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A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that…
The general formula for the interaction potential between two point electric charges which contains the lowest order corrections to the vacuum polarization is derived and investigated. Analytical derivation of this formula is based on the…
By considering momentum transfer in the Fermi constraint procedure, the stability of the initial nuclei and fragments produced in heavy-ion collisions can be further improved in the quantum molecular dynamics simulations. The case of the…
For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are…
In an external constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length, we consider the modification of the Coulomb potential of a point charge owing to the vacuum polarization. We…
Various many-body perturbation theory techniques for calculating electron behavior rely on {\it W}, the screened Coulomb interaction. Computing {\it W} requires complete knowledge of the dielectric response of the electronic system, and the…
We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge…
We describe the potential produced by a point electric charge placed into a constant magnetic field, so strong that the electron Larmour length is much shorter than its Compton length. The standard Coulomb law is modified due to the vacuum…
We present a computational methodology to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated by moving point…
Typical biomolecular systems such as cellular membranes, DNA, and protein complexes are highly charged. Thus, efficient and accurate treatment of electrostatic interactions is of great importance in computational modelling of such systems.…
This research note documents new developments regarding finite-element discretizations of the relativistic Beliaev-Budker Coulomb collision operator and the nonrelativistic Landau operator. Where energy conservation in a finite-element…
A ubiquitous approach to obtain transferable machine learning-based models of potential energy surfaces for atomistic systems is to decompose the total energy into a sum of local atom-centred contributions. However, in many systems…
Phase unwrapping is a key problem in many coherent imaging systems, such as synthetic aperture radar (SAR) interferometry. A general formulation for redundant integration of finite differences for phase unwrapping (Costantini et al., 2010)…
In this work a new expansions of Coulomb potential and interparticle distance, linear term $r_{12}$ are proposed. Except the singularities, the expansions converge to the exact value in the whole coordinate space including the vicinity of…
This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage…
A class of radial, polynomial cutoff functions $f_{\textrm{c}n}(r)$ for short-ranged pair potentials or related expressions is proposed. Their derivatives up to order $n$ and $n+1$ vanish at the outer cutoff $r_\textrm{c}$ and an inner…
I propose a method to calculate logarithmic interaction in two dimensions and coulomb interaction in three dimensions under periodic boundary conditions. This paper considers the case of a rectangular cell in two dimensions and an…
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is…
The current work presents a novel COllaborative Open-source Lattice Boltzmann Method framework, so-called CooLBM. The computational framework is developed for the simulation of single and multi-component multi-phase problems, along with a…
We present analytic expressions of the Coulomb interaction between a spherical and a deformed nuclei which are valid for all separation distance. We demonstrate their significant deviations from commonly used formulae in the region inside…