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Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…
We test the ability of Schwarzschild's orbit superposition method in measuring the mass content, scale radius and shape of a flattened dwarf spheroidal galaxy. Until now, most dynamical model efforts have assumed that dwarf spheroidal…
One of the promising sources of gravitational radiation is a binary system composed of compact stars. It is an important question how the rotation of the bodies and the eccentricity of the orbit affect the detectable signal. Here we present…
This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical…
We consider a compact hyperbolic antiprism. It is a convex polyhedron with $2n$ vertices in the hyperbolic space $\mathbb{H}^3$. This polyhedron has a symmetry group $S_{2n}$ generated by a mirror-rotational symmetry of order $2n$, i.e.…
Given $p\in [1,\infty]$, this article presents the novel basic volumetric estimates for the relative $p$-capacities with their applications to finding not only the sharp weak $(p,q)$-imbeddings but also the precise lower bounds of the…
New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model…
We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that…
A family of analytical potential-density pairs for flat galaxies with spheroidal halos is presented. The potential are obtained by means of the sum of two independent terms: a potential associated with a thin disc and a potential associated…
Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis,…
We express the entropy of a scalar field phi directly in terms of its spacetime correlation function W(x,y) = <phi(x) phi(y)>, assuming that the higher correlators are of "Gaussian" form. The resulting formula associates an entropy S(R) to…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
We have investigated the toroidal analog of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential $\Psi(R,Z)$ of a shell with a circular section at the pole of…
We present a new effective-one-body (EOB) model for eccentric binary coalescences. The model stems from the state-of-the-art model TEOBResumS$\_$SM for circularized coalescing black-hole binaries, that is modified to explicitly incorporate…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
We present results of numerical simulations of the flux (irradiance), F, and the degree of polarization (i.e. the ratio of polarized to total flux), P, of light that is reflected by Earth-like extrasolar planets orbiting solar-type stars,…
We examined the gravitational contraction of isothermal molecular cloud cores with slow rotation by means of two-dimensional numerical simulations. Applying a sink-cell method, we followed the evolution of the cloud cores up to the stages…
The optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbital-dependent approximations to the exchange-correlation energy…
We begin with an exact expression for the entropy of a system of hard spheres within the Hamming space. This entropy relies on probability marginals, which are determined by an extended set of Belief Propagation (BP) equations. The BP…
Eccentricity, an important parameter of gravitational waves, has been paid more and more attention because it can reflect the dynamics of compact object mergers. Obtaining an accurate and fast gravitational waveform template is of great…