Thin film liquid crystals with oblique anchoring and boojums

@article{Alama2020ThinFL,
  title={Thin film liquid crystals with oblique anchoring and boojums},
  author={Stan Alama and Lia Bronsard and Dmitry Golovaty},
  journal={Annales de l'Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire},
  year={2020}
}

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References

SHOWING 1-10 OF 22 REFERENCES
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal
We consider a nematic liquid crystal occupying the three-dimensional domain in the exterior of a spherical colloid particle. The nematic is subject to Dirichlet boundary conditions that enforce
Dimension Reduction for the Landau-de Gennes Model in Planar Nematic Thin Films
TLDR
This work uses the method of Gamma-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness and establishes a general convergence result.
Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films
TLDR
The method of Gamma-convergence is used to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness and establishes a general convergence result to an energy defined on the surface that involves a somewhat surprising remnant of the normal component of the tensor gradient.
Analysis of Nematic Liquid Crystals with Disclination Lines
We investigate the structure of nematic liquid crystal thin films described by the Landau–de Gennes tensor-valued order parameter model with Dirichlet boundary conditions on the sides of nonzero
Liquid crystal boojum-colloids
Colloidal particles dispersed in a liquid crystal (LC) lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic
Landau–de Gennes theory of anchoring transitions at a nematic liquid crystal–substrate interface
Abstract We have used Landau–de Gennes theory to study anchoring and anchoring transitions at the interface between a nematic liquid crystal and a smooth solid substrate. In contrast to earlier work
Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond
We study global minimizers of a continuum Landau–De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the
Topological dynamics of defects: boojums in nematic drops
The dynamics of creation, annihilation, and transformation of topological defects in a closed system with a vector-type order parameter is studied both theoretically and experimentally. The
Ginzburg-Landau Vortices
The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on
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