Related papers: Spherical-harmonic-analysis-based optimization of …
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
We provide new insights into backbending phenomenon within the symmetry-adapted framework which naturally describes the intrinsic deformation of atomic nuclei. For $^{20}\text{Ne}$, the canonical example of backbending in light nuclei, the…
Precise calculations of core properties in heavy-atom systems which are described by the operators heavily concentrated in atomic cores, like to hyperfine structure and P,T-parity nonconservation effects, usually require accounting for…
A new smoothing method for the improvement on the identification and quantification of spectral functions based on the previous knowledge of the signals that are expected to be quantified, is presented. These signals are used as weighted…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
We study the estimation of quadratic Sobolev-type integral functionals of an unknown density on the unit sphere. The functional is defined through fractional powers of the Laplace--Beltrami operator and provides a global measure of…
We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at $L$ using only $L^2$ samples. We obtain the optimal number of samples given by the…
The Slater orbitals are the natural basis functions in quantum molecular calculations. Three-center repulsion Coulomb-exchange integrals over Slater orbitals are evaluated analytically with arbitrary orbital exponents, first for linear…
This is the second of a series of three papers that present a methodology with the aim of creating a set of maps of the coronal density over a period of many years. This paper describes a method for reconstructing the coronal electron…
We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…
We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair interaction forms comprising a hard core and a combination of…
Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…
In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…