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

In this note, which is the second part of a three-part series, we focus on uniqueness sets specifically in the case of spaces of entire functions of exponential type. As in the first part, we consider sets with angular density; however, now…

For a fundamental solution of Laplace's equation on the $R$-radius $d$-dimensional hypersphere, we compute the azimuthal Fourier coefficients in closed form in two and three dimensions. We also compute the Gegenbauer polynomial expansion…

A Voigt profile function emerges in several physical investigations (e.g. atmospheric radiative transfer, astrophysical spectroscopy, plasma waves and acoustics) and it turns out to be the convolution of the Gaussian and the Lorentzian…

Aims. Galaxy mass models based on simple and analytical functions for the density and potential pairs have been widely proposed in the literature. Disk models constrained by kinematic data alone give information on the global disk structure…

A scheme within density functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg, et al., Phys. Rev. Lett. 91, 126402…

Some formulae are presented for finding two-integral distribution functions (DFs) which depends only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar…

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…

We present a systematic analytic study of the $p$-Bessel functions $\mathcal{J}_{\omega,\varphi}^{[p]}$, a novel class of generalized Bessel functions arising from Fourier analysis on planar domains bounded by $p$-circles, including…

The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…

The definition of local spatial densities by using sharply localized one-particle states is applied to spin-3/2 systems. Matrix elements of the electromagnetic current and the energy-momentum tensor are considered and integral expressions…

Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W, such that S (but not necessarily R) is reduced. For each such pair (R,S) we construct a family of W-invariant orthogonal…

We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of length scale. For hard cores, we obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form of…

Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…

We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the…

Potential-density pair basis sets can be used for highly efficient N-body simulation codes, but they suffer from a lack of versatility, i.e. a basis set has to be constructed for each different class of stellar system. We present numerical…

A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…

We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the…

This article introduces a family of analytical functions of the form x^{\nu} K_{\nu}(x), where K_{\nu} is the incomplete Bessel function of the third kind. This family of functions can describe the density profile, projected and integrated…

We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis set such as planewaves. Each basis function is localized…

A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…