Nematics, Knots and Non-orientable Surfaces

Abstract

Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena through control of their characteristic defects. The use of colloids in generating defects and knotted configurations in liquid crystals has been demonstrated for spherical and toroidal particles and shows promise for the development of novel photonic devices. Extending this existing work, we describe the full topological implications of colloids representing non-orientable surfaces and use it to construct torus knots and links of type ($p$,2) around multiply-twisted Möbius strips.

6 pages, 5 figures

References in corpus (9)

• Topological Insulators
• Non-Abelian Anyons and Topological Quantum Computation
• Reconfigurable knots and links in chiral nematic colloids
• Topological colloids
• Disclination Loops, Hedgehogs, and All That
• Orientability and energy minimization in liquid crystal models
• Colloids in Cholesterics: Size-Dependent Defects and Non-Stokesian Microrheology
• Nematic braids: topological invariants and rewiring of disclinations
• Smectics: Symmetry Breaking, Singularities, and Surfaces

Cited by in corpus (24)

• Liquid Crystal Colloids
• Topologically stable magnetization states on a spherical shell: curvature stabilized skyrmions
• Magnetochiral symmetry breaking in a Möbius ring
• Three-dimensional patterning of solid microstructures through laser reduction of colloidal graphene oxide in liquid-crystalline dispersions
• Knotted Defects in Nematic Liquid Crystals
• Weaving knotted vector fields with tunable helicity
• Antipolar ordering of topological defects in active liquid crystals
• Umbilic Lines in Orientational Order
• Global Defect Topology in Nematic Liquid Crystals
• Shape-controlled orientation and assembly of colloids with sharp edges in nematic liquid crystals
• Maxwell's Theory of Solid Angle and the Construction of Knotted Fields
• Linked and Knotted Gravitational Radiation
• Orientation Dependent Interaction and Self-assembly of Cubic Magnetic Colloids in a Nematic Liquid Crystal
• Complex electric double layers in charged topological colloids
• Colloidal Surfaces with Boundaries, Apex Boojums and Nested Elastic Self-Assembly of Nematic Colloids
• Contact Topology and the Structure and Dynamics of Cholesterics
• Field-controlled columnar and planar patterning of cholesteric colloids
• Nemato-elasticity of hybrid molecular-colloidal liquid crystals
• Woven Nematic Defects, Skyrmions and the Abelian Sandpile Model
• Symmetry breaking at a topological phase transition
• Efficient sampling of knotting-unknotting pathways for semiflexible Gaussian chains
• Nontrivial Causal Structures Engendered by Knotted Solitons
• Dislocations and Fibrations: The Topological Structure of Knotted Smectic Defects
• Elastomeric Nematic Colloids, Colloidal Crystals and Microstructures with Complex Topology