Related papers: Tight composites knots and chirality
This is a survey of the impact of Thurston's work on knot theory, laying emphasis on the two characteristic features, rigidity and flexibility, of 3-dimensional hyperbolic structures. We also lay emphasis on the role of the classical…
Many biological and synthetic materials self-assemble into helical or twisted aggregates. The shape is determined by a complex interplay between elastic forces and the orientation and chirality of the constituent molecules. We study this…
Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and "tennis racket" shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important…
Molecular chirality is a geometric property that is of great importance in chemistry, biology, and medicine. Recently, plasmonic nanostructures that exhibit distinct chiroptical responses have attracted tremendous interest, given their…
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…
An account of the transversality conditions of variational problems gives rise to essential results in the analysis of different physical phenomena. This powerful and elegant approach has proven to be fruitful in a diversity of variational…
The angular momentum quantization of chiral gapless modes confined to a circularly shaped interface between two different topological phases is investigated. By examining several different setups, we show analytically that the angular…
We introduce and attach an orbital chirality to off-center ions in crystals and consider its implications. Its relationship with the spin chirality of leptons and possibly anions is also discussed. The feature may bring new meaning to the…
We study how confinement affects topology and conformations in polymer films of varying thickness $h$. The knotting probability exhibits a maximum at intermediate thicknesses near the bulk radius of gyration $h \approx R_\mathrm{g,bulk}$,…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…
Molecular chirality, a form of stereochemistry most often describing relative spatial arrangements of bonded neighbors around tetrahedral carbon centers, influences the set of 3D conformers accessible to the molecule without changing its 2D…
The spontaneous emergence of chirality in crystalline solids has profound implications for electronic, optical, and topological properties, making the control of chiral phases a central challenge in materials design. Here, we investigate…
We consider knot invariants in the context of large $N$ transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicity constructed…
Chirality, an intrinsic handedness, is one of the most intriguing fundamental phenomena in nature. Materials composed of chiral molecules find broad applications in areas ranging from nonlinear optics and spintronics to biology and…
Chirality is a ubiquitous phenomenon in which a symmetry between left- and right-handed objects is broken, examples in nature ranging from subatomic particles and molecules to living organisms. In particle physics, the weak force is…
We introduce and explore the relation between knot invariants and quiver representation theory, which follows from the identification of quiver quantum mechanics in D-brane systems representing knots. We identify various structural…
Ring polymers are characterized by topology-specific entanglements called threadings. In the limit of large rings, it is conjectured that a "topological glass" should emerge due to the proliferation of threadings. In this study, we used…
We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as…
Screw rotations in nonsymmorphic space group symmetries induce the presence of hourglass and accordion shape band structures along screw invariant lines whenever spin-orbit coupling is nonnegligible. These structures induce topological…
In this text we describe the role of optical chirality in the context of plasmonics. We clearly distinguish between 2D an 3D optical chirality and connect the problem with reciprocity and time symmetry. We compare our analysis with recent…