Related papers: The coordinate-free approach to spherical harmonic…
We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boundary integral equation arising from the latter when constant…
Spherical $t$-designs are finite point sets on the unit sphere that enable exact integration of polynomials of degree at most $t$ via equal-weight quadrature. This concept has recently been extended to spherical $t$-design curves by the use…
We numerically integrate the semiclassical equations of motion for spherically symmetric Einstein-Maxwell theory with a dilaton coupled scalar field and look for zero temperature configurations. The solution we find is studied in detail…
A global analysis is presented of solutions for Laplace's equation on three-dimensional Euclidean space in one of the most general orthogonal asymmetric confocal cyclidic coordinate systems which admit solutions through separation of…
The definition of well-behaved coordinate charts for black hole spacetimes can be tricky, as they can lead for example to either unphysical coordinate singularities in the metric (e.g. $r=2M$ in the Schwarzschild black hole) or to an…
By using a generalization of Sturm-Liouville problems in discrete spaces, a basic class of symmetric orthogonal polynomials of a discrete variable with four free parameters, which generalizes all classical discrete symmetric orthogonal…
We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials. The method is applied to dislocation-void interactions in dislocation dynamics simulations. We obtain a complete set of…
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
The problem of resolving spherical harmonic components from numerical data defined on a rectangular grid has many applications, particularly for the problem of gravitational radiation extraction. A novel method due to Misner improves on…
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
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…
We study the evolution of shear-free spherically symmetric charged fluids in general relativity. We find a new parametric class of solutions to the Einstein-Maxwell system of field equations. Our charged results are a generalisation of…
Electrodynamic spherical harmonic is a second rank tensor in three-dimensional space. It allows to separate the radial and angle variables in vector solutions of Maxwell's equations. Using the orthonormalization for electrodynamic spherical…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
Black hole perturbation theory on spherically symmetric backgrounds has been instrumental in establishing various aspects about the gravitational dynamics close to black holes, and continues to be an interesting avenue to confront current…
We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We show in particular, that there is a map from exterior…
This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some…
A scalar field method to obtain transverse solutions of the vector Laplace and Helmholtz equations in spherical coordinates for boundary-value problems with azimuthal symmetry is described. Neither scalar nor vector potentials are used.…