Existence and Multiplicity of Radial Solutions Describing the Equilibrium of Nematic Liquid Crystals on Annular Domains

Pan, Tsorng‐Whay

doi:10.1006/jmaa.2000.6780

Cited by 3 publications

(10 citation statements)

References 13 publications

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“…By computing the second variation of the anisotropic OF energy and studying the resulting eigenvalue problem directly, we obtain new stability diagrams for the defect-free state in terms of δ, ρ, α, and k. Such stability diagrams can provide useful insight into the response of the defect-free state to different types of azimuthal perturbations. For k = 0, our results reduce to the previously reported results in [8][9][10][11][12]. An interesting conclusion is that the radially invariant defectfree state can largely be destabilized by radial perturbations and azimuthal perturbations are only relevant for weak anchoring or very small annular wells.…”

Section: Introductioncontrasting

confidence: 82%

“…Such stability diagrams can provide useful insight into the response of the defect‐free state to different types of azimuthal perturbations. For

k = 0

, our results reduce to the previously reported results in . An interesting conclusion is that the radially invariant defect‐free state can largely be destabilized by radial perturbations and azimuthal perturbations are only relevant for weak anchoring or very small annular wells.…”

Section: Introductioncontrasting

confidence: 81%

“…In the weak anchoring case, we analyze the defect-free state in terms of δ, ρ, α, and k, which is the azimuthal order of the perturbation. While our results, both with strong and weak anchoring, are partially captured by the results in [8][9][10][11][12], our method of proof is different. By computing the second variation of the anisotropic OF energy and studying the resulting eigenvalue problem directly, we obtain new stability diagrams for the defect-free state in terms of δ, ρ, α, and k. Such stability diagrams can provide useful insight into the response of the defect-free state to different types of azimuthal perturbations.…”

Section: Introductioncontrasting

confidence: 63%

“…Here, we give a brief overview. The papers [7][8][9][10][11][12][13][14] are directly relevant to our work. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [8], the author studies the stability and multiplicity of nematic radial equilibria on a 2D annulus with strong uniform anchoring. In Refs.…”

Section: Introductionmentioning

confidence: 99%

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Nematic Equilibria on a Two‐Dimensional Annulus

et al. 2017

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We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, in the Oseen-Frank theoretical framework. We analyze a radially invariant defect-free state and compute analytic stability criteria for this state in terms of the elastic anisotropy, annular aspect ratio, and anchoring strength. In the strong anchoring case, we define and characterize a new spiral-like equilibrium which emerges as the defectfree state loses stability. In the weak anchoring case, we compute stability diagrams that quantify the response of the defect-free state to radial and azimuthal perturbations. We study sector equilibria on sectors of an annulus, including the effects of weak anchoring and elastic anisotropy, giving novel insights into the correlation between preferred numbers of boundary defects and the geometry. We numerically demonstrate that these sector configurations can approximate experimentally observed equilibria with boundary defects.

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Section: Introductioncontrasting

confidence: 82%

“…Such stability diagrams can provide useful insight into the response of the defect‐free state to different types of azimuthal perturbations. For

k = 0

Section: Introductioncontrasting

confidence: 81%

Section: Introductioncontrasting

confidence: 63%

“…Here, we give a brief overview. The papers [7][8][9][10][11][12][13][14] are directly relevant to our work. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [8], the author studies the stability and multiplicity of nematic radial equilibria on a 2D annulus with strong uniform anchoring. In Refs.…”

Section: Introductionmentioning

confidence: 99%

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Nematic Equilibria on a Two‐Dimensional Annulus

et al. 2017

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Stationary Shear Flows of Nematic Liquid Crystals: A Comprehensive Study via Ericksen–Leslie Model

2021

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Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus

Lewis¹,

Aarts²,

Howell³

et al. 2017

SIAM J. Appl. Math.

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We study the azimuthal defect-free nematic state on a two-dimensional annulus within a simplified and reduced two-dimensional Landau-de Gennes model for nematic liquid crystals. We perform a detailed asymptotic analysis of the instabilities of the defect-free state in terms of a dimensionless material and temperature-dependent variable and the annular aspect ratio. The asymptotic analysis is accompanied by a rigorous local stability result, again in terms of a dimensionless material and temperature-dependent parameter and annular aspect ratio. In contrast to Oseen-Frank predictions, the defect-free state can be unstable in this model, with elastic isotropy and strong anchoring, for a range of macroscopically relevant annular aspect ratios.

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Existence and Multiplicity of Radial Solutions Describing the Equilibrium of Nematic Liquid Crystals on Annular Domains

Cited by 3 publications

References 13 publications

Nematic Equilibria on a Two‐Dimensional Annulus

Nematic Equilibria on a Two‐Dimensional Annulus

Stationary Shear Flows of Nematic Liquid Crystals: A Comprehensive Study via Ericksen–Leslie Model

Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus

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