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Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions

Published online by Cambridge University Press:  01 June 2009

FERNANDO P. DA COSTA ,
EUGENE C. GARTLAND JR. ,
MICHAEL GRINFELD  and
JOÃO T. PINTO
FERNANDO P. DA COSTA
Affiliation:
Departamento de Ciências e Tecnologia, Universidade Aberta, Rua Fernão Lopes, 9, 2° Dto., P-1000-132 Lisboa, Portugal, and Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1, P-1049-001 Lisboa, Portugal email: fcosta@univ-ab.pt
EUGENE C. GARTLAND JR.
Affiliation:
Department of Mathematical Sciences, Kent State University, P.O. Box 5190, Kent, OH 44242-0001, USA email: gartland@math.kent.edu
MICHAEL GRINFELD
Affiliation:
Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK email: caas05@maths.strath.ac.uk
JOÃO T. PINTO
Affiliation:
Department of Mathematics and Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, TU Lisbon, Av. Rovisco Pais, 1, P-1049-001 Lisboa, Portugal email: jpinto@math.ist.utl.pt
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Abstract

Motivated by a recent investigation of Millar and McKay [Director orientation of a twisted nematic under the influence of an in-plane magnetic field. Mol. Cryst. Liq. Cryst435, 277/[937]–286/[946] (2005)], we study the magnetic field twist-Fréedericksz transition for a nematic liquid crystal of positive diamagnetic anisotropy with strong anchoring and pre-twist boundary conditions. Despite the pre-twist, the system still possesses ℤ2 symmetry and a symmetry-breaking pitchfork bifurcation, which occurs at a critical magnetic-field strength that, as we prove, is above the threshold for the classical twist-Fréedericksz transition (which has no pre-twist). It was observed numerically by Millar and McKay that this instability occurs precisely at the point at which the ground-state solution loses its monotonicity (with respect to the position coordinate across the cell gap). We explain this surprising observation using a rigorous phase-space analysis.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 20 , Issue 3 , June 2009 , pp. 269 - 287
Copyright
Copyright © Cambridge University Press 2009

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