Hyperbolic Interfaces

Abstract

Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as scientists. Here I show that a special class of surfaces of constant negative Gaussian curvature can be obtained in fluid interfaces equipped with an orientational ordered phase. These arise in various soft and biological materials, such as nematic liquid crystals, cytoskeletal assemblies, or hexatic colloidal suspensions. The purely hyperbolic morphology originates from the competition between surface tension, that reduces the area of the interface at the expense of increasing its Gaussian curvature, and the orientational elasticity of the ordered phase, that in turn suffers for the distortion induced by the underlying curvature.

5 pages, 2 figures

References in corpus (10)

• The Geometry of Soft Materials: A Primer
• Two-Dimensional Matter: Order, Curvature and Defects
• Scaling of Traction Forces with Size of Cohesive Cell Colonies
• Vortices in Superfluid Films on Curved Surfaces
• Frank's constant in the hexatic phase
• Morphology of Nematic and Smectic Vesicles
• Minimal surfaces bounded by elastic lines
• Defects in nematic membranes can buckle into pseudospheres
• Defect generation and deconfinement on corrugated topographies
• Frustrated order on extrinsic geometries

Cited by in corpus (5)

• Equilibrium configurations of nematic liquid crystals on a torus
• On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry
• Influence of the Extrinsic Curvature on 2D Nematic Films
• Stresses in curved nematic membranes
• Phase separation on a hyperbolic lattice