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On the Dynamics of the Weak Fréedericksz Transition for Nematic Liquid Crystals

Published online by Cambridge University Press:  02 November 2016

Peder Aursand*
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Gaetano Napoli*
Dipartimento di Ingegneria dell'Innovazione, Università del Salento, via per Monteroni, 73100 Lecce, Italy
Johanna Ridder*
Department of Mathematics, University of Oslo, P.O.Box 1053, Blindern, 0316 Oslo, Norway
*Corresponding author. Email (P. Aursand), (G. Napoli), (J. Ridder)
*Corresponding author. Email (P. Aursand), (G. Napoli), (J. Ridder)
*Corresponding author. Email (P. Aursand), (G. Napoli), (J. Ridder)
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We propose an implicit finite-difference method to study the time evolution of the director field of a nematic liquid crystal under the influence of an electric field with weak anchoring at the boundary. The scheme allows us to study the dynamics of transitions between different director equilibrium states under varying electric field and anchoring strength. In particular, we are able to simulate the transition to excited states of odd parity, which have previously been observed in experiments, but so far only analyzed in the static case.

Research Article
Copyright © Global-Science Press 2016 

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[1] Aursand, P. and Koley, U.. Local discontinuous Galerkin methods for a nonlinear variational wave equation modeling liquid crystals. Preprint, 2014.Google Scholar
[2] Bevilacqua, G. and Napoli, G.. Parity of the weak Fréedericksz transition. Eur. Phys. J. E, 35(12):15, 2012.CrossRefGoogle ScholarPubMed
[3] Bryan-Brown, G. P., Wood, E. L., and Sage, I. C.. Weak surface anchoring of liquid crystals. Nature, 399(6734):338340, 1999.CrossRefGoogle Scholar
[4] da Costa, F. P., Grinfeld, M., Mottram, N. J., and Pinto, J. T.. Uniqueness in the Freedericksz transition with weak anchoring. J. Diff. Eq., 246(7):25902600, 2009.CrossRefGoogle Scholar
[5] De Gennes, P. G. and Prost, J.. The Physics of Liquld Crystals. Clarendon Press, Oxford, 1993.Google Scholar
[6] Kumar, T. A., Sathyanarayana, P., Sastry, V. S. S., Takezoe, H., Madhusudana, N. V., and Dhara, S.. Temperature- and electric-field-induced inverse Freedericksz transition in a nematogen with weak surface anchoring. Phys. Rev. E, 82(1):011701, 2010.CrossRefGoogle Scholar
[7] Luckhurst, G. R., Dunmur, D. A., and Fukuda, A.. Physical properties of liquid crystals: nematics. IET, 2001.Google ScholarPubMed
[8] Napoli, G.. Weak anchoring effects in electrically driven Freedericksz transitions. J. Phys. A Math. Gen., 39(1):11, 2006.CrossRefGoogle Scholar
[9] Nehring, J., Kmetz, A. R., and Scheffer, T. J.. Analysis of weak-boundary-coupling effects in liquid-crystal displays. J. Appl. Phys., 47(3):850857, 2008.CrossRefGoogle Scholar
[10] Rapini, A. and Papoular, M.. Distorsion d’une lamelle nématique sous champ magnétique conditions d’ancrage aux parois. J. Phys. Colloq., 30(C4):C454, 1969.CrossRefGoogle Scholar
[11] Stewart, I. W.. The static and dynamic continuum theory of liquid crystals: a mathematical introduction. CRC Press, 2004.Google Scholar
[12] Virga, E. G.. Variational theories for liquid crystals, volume 8. CRC Press, 1994.CrossRefGoogle Scholar
[13] Xu, G., Shu, C.-Q., and Lin, L.. Perturbed solitons in nematic liquid crystals under time-dependent shear. Phys. Rev. A, 36(1):277284, 1987.Google ScholarPubMed