Steady state solutions in a model of a cholesteric liquid crystal sample

da Costa, F. P., Grinfeld, M., Mottram, N. J. , Pinto, J. T. and Xayxanadasy, K. (2021) Steady state solutions in a model of a cholesteric liquid crystal sample. Afrika Matematika, 32, pp. 645-672. (doi: 10.1007/s13370-020-00851-9)

Abstract

Motivated by recent mathematical studies of Fréedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [(da Costa et al. in Eur J Appl Math 20:269–287, 2009), (da Costa et al. in Eur J Appl Math 28:243–260, 2017), (McKay in J Eng Math 87:19–28, 2014), (Millar and McKay in Mol Cryst Liq Cryst 435:277/[937]–286/[946], 2005)], we consider a model for the director configuration obtained within the framework of the Frank-Oseen theory and consisting of a nonlinear ordinary differential equation in a bounded interval with non-homogeneous mixed boundary conditions (Dirichlet at one end of the interval, Neumann at the other). We study the structure of the solution set using the depth of the sample as a bifurcation parameter. Employing phase space analysis techniques, time maps, and asymptotic methods to estimate integrals, together with appropriate numerical evidence, we obtain the corresponding novel bifurcation diagram and discuss its implications for liquid crystal display technology. Numerical simulations of the corresponding dynamic problem also provide suggestive evidence about stability of some solution branches, pointing to a promising avenue of further analytical, numerical, and experimental studies.

• Item Type: Articles
• Additional Information: FPdC and JTP were partially funded by FCT/Portugal through project CAMGSD UID/MAT/04459/2020. FPdC acknowledges financial support provided by the University of Strathclyde David Anderson Research Professorship.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mottram, Professor Nigel
• Authors: da Costa, F. P., Grinfeld, M., Mottram, N. J., Pinto, J. T., and Xayxanadasy, K.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Afrika Matematika
• Publisher: Springer
• ISSN: 1012-9405
• ISSN (Online): 2190-7668
• Published Online: 28 October 2020
• Copyright Holders: Copyright © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2020
• First Published: First published in Afrika Matematika 32:645-672
• Publisher Policy: Reproduced in accordance with the publisher copyright policy