Related papers: Properties of Villarceau Torus
Multistep denaturation in a short circular DNA molecule is analyzed by a mesoscopic Hamiltonian model which accounts for the helicoidal geometry. Computation of melting profiles by the path integral method suggests that stacking…
In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth $6$ is obtained. It is proved that every such graph, with the exception of the Desargues graph on $20$ vertices, is either a skeleton of a…
In a gravitational virialized bound system built up of two components, one of which is embedded in the other, the Clausius' virial energy of one subcomponent is not, in general, equal to its total potential energy, as occurs in a single…
Replacing vector type of interaction of the Thirring-Wess model by the chiral type a new model is presented which is termed here as chiral Thirring-Wess model. Ambiguity parameters of regularization is so chosen that the model falls into…
The analysis of twisted (vortex) paraxial photons and electrons is fulfilled in the framework of relativistic quantum mechanics. The use of the Foldy-Wouthuysen representation radically simplifies a description of relativistic electrons and…
The recently observed large Rashba-type spin splitting in the BiTeX (X = I, Br, Cl) bulk states due to the absence of inversion asymmetry and large charge polarity enables observation of the transition in Fermi surface topology from…
Toroidal vortices are whirling disturbances rotating about a ring-shaped core while advancing in the direction normal to the ring orifice. Toroidal vortices are commonly found in nature and being studied in a wide range of disciplines. Here…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
Torus canards are solutions of slow/fast systems that alternate between attracting and repelling manifolds of limit cycles of the fast subsystem. A relatively new dynamic phenomenon, torus canards have been found in neural applications to…
It is shown that the IIB matrix model compactified on a six-dimensional torus with a nontrivial topology can provide chiral fermions and matter content close to the standard model on our four-dimensional spacetime. In particular, generation…
An irrational toric variety X is an analytic subset of the simplex associated to a finite configuration of real vectors. The positive torus acts on X by translation, and we consider limits of sequences of these translations. Our main result…
Under supercoiling constraints, naked DNA, such as a large part of bacterial DNA, folds into braided structures called plectonemes. The double-helix can also undergo local structural transitions, leading to the formation of denaturation…
Valleytronics has emerged as a promising paradigm, enabling comprehensive control of the valley degree of freedom (DoF) for energy-efficient and high-speed information processing. However, backscattering-induced valley depolarization…
We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus on complex balanced mass-action systems, which have also been called toric. They are known or conjectured to enjoy very strong dynamical…
We prove that a 3--dimensional hyperbolic cusp with convex polyhedral boundary is uniquely determined by its Gauss image. Furthermore, any spherical metric on the torus with cone singularities of negative curvature and all closed…
Regular ring lattices (RRLs) are defined as peculiar undirected circulant graphs constructed from a cycle graph, wherein each node is connected to pairs of neighbors that are spaced progressively in terms of vertex degree. This kind of…
We present the field-line modeling, design and construction of a prototype circular-coil tokamak-torsatron hybrid called Proto-CIRCUS. The device has a major radius R = 16 cm and minor radius a < 5 cm. The six "toroidal field" coils are…
Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
Discrete vortex, formed by a one-dimensional (1D) ring array of lasers, contains high output power as compared to a conventional continuous vortex, therefore, has attracted considerable interest due to widespread applications in various…
In this work, we introduce a new graph convexity, that we call Cycle Convexity, motivated by related notions in Knot Theory. For a graph $G=(V,E)$, define the interval function in the Cycle Convexity as $I_{cc}(S) = S\cup \{v\in V(G)\mid…