Costa, Fernando Pestana daGartland Jr, Eugene C.Grinfeld, MichaelPinto, João Teixeira2010-05-142010-05-142009COSTA, 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. 269–2870956-7925 (Print)1469-4425 (Online)http://hdl.handle.net/10400.2/1467Motivated 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.engPendulum equationLiquid crystalsNon-homogeneous Dirichlet boundary value problemsBifurcation theoryTime mapsPhase plane analysisTwist-Fréedericksz transitionLiquid crystalsjournal article