Related papers: Action-based distribution functions for spheroidal…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
Analytic distribution functions (DFs) for the Galactic disc are discussed. The DFs depend on action variables and their predictions for observable quantities are explored under the assumption that the motion perpendicular to the Galactic…
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…
Simple analytical models, such as the Hernquist model, are very useful tools to investigate the dynamical structure of galaxies. Unfortunately, most of the analytical distribution functions are either isotropic or of the Osipkov-Merritt…
We extend models of our Galaxy based on distribution functions (DFs) that are analytic functions of the action integrals to extended distribution functions (EDFs), which have an analytic dependence on metallicity as well. We use a simple,…
We calculate the distribution function of astronomical objects (like galaxies and/or smooth halos of different kinds) gravitational fields due to their tidal in- teraction. For that we apply the statistical method of Chandrasekhar (1943),…
We present a new iterative method for constructing equilibrium phase models of stellar systems. Importantly, this method can provide phase models with arbitrary mass distributions. The method is based on the following principle. Our task is…
Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating…
We present a rigorous and practical way of constraining the Galactic potential based on the phase-space information for many individual stars. Such an approach is needed to dynamically model the data from ongoing spectroscopic surveys of…
The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential has previously been computed through perturbation theory within the phase-space coordinates of the unperturbed axisymmetric…
We present dynamical distribution functions for evolved stars in the inner galactic plane. We use an axisymmetric, two-component Stackel potential that satisfies recent constraints on the galactic potential, amongst others a slightly…
The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas…
Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
In the Fornax dwarf spheroidal galaxy the globular clusters are distributed widely, without any significant central concentration. Oh et al. pointed out that such a distribution is paradoxical: dynamical friction effects estimated using…
An action functional is developed for nonlinear dislocation dynamics. This serves as a first step towards the application of effective field theory in physics to evaluate its potential in obtaining a macroscopic description of dislocation…
We propose a method for constructing the time-dependent phase space distribution function (DF) of a collisionless system from an isolated kinematic snapshot. In general, the problem of mapping a single snapshot to a time-dependent function…
Estimation of the distribution function f and potential Phi of hot stellar systems from kinematical data is discussed. When the functional forms of f and Phi are not specified a priori, accurate estimation of either function requires very…
Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times…
We present the results of an attempt to adapt the distribution function formalism to characterize large-scale structures like clusters of galaxies that form in a cosmological N-body simulation. While galaxy clusters are systems that are not…