相关论文: A New 3D Potential-Density Basis Set

An unambiguous definition of the electromagnetic spatial densities for a spin-1/2 system is proposed and worked out in the zero average momentum frame and in moving frames. The obtained results are compared with the traditional definition…

We present a construction of a wavelet-type orthonormal basis for the space of radial $L^2$-functions in $\R^3$ via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by…

A new potential is presented for spherical galaxies. The technique of the construction of our model is similar to that given by An and Evans. In a special case, its mass density becomes a special one of the Hernquist model. Another special…

In this paper we obtain some properties of orthogonal polynomials given by a weight function which is a limit density of a rescaled discrete-time quantum walk on the line.

In this paper, we derive a Laplace-type integral representations for both the generalized Bessel function and the Dunkl kernel associated with the rank-two root system of type B_2. The derivation of the first one elaborates on the integral…

We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights $(w_1,w_2)$ on the positive real line, with $w_1(x)=x^\alpha e^{-x}$ the gamma density and $w_2(x) = x^\alpha…

A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…

The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel…

Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form but any minimal cells can…

We study differential operators associated with families of polynomials orthonormal with respect to certain measures. These operators, when applied to the Fourier transforms of such measures, produce basis functions for expansions of…

The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…

The onset of condensation of hard spheres in a gravitational field is studied using density functional theory. In particular, we find that the local density approximation yields results identical to those obtained previously using the…

In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic…

We demonstrate the high accuracy of the density splitting method to compute the gravitational potential and field in the plane of razor-thin, axially symmetric discs, as preliminarily outlined in Pierens & Hure (2004). Because residual…

In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of…

We present a detailed study of the use of localized spherical-wave basis sets, first introduced in the context of linear-scaling, in first-principles density-functional calculations. Several parameters that control the completeness of this…

We consider the presence of oscillations in the primordial bispectrum, inspired by three different cosmological models; features in the primordial potential, resonant type non-Gaussianities and deviation from the standard Bunch Davies…

We study Density Functional Theory models for systems which are translationally invariant in some directions, such as a homogeneous 2-d slab in the 3-d space. We show how the different terms of the energy are modified and we derive reduced…

This work presents new Gaussian single- and double-zeta basis sets optimized for stochastic density functional theory (sDFT) using real-space auxiliary grids. Previous studies showed standard basis sets like STO-3G and 6-31G are sub-optimal…

The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…