Related papers: A New 3D Potential-Density Basis Set
We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential--density basis functions. The potential and density functions of the new set have finite central…
A class of complete potential-density basis sets in cylindrical (R,phi,z) coordinates is presented. This class is suitable for stability studies of galactic disks in three dimensions and includes basis sets tailored for disks with vertical…
A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are…
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…
We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional…
The projected properties of triaxial generalization of the modified Hubble mass models are studied. These models are constructed by adding the additional radial functions, each multiplied by a low-order spherical harmonic, to the models of…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
We present an approach based on density-functional theory for the calculation of fundamental gaps of both finite and periodic two-dimensional (2D) electronic systems. The computational cost of our approach is comparable to that of total…
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…
The basis of the identity representation of a polyhedral group is able to describe functions with symmetries of a platonic solid, i.e., 3-D objects which geometrically obey the cubic symmetries. However, to describe the dynamic of assembles…
In a series of papers we study the stellar dynamics of the grand design barred-spiral galaxy NGC~1300. In the first paper of this series we estimate the gravitational potential and we give it in a form suitable to be used in dynamical…
Wigner functions are broadly used to probe non-classical effects in the macroscopic world. Here we develop an orbital-free functional framework to compute the 1-body Wigner quasi-probability for both fermionic and bosonic systems. Since the…
We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…
Biorthonormal basis function expansions are widely used in galactic dynamics, both to study problems in galactic stability and to provide numerical algorithms to evolve collisionless stellar systems. They also provide a compact and…
We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap…
A family of potential--density pairs has been found for spherical halos and bulges of galaxies in the Newtonian limit of scalar--tensor theories of gravity. The scalar field is described by a Klein--Gordon equation with a source that is…
We present analytical potential-density pairs in three dimensions for the gravitational field of galaxies, obtained by thickening the multipolar expansion up to the quadrupole term. These may be interpreted as generalizations of the…