Related papers: Spherical-harmonic-analysis-based optimization of …
An analysis of the analytical solution of the Schr\"{o}dinger equation (which is a second order differential equation) for $H_2^+$ shows that the second linear independent solution of this equation is a square integrable function and…
Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…
Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device.…
Nowadays integration of mass matrix components in the element domain is performed using various numerical integration schemes, each one possess different level of accuracy, alters in number of integration (Gauss) points and requires…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…
Oscillating integrals often arise in the theoretical description of phenomena in chemical physics, in particular in atomic and molecular collisions, and in spectroscopy. A computer code for the numerical evaluation of the oscillatory…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs…
A multiscale QM/classical approach is presented, that is able to model the optical properties of complex nanostructures composed of a molecular system adsorbed on metal nanoparticles. The latter are described by a combined…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of an oblique-basis shell-model theory. The method is applied to nuclei by combining traditional spherical shell-model states with SU(3) collective…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the…
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from…