Geometric theory of topological defects: methodological developments and new trends

Abstract

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the art of the differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics, and conclude with a review on defect engineering for transport phenomena.

References in corpus (19)

• Traversable wormholes: Some simple examples
• General Relativity in Electrical Engineering
• Disclinations, dislocations and continuous defects: a reappraisal
• Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation
• The next generation of analogue gravity experiments
• On the deflection of light by topological defects in nematic liquid crystals
• Generation of vector beams with liquid crystal disclination lines
• Controllable shifting, steering, and expanding of light beam based on multi-layer liquid-crystal cells
• A locally finite model for gravity
• Cosmology in the laboratory: an analogy between hyperbolic metamaterials and the Milne universe
• Generation of hard twisted photons by charged particles in cholesteric liquid crystals
• Principles of thermal design with nematic liquid crystals
• Retrieving the saddle-splay elastic constant $K_{24}$ of nematic liquid crystals from an algebraic approach
• Thermal diode made by nematic liquid crystal
• Generation of optical vorticity from topological defects
• Probing the cosmological singularity with a particle
• Quantum influence of topological defects on a relativistic scalar particle with Cornell-type potential in cosmic string space-time with a spacelike dislocation
• The wiggly cosmic string as a waveguide for massless and massive fields
• Classical Kalb-Ramond field theory in curved spacetimes