Related papers: New biorthogonal potential--density basis function…
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are expressed in terms of Bernstein polynomials and augment the…
We explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark matter haloes by Dekel et al. This…
Using the optimized effective potential method in conjunction with the semi-analytical approximation due to Krieger, Li and Iafrate, we have performed fully self-consistent exact exchange-only density-functional calculations for diatomic…
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…
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the…
In a recent paper [M. G\"ul et al., Phys. Rev. E, 110 (6), 064115] we showed that test particle sum rules, which address the excess chemical potential and isothermal compressibility, could be used to develop new and accurate classical…
We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff…
We develop a potential-theoretic and functional framework for the fractional--logarithmic Laplacian $(-\Delta)^{s+\ln}$ and its inhomogeneous counterpart $(\lambda I-\Delta)^{s+\ln}$ with $\lambda>1$. Their inverses yield logarithmic…
Bessel and modified Bessel functions of imaginary order $i\nu$ ($\nu >0$) are studied. Asymptotic expansions are derived as $\nu \to \infty$ that are uniformly valid in unbounded complex domains, with error bounds provided. Coupled with…
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…
An expansion of a density field or particle distribution in basis functions which solve the Poisson equation both provides an easily parallelized n-body force algorithm and simplifies perturbation theories. The expansion converges quickly…
Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set…
Context. Dynamically self-consistent galactic models are necessary for analysing and interpreting star counts, stellar density distributions, and stellar kinematics in order to understand the formation and the evolution of our Galaxy. Aims.…
This is a follow-up of our recently proposed work on pseudopotential calculation (Ref. [21]) of atoms and molecules within DFT framework, using cartesian coordinate grid. Detailed results are presented to demonstrate the usefulness,…
By using various properties of the complete elliptic integrals, we have derived an alternative expression for the gravitational potential of axially symmetric bodies, which is free of singular kernel in contrast with the classical form.…
We propose a second version of the van der Waals density functional (vdW-DF2) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient…
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 Jeans equations give the second moments or stresses required to support a stellar population against the gravity field. A general solution of the Jeans equations for arbitrary axisymmetric scale-free densities in flattened scale-free…
We consider the Fock space weighted by $e^{-\alpha |z|^{2}}$, of entire and quasi-periodic (modulo a weight dependent on $\nu $) functions on ${C}$. The quotient space $\mathbb{C}/\mathbb{Z}$, called `The flat cylinder', is represented by…
In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the…