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

David B Emerson,Patrick E Farrell,James H Adler,Scott P Maclachlan,Timothy J Atherton

doi:10.1080/02678292.2017.1365385

David B Emerson, Patrick E Farrell + Show 3 more

Open Access

https://doi.org/10.1080/02678292.2017.1365385

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Abstract

ABSTRACTWe 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.

Highlights

Cholesteric liquid crystals are complex fluids that exhibit long-range orientational order, elasticity, local alignment at surfaces, optical activity and response to external stimuli [1]
To resolve the sequence of transitions that occurs around one of the maximally strained solutions, we visualise a bifurcation diagram in Figure 5 for an elliptical domain with aspect ratio μ 1⁄4 1:5 and with the preferred pitch ranging from q0 1⁄4 5 to q0 1⁄4 9
We present a new technique, deflation, for recovering equilibrium solutions of the free energy of a liquid crystal

Summary

Introduction

Cholesteric liquid crystals are complex fluids that exhibit long-range orientational order, elasticity, local alignment at surfaces, optical activity and response to external stimuli [1]. The interaction of geometric and internal frustration is expected to lead to a rich solution set because they permit multiple ways of relieving the frustration: one solution might accommodate an incommensurate number of cholesteric periods by folding the layers; another might introduce a defect. These parameters yield an extremisation problem that we anticipate a priori to be very challenging to explore by naive multistart methods

Deflation

À vkpU þ α

Results

Conclusion