2017/06/14 by David B. Emerson, Patrick E. Farrell, Emerson, David B. +7
Physics and Astronomy · #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft
paper · pdf · doi:10.48550/arxiv.1706.04597
9 pages, 6 figures
arxiv created 2017/06/14 · arxiv updated 2017/06/15
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.