholesteric liquid crystal confined to anelliptical channel. The system is geometrically frustrated because thecholesteric prefers to adopt a uniform rate of twist deformation, but theelliptical domain precludes this. The frustration is resolved by deformation ofthe layers or introduction of defects, leading to a particularly rich family ofequilibrium configurations. To identify the solution set, we adapt and apply anew family of algorithms, known as deflation methods, that iteratively modifythe free energy extremisation problem by removing previously known solutions. Asecond algorithm, deflated continuation, is used to track solution branches asa function of the aspect ratio of the ellipse and preferred pitch of thecholesteric.

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