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

Grinfeld, M. and Da Costa, F.P. and Gartland, E.C. and Pinto, J.T. (2009) Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions. European Journal of Applied Mathematics, 20 (3). pp. 269-287. ISSN 0956-7925

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    Abstract

    Motivated by a recent investigation of Millar and McKay [Mol. Cryst. Liq. Cryst., 435, 277/[937]-286/[946] (2005)], we study the magnetic field twist-Fr´eedericksz 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-Fr´eedericksz tran- sition (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.

    Item type: Article
    ID code: 13690
    Keywords: bifurcation analysis, twist-freedericksz transition, liquid-crystal cell, Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 13 Jan 2010 11:29
      Last modified: 14 Mar 2012 15:44
      URI: http://strathprints.strath.ac.uk/id/eprint/13690

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