Related papers: On Covering a Solid Sphere with Concentric Spheres…
Playing a role in the locomotion of some animals such as the water strider, the formation and dynamics of a semi vortex ring connected to a free surface are experimentally investigated. This semi vortex ring is generated by the circular…
Normal contact behaviour between non adhesive fractal rough particles is studied using a finite element method (FEM). A series of spherical grain surfaces with distinguished roughness features are generated by means of Spherical Harmonics.…
Our start point is a 3D piecewise smooth vector field defined in two zones and presenting a shared fold curve for the two smooth vector fields considered. Moreover, these smooth vector fields are symmetric relative to the fold curve, giving…
Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic…
We study geodetic lines on a surface generated by a small deformation of the standard 2D-sphere. We construct an auxiliary hamiltonian system with the view of describing geodetic coils and almost closed geodesics, by using the fact that…
Historically, the observation of half-spin particles was one of the most surprising features of quantum mechanics. They are often described as "objects that do not come back to their initial state after one turn but do after two turns".…
We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…
Unique features of particle orbits produce novel signatures of gravitational observable phenomena, and are quite useful in testing compact astrophysical objects in general relativity or modified theories of gravity. Here we observe a…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
Spherical $t$-designs on $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of…
We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder…
We introduce a new family of random compact metric spaces $\mathcal{S}_\alpha$ for $\alpha\in(1,2)$, which we call stable shredded spheres. They are constructed from excursions of $\alpha$-stable L\'evy processes on $[0,1]$ possessing no…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
We present a computational method for detecting highly singular members in families of algebraic varieties. Applying this approach to a family of numerical Godeaux surfaces, we obtain explicit examples with many singularities. In…
Given a combinatorial $(d-1)$-sphere $S$, to construct a combinatorial $d$-sphere $S^{\hspace{.2mm}\prime}$ containing $S$, one usually needs some more vertices. Here we consider the question whether we can do one such construction without…
Recent observations by the Event Horizon Telescope (EHT) indicate that the shadow of the compact object at our Galaxy's center (Sgr A*) closely resembles that of a Schwarzschild black hole. However, identifying the presence and exact…
Results of number of geometric operations (often used in technical practise, as e.g. the operation of blending) are in many cases surfaces described implicitly. Then it is a challenging task to recognize the type of the obtained surface,…
Higher spatial resolution and larger imaging scene are always the goals pursued by advanced space-borne SAR system.High resolution and wide swath SAR imaging can provide more information about the illuminated scene of interest on one…
Utilizing the electric Harrison transformation developed in five-dimensional minimal supergravity, we construct an exact solution characterizing non-BPS charged rotating black holes with a horizon cross-section of a lens space L(n;1). Among…
Given R\subset N, an (R,k)$-sphere is a k-regular map on the sphere whose faces have gonalities i\in R. The most interesting/useful are (geometric) fullerenes, i.e., (\{5,6\},3)$-spheres. Call \kappa_i=1 + \frac{i}{k} - \frac{i}{2} the…