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

## TL;DR

This paper investigates equilibrium configurations of cholesteric liquid crystals in elliptical channels, employing deflation algorithms to identify multiple solutions and analyze how these configurations change with geometric and material parameters.

## Contribution

It introduces the application of deflation and deflated continuation algorithms to study complex equilibrium states in cholesteric liquid crystals within elliptical geometries.

## Key findings

- Multiple equilibrium configurations are identified for different aspect ratios and pitches.
- Deflation algorithms effectively find diverse solutions in frustrated liquid crystal systems.
- Solution branches vary significantly with geometric and material parameters.

## 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.