Related papers: Properties of Villarceau Torus
We study higher-dimensional homological analogues of bond percolation on a square lattice and site percolation on a triangular lattice. By taking a quotient of certain infinite cell complexes by growing sublattices, we obtain finite cell…
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin-Kasteleyn random…
In this paper Moussouris' algorithm for the decomposition of spin networks is reviewed and the implicit assumptions made in the Decomposition Theorem relating a spin network with its state sum are examined. It is found that the theorem in…
Toll convexity is a variation of the so-called interval convexity. A tolled walk $T$ between $u$ and $v$ in $G$ is a walk of the form $T: u,w_1,\ldots,w_k,v,$ where $k\ge 1$, in which $w_1$ is the only neighbor of $u$ in $T$ and $w_k$ is…
We give further evidence that genus-one fibers with multi-sections are mirror dual to fibers with Mordell-Weil torsion. In the physics of F-theory compactifications this implies a relation between models with a non-simply connected gauge…
The sequence-dependent elasticity of double-helical DNA on a nm length scale can be captured by the rigid base-pair model, whose strains are the relative position and orientation of adjacent base-pairs. Corresponding elastic potentials have…
We report on the experimental observation of topologically protected edge waves in a two-dimensional elastic hexagonal lattice. The lattice is designed to feature K point Dirac cones that are well separated from the other numerous elastic…
Self-similar curves are a recurring motif in nature. The tension-free stationary states of conformally invariant energies describe the simplest curves of this form. Planar logarithmic spirals, for example, are associated with conformal…
In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise…
We introduce a family of dual-unitary circuits in 1+1 dimensions which constitute a discrete analog of conformal field theories. These circuits are quantum cellular automata which are invariant under the joint action of Lorentz and scale…
We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biologies, such as…
As characteristic lengths in plasmonics rapidly approach the sub-nm regime, quantum-informed models that can capture those aspects of the quantum nature of the electron gas that are not accessible by the standard approximations of classical…
Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…
There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. This paper reports numerical experiments performed for an explicit two-parameter family of vector fields…
Although the topological phases are difficult to be realized in organic molecular crystals, we demonstrate here that they can emerge in the \tau-type organic layered conductors, \tau-(EDO-S,S-DMEDT-TTF)_2X_{1+y} and…
We resume the study initiated in \cite{CL}. For a generic curve $C$ in an ample linear system $\vert \mathcal{L} \vert$ on a toric surface $X$, a vanishing cycle of $C$ is an isotopy class of simple closed curve that can be contracted to a…
The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We…
Curves in ${\mathbb R}^n$ for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For $n= 3,4$, spherical curves of this kind are also…
We present a detailed study on the behaviour of vortex cores in Bi_2Sr_2CaCu_2O_{8+\delta} using scanning tunneling spectroscopy. The very irregular distribution and shape of the vortex cores imply a strong pinning of the vortices by…
The recent discovery that linearly polarized light with a helical wavefront can exhibit vortex dichroism (also referred to as helical dichroism) has opened up new horizons in chiroptical spectroscopy with structured chiral light. Recent…