Related papers: Nematics, Knots and Non-orientable Surfaces

Self-assembly of colloidal particles is poised to become a powerful composite material fabrication technique, but remains challenged by a limited control over the ensuing structures. We develop a new breed of nematic colloids that are…

Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…

This paper is a survey on the theory of knotoids and braidoids. Knotoids are open ended knot diagrams in surfaces and braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids in…

Topological defects play a key role in a variety of physical systems, ranging from high-energy to solid state physics. They yield fascinating emergent phenomena and serve as a bridge between the microspic and macroscopic world. A skyrmion…

Creation and control of topological complex excitations play crucial roles in both fundamental physics and modern information science. Torons are a sophisticated class of 3D chiral polar topological structures with both skyrmionic…

Achieving control over the directionality of active colloids is essential for their use in practical applications such as cargo carriers in microfluidic devices. So far, guidance of spherical Janus colloids was mainly realized using…

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…

Understanding and controlling the director field configuration, shape, and orientation in nematic and cholesteric liquid crystals is of fundamental importance in several branches of science. Liquid crystalline droplets, also known as…

In this paper we discuss the applications of knotoids to modelling knots in open curves and produce new knotoid invariants. We show how invariants of knotoids generally give rise to well-behaved measures of how much an open curve is…

Topological wave structures, such as vortices and skyrmions, appear in a variety of quantum and classical wave fields, including optics and acoustics. In particular, optical vortices have found numerous applications ranging from quantum…

We present a new range of solutions of the Maxwell equations in vacuum in which the topology of the field lines is that of the whole torus knots set. Knotted electromagnetic fields are solutions of the Maxwell equations in vacuum in which…

Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external…

Topological defects are singularities within a field that cannot be removed by continuous transformations. The definition of these irregularities requires an ordered reference configuration, calling into question whether they exist in…

Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number of additional topological invariants for cholesteric…

When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological…

We give a topological classification of defect lines in cholesteric liquid crystals using methods from contact topology. By focusing on the role played by the chirality of the material, we demonstrate a fundamental distinction between…

We construct a family of exact solutions to Maxwell's equations in which the points of zero intensity form knotted lines topologically equivalent to a given but arbitrary algebraic link. These lines of zero intensity, more commonly referred…

Structured light beams with space-variant polarization can be efficiently generated using voltage-tunable nematic liquid-crystal (Q-plate). By appropriately selecting the input state and the retardation of the Q-plate, an optical field…

We study elastic interactions between colloidal particles and deformation landscapes of undulations in a cholesteric liquid crystal under an electric field applied normal to cholesteric layers. The onset of undulation instability is…

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in the 2-sphere, up to orientation reversion and rotation, and knots with a strong inversion, up to conjugacy. This correspondence…