Related papers: The potential of discs from a "mean Green function…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
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…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We calculate ab initio the gravitational potential energy per unit area for a gravitationally coupled multi-component galactic disk of stars and gas, which is given as the integration over vertical density distribution, vertical…
We present a new method for generating the gravitational field of thin disks within the Weyl class of static and axially symmetric spacetimes. Such a gravitational field is described by two metric functions: one satisfies the Laplace…
We investigate the particle and kinetic-energy densities for $N$ non-interacting fermions confined in a local potential. Using Gutzwiller's semi-classical Green function, we describe the oscillating parts of the densities in terms of closed…
The gravitational potential is a key function involved in many astrophysical problems. Its evaluation inside continuous media from Newton's law is known to be challenging because of the diverging kernel 1/|r-r'|. This difficulty is…
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…
Toroidal structures are a common feature in a wide variety of astrophysical objects, including dusty tori in AGNs, rings in galaxies, protoplanetary disks, and others. The matter distribution in such structures is not homogeneous and can be…
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…
A continuum version of the virial theorem is derived for a radiating self-gravitating accretion disc around a compact object. The central object is point-like, but we can avoid the regularization of its gravitational potential. This is…
We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for…
In a mean-field approximation within Kinetic Field Theory, it is possible to derive an accurate analytic expression for the power spectrum of present-day non-linear cosmic density fluctuations. It depends on the theory of gravity and the…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…
In 2D-simulations of self-gravitating gaseous discs, the potential is often computed in the framework of "softened gravity" initially designed for N-body codes. In this special context, the role of the softening length LAMBDA is twofold: i)…
A model for the static weak-field macroscopic medium is analyzed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of…
Estimates of the dynamical surface mass density at the solar Galactocentric distance are commonly derived assuming that the disk is in vertical equilibrium with the Galactic potential. This assumption has recently been called into question,…
For mature spiral galaxies, the rotation velocities quickly increase from the galactic center and achieve a constant velocity from the core to the periphery. This dynamic behavior is described by models balancing Newtonian gravitational and…
We investigate the gravitational potentials generated by axisymmetric, razor-thin disks. Within certain limitations, the potential on one side of the disk is shown to be equivalent to the potential produced by a linear mass distribution…
The equations governing the vertical structure of a stationary keplerian accretion disc are presented. The model is based on the alpha-viscosity, includes self-gravity, convective transport and turbulent pressure. A few properties of the…