TY - JOUR
T1 - Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions
AU - Da Costa, Fernando P.
AU - Gartland Jr., Eugene C.
AU - Grinfeld, Michael
AU - Pinto, Joao T.
PY - 2009/6
Y1 - 2009/6
N2 - Motivated by a recent investigation of Millar and McKay [Mol. Cryst. Liq. Cryst., 435,
277/[937]-286/[946] (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.
AB - Motivated by a recent investigation of Millar and McKay [Mol. Cryst. Liq. Cryst., 435,
277/[937]-286/[946] (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.
KW - bifurcation analysis
KW - twist-freedericksz transition
KW - liquid-crystal cell
U2 - 10.1017/SO956792509007827
DO - 10.1017/SO956792509007827
M3 - Article
SN - 0956-7925
VL - 20
SP - 269
EP - 287
JO - European Journal of Applied Mathematics
JF - European Journal of Applied Mathematics
IS - 3
ER -