Related papers: Simple Three-Integral Scale-Free Galaxy Models
We consider Friedmann-Lema\^{\i}tre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological…
The Vlasov-Einstein system describes the evolution of an ensemble of particles (such as stars in a galaxy, galaxies in a galaxy cluster etc.) interacting only by the gravitational field which they create collectively and which obeys…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
In situ measurements of kinetic scale current sheets in the solar wind show that they are often approximately force-free although the plasma beta is of order one. They frequently display systematic asymmetric and anti-correlated spatial…
Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
Applying functional differentiation to the density field with Newtonian gravity, we obtain the static, nonlinear equation of the three-point correlation function $\zeta$ of galaxies, to the third order density perturbations. We make the…
This study examines the possibility of starting the process of collapsing and forming stars from a fractional molecular cloud. Although the Verlinde's approach is employed to derive the corresponding gravitational potential, the results are…
We use Schwarzschild's orbit superposition method to build self-consistent models of elliptical galaxies with scale-free potentials. Our exhaustive study of all physical shapes and central densities for galaxies with scale-free potentials…
We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background…
We perform a linear dynamical stability analysis of a general hydrodynamic model of chemotactic aggregation [Chavanis & Sire, Physica A, in press (2007)]. Specifically, we study the stability of an infinite and homogeneous distribution of…
We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical…
This paper describes a general investigation of stationary oscillations of galaxies. It begins with a linear analysis of modes of oscillation with continuous spectra of real frequencies. Such modes are gravitational analogues of the van…
A new class of exact electrostatic solutions of the Vlasov-Maxwell equations based on the Jeans's theorem is proposed for studying the evolution and properties of two-dimensional anisotropic plasmas that are far from thermodynamic…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of…
The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech^2 law, as shown in the classic work by Spitzer (1942). This is obtained assuming that the radial and vertical motions are decoupled…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We get the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-Dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions…
I present a general family of dynamical models with simple analytical potential-density pairs suited to model galactic bulges and nuclei with double power-law radial density profiles and an optional central black hole. Analytical…