Related papers: Tight composites knots and chirality
Chirality is ubiquitous from microscopic to macroscopic phenomena in physics and biology, such as fermionic interactions and DNA duplication. In photonics, chirality has traditionally represented differentiated optical responses for right…
We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the…
Massive higher spin fields are notoriously difficult to introduce interactions when they are described by symmetric (spin)-tensors. An alternative approach is to use chiral description that does not have unphysical longitudinal modes. For…
We analyze how chirality can generate pulling optical forces and left-handed torques by cross-coupling linear-to-angular momenta between the light field and the chiral object. In the dipolar regime, we reveal that such effects can emerge…
The flow of time moves in one direction in any spatial position and orientation in this universe. Chiral objects, which lack mirror symmetry, retain their chirality regardless of their position or orientation. Despite being seemingly…
We investigate the effect of knot type on the properties of a ring polymer confined to a slit. For relatively wide slits, the more complex the knot, the more the force exerted by the polymer on the walls is decreased compared to an…
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of…
We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order.…
Chiral phonons have been proposed to be involved in various physical phenomena, yet the chirality of molecular normal modes has not been well defined mathematically. Here we examine two approaches for assigning and quantifying the chirality…
Racks and quandles are rich algebraic structures that are strong enough to classify knots. Here we develop several fundamental categorical aspects of the theories of racks and quandles and their relation to the theory of permutations. In…
Chirality manifests across multiple scales, yielding unique phenomena that break mirror symmetry. In chiral materials, unexpectedly large spin-filtering or photogalvanic effects have been observed even in materials composed of light…
Chiral metal halide perovskites have emerged as promising optoelectronic materials for emission and detection of circular polarized visible light. Despite chirality being realized by adding chiral organic cations or ligands, the chiroptical…
We reveal a previously unknown continuous symmetry and conservation law in the equations of linear isotropic elasticity, which describe the chirality of elastic waves. We show that the integral chirality is determined by the population…
The role of the topology and its relation with the geometry of biopolymers under different physical conditions is a nontrivial and interesting problem. Aiming at understanding this issue for a related simpler system, we use Monte Carlo…
Nonequilibrium active polymers provide a minimal framework to investigate biopolymers such as DNA and chromatin under the action of molecular motors. Here we study active ring polymers with controlled topology and show that knot type…
The ability to create surface structures with precisely controlled chirality remains a major challenge in laser-matter interaction experiments. In this work, we theoretically study the interaction of vortex laser beams, characterized by…
Topology concepts have significantly deepened of our understanding in recent years of the electronic properties of one-dimensional (1D) nano structures such as the graphene nanoribbons. Controlling topological electronic properties of GNRs…
Massive brute-force compute campaigns relying on demanding ab initio calculations routinely search for novel materials in chemical compound space, the vast virtual set of all conceivable stable combinations of elements and structural…
In this paper we outline a topological framework for constructing 2-periodic knitted stitches and an algebra for joining stitches together to form more complicated textiles. Our topological framework can be constructed from certain…
Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…