Equilibrium configurations of nematic liquid crystals on a torus

Abstract

The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our aim is to show how a different modeling of the effect of extrinsic curvature acts as a selection principle among equilibria of the classical energy, and how new configurations emerge. In particular, our analysis predicts the existence of new stable equilibria with complex windings.

9 pages, 6 figures. This version is to appear on Phys. Rev. E

References in corpus (3)

• Two-Dimensional Matter: Order, Curvature and Defects
• Nematic textures in spherical shells
• Hyperbolic Interfaces

Cited by in corpus (13)

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• Nematic liquid crystals on curved surfaces - a thin film limit
• Defect patterns of two-dimensional nematic liquid crystals in confinement
• Influence of the Extrinsic Curvature on 2D Nematic Films
• Cooling a spherical nematic shell
• Substrate curvature governs texture orientation in thin films of smectic block copolymers
• Hydrodynamic interactions in polar liquid crystals on evolving surfaces
• Passive defect driven morphogenesis in nematic membranes
• Topological and non-topological kink families in non-linear $({\mathbb{S}}^1\times {\mathbb{S}}^1)$-Sigma models