Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-c...

• Author(s): Costa, Fernando Pestana da ; Gartland Jr, Eugene C. ; Grinfeld, Michael ; Pinto, João Teixeira
• Date: 2009
• Persistent ID: http://hdl.handle.net/10400.2/1467
• Origin: Repositório Aberto da Universidade Aberta
• Subject(s): Pendulum equation; Liquid crystals; Non-homogeneous Dirichlet boundary value problems; Bifurcation theory; Time maps; Phase plane analysis; Twist-Fréedericksz transition; Liquid crystals
• Document Type: Article
• Language: English

Description

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.