Related papers: On Covering a Solid Sphere with Concentric Spheres…
An evolution of a spherical region, subjected to uniform buoyancy force, is investigated. Incompressibility and axial symmetry are assumed, together with a buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet and…
The unusual electronic properties of the quantum spin Hall or Chern insulator become manifest in the form of robust edge states when samples with boundaries are studied. In this work, we ask if and how the topologically non-trivial…
Based on the concept of complementary media, we propose a novel design which can enhance the electromagnetic wave scattering cross section of an object so that it looks like a scatterer bigger than the scale of the device. Such a…
We show that every quadrangulation of the sphere can be transformed into a $4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident edges at a…
Eight models for the coherence of the quasi-monochromatic light from spherical incoherent sources are constructed by placing incoherent monopole and dipole sources on the surface of a sphere, inside a ball and on a plane circular disk. All…
We show that dielectric spheres can be cloaked by a shell of amorphously arranged metallic nanoparticles. The shell represents an artificial medium with tunable effective properties that can be adjusted such that the scattered signals of…
Transport experiments provide conflicting evidence on the possible existence of fractional order within integer quantum Hall systems. In fact integer edge states sometimes behave as monolithic objects with no inner structure, while other…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked…
We study the optical appearance of a thin accretion disk around the strongly naked static Janis-Newman-Winicour singularity. The solution does not possess a photon sphere, which results in the formation of a complex structure of bright…
We characterize normal $3$-pseudomanifolds with $g_2\leq4$. We know that if a $3$-pseudomanifold with $g_2\leq4$ does not have any singular vertices then it is a $3$-sphere. We first prove that a normal $3$-pseudomanifold with $g_2\leq4$…
We computer model a free-standing vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. Here we model the bilayer using a computer assembly procedure that starts from a single layer…
A low-energy neutral quasiparticle in a fractional quantum Hall system appears in the latter's energy spectrum on a sphere as a series of many-body excited states labeled by the angular momentum $L$ and whose energy is a smooth function of…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
Releasing shell-shaped Bose-Einstein condensates from their confinement produces a spherically symmetric density distribution characterized by concentric ripples surrounding a central peak. Here we investigate how a vortex-antivortex dipole…
We calculate the virtually-cyclic dimension of the mapping class group of a sphere with at most six punctures. As an immediate consequence, we obtain the virtually-cyclic dimension of the mapping class group of the twice-holed torus and of…
Composed of square particles, the tetratic phase is characterised by a four-fold symmetry with quasi-long-range orientational order but no translational order. We construct the elastic free energy for tetratics and find a closed form…
Particle shape is a critical parameter that plays an important role in self-assembly, for example, in designing targeted complex structures with desired properties. In the last decades an unprecedented range of monodisperse nanoparticle…
We examine the gravitational collapse and black hole formation of multiple non--spherical configurations constructed from Szekeres dust models with positive spatial curvature that smoothly match to a Schwarzschild exterior. These…