Related papers: Disclination Loops, Hedgehogs, and All That
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular field configurations, often markedly…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
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…
Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction,…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
Colloids dispersed in nematic liquid crystals form topological composites in which colloid-associated defects mediate interactions while adhering to fundamental topological constraints. Better realising the promise of such materials…
Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable…
Using computer simulations we investigate the microscopic structure of the singular director field within a nematic droplet. As a theoretical model for nematic liquid crystals we take hard spherocylinders. To induce an overall topological…
Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which describe the dynamics of field singularities using gauge fields.…
Topological solitons are knots in continuous physical fields classified by non-zero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to condensed matter and cosmology, they remain…
Field theories predict that phase transitions sequentially breaking continuous and discrete symmetries can generate hybrid topological structures in which defects of different dimensionalities merge. We report experimental and numerical…
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
Stable array of point defects was generated in nematic liquid crystal. Point defects with topological charge of +1 and -1 (hedgehogs) were generated in vertically aligned liquid crystal cell. The hedgehogs were arranged in square or…
Topology transcends boundaries that conventionally delineate physical, biological and engineering sciences. Our ability to mathematically describe topology, combined with our access to precision tracking and manipulation approaches, has…
Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are…
We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the…