Liquid Crystals on Deformable Surfaces

Abstract

Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the surface. We derive thermodynamically consistent Frank-Oseen-Helfrich and Landau-de Gennes-Helfrich models which consider the simultaneous relaxation of the director/Q-tensor fields and the surface. The resulting systems of vector- or tensor-valued surface partial differential equation and geometric evolution laws are numerically solved to tackle the rich dynamics of these systems and to compute the resulting equilibrium shapes. The results strongly depend on the intrinsic and extrinsic curvature contributions and can lead to unexpected asymmetric shapes.

References in corpus (23)

• Topology and Dynamics of Active Nematic Vesicles
• Grain Boundary Scars and Spherical Crystallography
• Virus shapes and buckling transitions in spherical shells
• Two-Dimensional Matter: Order, Curvature and Defects
• Towards a Tetravalent Chemistry of Colloids
• Topological Defects in Spherical Nematics
• Surface free energies for nematic shells
• Solving the incompressible surface Navier-Stokes equation by surface finite elements
• Topological Defects in Nematic Droplets of Hard Spherocylinders
• A finite element approach for vector- and tensor-valued surface PDEs
• Antipolar ordering of topological defects in active liquid crystals
• Orientational order on surfaces - the coupling of topology, geometry, and dynamics
• Coarse-Grained Modeling of a Deformable Nematic Vesicle
• n-atic Order and Continuous Shape Changes of Deformable Surfaces of Genus Zero
• Equilibrium configurations of nematic liquid crystals on a torus
• Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
• Frustrated order on extrinsic geometries
• Dimension reduction for the Landau-de Gennes model on curved nematic thin films
• Liquid Crystals on Deformable Surfaces
• Nematic liquid crystals on curved surfaces - a thin film limit
• Spherical nematics with a threefold valence
• Influence of the Extrinsic Curvature on 2D Nematic Films
• Curvature-driven stability of defects in nematic textures over spherical disks

Cited by in corpus (12)

• Liquid Crystals on Deformable Surfaces
• Active Flows on Curved Surfaces
• A numerical approach for fluid deformable surfaces with conserved enclosed volume
• Coordinated motion of epithelial layers on curved surfaces
• Effects of local curvature on epithelia tissue -- coordinated rotational movement and other spatiotemporal arrangements
• Spectral methods for solving elliptic PDEs on unknown manifolds
• Active smectics on a sphere
• Chiral fluid membranes with orientational order and multiple edges
• A meshfree collocation scheme for surface differential operators on point clouds
• Mesoscale modeling of deformations and defects in thin crystalline sheets
• Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals
• A parametric finite element method for the incompressible Navier--Stokes equations on an evolving surface