Related papers: A method for solving the linearized Boltzmann equa…
We present a method for solving the two-dimensional linearized collisionless Boltzmann equation using Fourier expansion along the orbits. It resembles very much solutions present in the literature, but it differs by the fact that everything…
A general solution of the Jeans equations for oblate scale-free logarithmic potentials is given. This provides all possible second velocity moments that can hold up a stellar population of flattened scale-free density against the gravity…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear…
In the Gaia era, understanding the effects of the perturbations of the Galactic disc is of major importance in the context of dynamical modelling. In this theoretical paper we extend previous work in which, making use of the epicyclic…
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…
We study the explicitly time-dependent response of a razor-thin axisymmetric disc to externally imposed perturbations by recasting the linearized Collisionless Boltzmann equation as an integral equation and applying Kalnajs' matrix method.…
We present the Boltzmann moment equation approach for the dynamics of stars (BEADS-2D), which is a finite-difference Eulerian numerical code designed for the modelling of anisotropic and non-axisymmetric flat stellar disks. The BEADS-2D…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
We present general series solutions to the Tolman-Oppenheimer-Volkoff equations for compact stellar objects. We develop an algorithm to compute the coefficients of the power series in terms of the equation of state and its derivatives with…
We present a method for constructing equilibrium disks with net angular momentum in general relativity. The method solves the relativistic Vlasov equation coupled to Einstein's equations for the gravitational field. We apply the method to…
The time evolution of initially balanced, rapidly rotating models for an isolated disk of highly flattened galaxies of stars is calculated. The method of direct integration of the Newtonian equations of motion of stars over a time span of…
Starting from an axisymmetric equilibrium distribution function (DF) in action space, representing a Milky Way thin disc stellar population, we use the linearized Boltzmann equation to explicitly compute the response to a three-dimensional…
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The…
We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…
We study the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carry out the analysis by developing a numerical resolution of the 2D2V Collisionless Boltzmann…
Considering galaxies as self - gravitating systems of many collisionless particles allows to use methods of statistical mechanics inferring the distribution function of these stellar systems. Actually, the long range nature of the…
The advent of datasets of stars in the Milky Way with six-dimensional phase-space information makes it possible to construct empirically the distribution function (DF). Here, we show that the accelerations can be uniquely determined from…
The linear stability analysis of the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in space exploration, where rarefaction effects can render the Navier Stokes equations invalid. Since…