Motivated by a recent investigation of Millar and McKay [Mol. Cryst. Liq. Cryst., 435, 277/-286/ (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.
- bifurcation analysis
- twist-freedericksz transition
- liquid-crystal cell
Da Costa, F. P., Gartland Jr., E. C., Grinfeld, M., & 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), 269-287. https://doi.org/10.1017/SO956792509007827