Related papers: Exploring non-Euclidean photonics: Pseudosphere mi…
It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the…
A mechanism is discussed to obtain light scalar fields from a spontaneously broken continuous symmetry without explicitly breaking it. If there is a continuous manifold of classical vacua in orbit space, its tangent directions describe…
Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…
The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…
We present the geodesics on homogeneous and isotropic negatively curved spaces in a simple form suitable for application to cosmological problems. We discuss how the patterns in the microwave sky of anisotropic homogeneous universes can be…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
The paper shows that under some mild conditions $n$-dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on $n$-dimensional spheres…
We use global bifurcation techniques to establish the existence of arbitrarily many geometrically distinct nonplanar embedded smooth minimal 2-spheres in sufficiently elongated 3-dimensional ellipsoids of revolution. More precisely, we…
The structure and the magnetic properties of an InGaAs/Fe3Si superlattice in a cylindrical geometry are investigated by electron microscopy techniques, x-ray diffraction and magnetometry. To form a radial superlattice, a pseudomorphic…
This note is a continuation of the paper [2] (see references). We describe some natural pseudogroup structures on almost complex manifolds of type $m$. A kind of coherency is discussed for the sheaf of almost holomorphic functions.
In recent years, metasurfaces composed of lumped circuit components, including nonlinear Schottky diodes, have been reported to be capable of sensing particular electromagnetic waves even at the same frequency depending on their waveforms,…
We analyze the existence, stability, and mobility of gap solitons (GSs) in a periodic photonic structure built into a nonlocal self-defocusing medium. Counter-intuitively, the GSs are supported even by a highly nonlocal nonlinearity, which…
We theoretically study a topological nanospaser, which consists of a silver nanospheroid and MoS$_2$ monolayer ake of a circular shape. The metal nanospheroid acts as a plasmonic nanoresonator that supports two rotating modes, which are…
The topological lasers, which are immune to imperfections and disorders, have been recently demonstrated based on many kinds of robust edge states, being mostly at microscale. The realization of 2D on-chip topological nanolasers, having the…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
The interaction between electromagnetic waves and objects is strongly affected by the shape and material composition of the latter. Artificially created materials, formed by a subwavelength structuring of their unit cells, namely…
We deal with minimal surfaces in spheres that are locally isometric to a pseudoholomorphic curve in a totally geodesic $\mathbb{S}^{5}$ in the nearly K{\"a}hler sphere $\mathbb{S}^6$. Being locally isometric to a pseudoholomorphic curve in…
We investigate the behaviour of light rays in an open universe with a partly periodic horn topology. The geodesics can be solved exactly and the periodic topology creates characteristic new effects in temperature maps of the microwave…
For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.
In the present paper, we propose a new discrete surface theory on 3-valent embedded graphs in the 3-dimensional Euclidean space which are not necessarily discretization or approximation of smooth surfaces. The Gauss curvature and the mean…