Related papers: On a spherical code in the space of spherical harm…
The spherical harmonics $Y_{\ell m}(\theta,\varphi)$ are complex-valued functions on the surface of a sphere, and have found widespread application in physics and astronomy. Every physics students knows them from quantum mechanics and…
We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold…
We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.
This paper introduces a contribution made to one of the newest methods for simulating indirect lighting in dynamic scenes , the cascaded light propagation volumes . Our contribution consists on using Spherical Radial Basis Functions instead…
We provide a construction method for biharmonic submanifolds in cohomogeneity one manifolds. In particular, we give new examples of biharmonic submanifolds and study the normal index of these submanifolds. We use this strategy to construct…
In this article, we present a $T$-matrix method for numerical computation of second-harmonic generation from clusters of arbitrarily distributed spherical particles made of centrosymmetric optical materials. The electromagnetic fields at…
We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n ,\, n \geq 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory.…
We compute the fundamental group of the "moduli space" of classical solutions of the two dimensional Euclidean $S^n$-model.
We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square $[0,1]^2$ to a spherical ellipse (i.e. the projection of the disk onto the…
Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics.
We consider the energy functional on the space of sections of a sphere bundle over a Riemannian manifold (M, <,>) equipped with the Sasaki metric and we discuss the characterising condition for critical points. Likewise, we provide a useful…
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their…
In their seminal 1981 article, Sacks-Uhlenbeck famously proved the existence of non-trivial harmonic 2-spheres in every closed Riemannian manifold with non-zero second homotopy group. Their arguments heavily rely on PDE techniques. The…
We present a new method to construct Virtual Element spaces on polygons with curved edges.
We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic…
In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.
Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which…
This manuscript is the first in a series of instalments that investigate spherically symmetric solutions within the effective dynamics program of Loop Quantum Gravity. The choice of lattice is adapted such that it remains invariant under a…