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We show that the observational data recently provided by Giovanelli et al. (1996 a, b) and discussed by Bahcall and Oh (1996) concerning the velocity distribution of clusters of galaxies can be naturally fitted by a statistical distribution…
We present a method for recovering the distribution functions of edge-on thin axisymmetric disks directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the line-of-sight…
Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…
The stellar velocity distribution function (DF) in the solar vicinity is re-examined using data from the SDSS APOGEE survey's DR16 and \emph{Gaia} DR2. By exploiting APOGEE's ability to chemically discriminate with great reliability the…
We present numerical studies of the properties of the stellar velocity distribution in galactic disks which have developed a saturated, two-armed spiral structure. In previous papers we used the Boltzmann moment equations (BME) up to second…
We present the results of a new, non-parametric method to reconstruct the Galactic dark matter profile directly from observations. Using the latest kinematic data to track the total gravitational potential and the observed distribution of…
Given a redshift survey of galaxies with measurements of apparent magnitudes, we present a novel method for measuring the growth rate $f(\Omega)$ of cosmological linear perturbations. We use the galaxy distribution within the survey to…
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and…
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…
We search for evidence of dark matter in the Milky Way by utilizing the stellar number density distribution and kinematics measured by the Sloan Digital Sky Survey (SDSS) to heliocentric distances exceeding ~10 kpc. We employ the…
We present a family of self-consistent axisymmetric stellar systems that have analytic distribution functions (DFs) of the form f(J), so they depend on three integrals of motion and have triaxial velocity ellipsoids. The models, which are…
We present an approach to the design of distribution functions that depend on the phase-space coordinates through the action integrals. The approach makes it easy to construct a dynamical model of a given stellar component. We illustrate…
We calculate the distribution of electrons in clusters of galaxies, resulting from thermalization processes in the presence of stochastic acceleration due to plasma waves. We show that the electron distribution can deviate from a…
The Boltzmann equation, an integro-differential equation for the molecular distribution function in the physical and velocity phase space, governs the fluid flow behavior at a wide range of physical conditions, including compressible,…
A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution…
We present a series of three-dimensional discrete Boltzmann (DB) models for compressible flows in and out of equilibrium. The key formulating technique is the construction of discrete equilibrium distribution function through inversely…
Peculiar motion introduces systematic variations in the observed luminosity distribution of galaxies. This allows one to constrain the cosmic peculiar velocity field from large galaxy redshift surveys. Using around half a million galaxies…
A hierarchical Bayesian model is applied to the Cosmicflows-3 catalog of galaxy distances in order to derive the peculiar velocity field and distribution of matter within $z \sim 0.054$. The model assumes the $\Lambda$CDM model within the…
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 study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…