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

Costa, Fernando Pestana da; Gartland Jr, Eugene C.; Grinfeld, Michael; Pinto, João Teixeira

http://hdl.handle.net/10400.2/1467

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Authors

Costa, Fernando Pestana da

Gartland Jr, Eugene C.

Grinfeld, Michael

Pinto, João Teixeira

Abstract(s)

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. Cryst 435, 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 z_2 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.

Keywords

Pendulum equation Liquid crystals Non-homogeneous Dirichlet boundary value problems Bifurcation theory Time maps Phase plane analysis Twist-Fréedericksz transition Liquid crystals

URI

http://hdl.handle.net/10400.2/1467

Citation

COSTA, Fernando Pestana da [et al.] - Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions. " European Journal of Applied Mathematics" [Em linha]. ISSN 0956-7925 (Print) 1469-4425 (Online). Vol. 20 (2009), p. 269–287