|Authors||D. B. Emerson, P. E. Farrell, J. H. Adler, M. C. MacLachlan and T. J. Atherton|
|Title||Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms|
|Project(s)||Center for Biomedical Computing (SFF)|
|Publication Type||Journal Article|
|Year of Publication||2017|
|Publisher||Taylor & Francis Online|
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.