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 (71)

• Cosmological Experiments in Condensed Matter Systems
• Cosmic Evolution in a Cyclic Universe
• Traversable wormholes: Some simple examples
• From Big Crunch to Big Bang
• General Relativity in Electrical Engineering
• Historical roots of gauge invariance
• How generic is cosmic string formation in SUSY GUTs
• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
• Observation of thermal Hawking radiation at the Hawking temperature in an analogue black hole
• Planck 2013 results. XXV. Searches for cosmic strings and other topological defects
• Superfluid analogies of cosmological phenomena
• Sonic black holes in dilute Bose-Einstein condensates
• Cosmic String Interpretation of NANOGrav Pulsar Timing Data
• Disclinations, dislocations and continuous defects: a reappraisal
• Natural Wormholes as Gravitational Lenses
• Pancharatnam-Berry phase optical elements for wavefront shaping in the visible domain: switchable helical modes generation
• Has NANOGrav found first evidence for cosmic strings?
• Essential and inessential features of Hawking radiation
• Topological structure and dynamics of three dimensional active nematics
• Topological Defects and Structure Formation
• From NANOGrav to LIGO with metastable cosmic strings
• Cosmic microwave background anisotropy from wiggly strings
• Geometric Theory of Defects
• Thermal rectification in bulk materials with asymmetric shape
• Semilocal Topological Defects
• Rotating effects on the scalar field in the cosmic string spacetime, in the spacetime with space-like dislocation and in the spacetime with a spiral dislocation
• Towards a metamaterial simulation of a spinning cosmic string
• Riemannian geometry of irrotational vortex acoustics
• Lensing effects in a nematic liquid crystal with topological defects
• The next generation of analogue gravity experiments
• Observing Correlated Production of Defects-Antidefects in Liquid Crystals
• On the optical-mechanical analogy in general relativity
• Scattering on Dislocations and Cosmic Strings in the Geometric Theory of Defects
• Transonic Elastic Model for Wiggly Goto-Nambu String
• Geodesics around line defects in elastic solids
• Black and White Holes at Material Junctions
• Geodesics around a dislocation
• Liquid crystal hyperbolic metamaterial for wide-angle negative-positive refraction and reflection
• On the deflection of light by topological defects in nematic liquid crystals
• Generation of vector beams with liquid crystal disclination lines
• Molecular simulation and theory of a liquid crystalline disclination core
• Deformations of the spin currents by topological screw dislocation and cosmic dispiration
• Controllable shifting, steering, and expanding of light beam based on multi-layer liquid-crystal cells
• A locally finite model for gravity
• Metric approach for sound propagation in nematic liquid crystals
• Optics near an hyperbolic defect
• Diffraction of light by topological defects in liquid crystals
• Propagation of acoustic waves in a von-Kármán vortex street like configuration of disclinations
• Geometrical optics limit of phonon transport in a channel of disclinations
• 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
• Modeling Kleinian cosmology with electronic metamaterials
• Use of Quadratic Differentials for Description of Defects and Textures in Liquid Crystals and 2+1 Gravity
• Scalar Casimir effect in a high-dimensional cosmic dispiration spacetime
• Generation of optical vorticity from topological defects
• Renormalized scalar propagator around a dispiration
• The no-defect conjecture in cosmic crystallography
• Probing the cosmological singularity with a particle
• Use of meanders and train tracks for description of defects and textures in liquid crystals and 2+1 gravity
• Tailoring diffusion in analogue spacetimes
• Optical concentrator from a hyperbolic liquid crystal metamaterial
• The wiggly cosmic string as a waveguide for massless and massive fields
• Quantum influence of topological defects on a relativistic scalar particle with Cornell-type potential in cosmic string space-time with a spacelike dislocation
• Classical Kalb-Ramond field theory in curved spacetimes
• Spacetime Defects: von Kármán vortex street like configurations
• Tubes of magnetic flux and electric current in space physics
• On the energy of topological defect lattices
• Scalar self-interaction in the spacetime of a cosmic dispiration