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Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions.
- Source :
-
European Journal of Applied Mathematics . Jun2009, Vol. 20 Issue 3, p269-287. 19p. 7 Graphs. - Publication Year :
- 2009
-
Abstract
- 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 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-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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09567925
- Volume :
- 20
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- European Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 39773402
- Full Text :
- https://doi.org/10.1017/S0956792509007827