Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions

Fernando P. Da Costa, Eugene C. Gartland Jr., Michael Grinfeld, Joao T. Pinto

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3 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages269-287
Number of pages18
JournalEuropean Journal of Applied Mathematics
Volume20
Issue number3
DOIs
Publication statusPublished - Jun 2009

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Nematic liquid crystals
Nematic Liquid Crystal
Bifurcation Analysis
Twist
Ground state
Anisotropy
Boundary conditions
Magnetic fields
Cell
Ground State Solution
Pitchfork Bifurcation
Symmetry Breaking
Phase Space
Magnetic Field

Keywords

  • bifurcation analysis
  • twist-freedericksz transition
  • liquid-crystal cell

Cite this

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title = "Bifurcation analysis of the twist-Freedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions",
abstract = "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.",
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year = "2009",
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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

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