Related papers: Cored DARKexp systems with finite size: numerical …
The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…
The problem of a spin-free electron with mass $m$, charge $e$ confined onto a ring of radius $R_0$ and with an attractive Dirac delta potential with scaling factor (depth) $\kappa$ in non-relativistic theory has closed form analytical…
The gravitational collapse of a barotropic perfect fluid having the Equation of State (EoS) $p=k\rho$, where $k$ is constant, is studied here in the framework of general relativity. We examine the restrictions on the Misner-Sharp mass…
This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy…
We derive in this note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates.…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
[Abridged] We have analysed the mass and velocity distributions of two samples of relaxed elliptical-like-objects (ELOs) identified, at z=0, in a set of self-consistent hydrodynamical simulations operating in the context of a concordance…
We investigate the connection between collisionless equilibria and the phase-space relation between density $\rho$ and velocity dispersion $\sigma$ found in simulations of dark matter halo formation, $F=\psd \propto r^{-\alpha}$.…
We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos') at selected temperatures and degeneracy parameters within general relativity. Our…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
According to the current concordance cosmological model, the dark matter (DM) particles are collision-less and produce self-gravitating structures with a central cusp which, generally, is not observed. The observed density tends to a…
A new class of self-gravitating collapsing star models with perfect fluid distributions is discussed in this work. The paper has a comprehensive analysis of a homogeneous gravitational collapsing system wherein using a parametrization…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
We consider spherically symmetric static solutions of the Einstein equations with a positive cosmological constant $\Lambda,$ which are regular at the centre, and we investigate the influence of $\Lambda$ on the bound of M/R, where M is the…
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differs from the diffusion strength perpendicular to this notable…
We provide a complete picture of the self-gravitating non-relativistic gas at thermal equilibrium using Monte Carlo simulations (MC), analytic mean field methods (MF) and low density expansions. The system is shown to possess an infinite…
Energy density functional (EDF) theory provides a unified framework for the description of nuclei and of infinite nuclear matter. In principle, it facilitates direct connections between nuclear data and the nuclear equation of state (EoS).…
In this paper we reconsider a series expansion for a dark matter distribution function in the spherically symmetric anisotropic limit. We show here that the expansion may be renormalized so that the series does converge in time to an…
One usually thinks of a radial density profile as having a monotonically changing logarithmic slope, such as in NFW or Einasto profiles. However, in two different classes of commonly used systems, this is often not the case. These classes…
The formation and stability of collisionless self-gravitating systems are long standing problems, which date back to the work of D. Lynden-Bell on violent relaxation and extends to the issue of virialization of dark matter (DM) halos. An…