Antonov problem and quasi-equilibrium states in an N-body system

Antonov Problem and Quasi-Equilibrium States in N-body System

In this paper, a quantitative characterization for the evolutionary sequence of stellar self-gravitating system is investigated, focusing on the pre-collapse stage of the long-term dynamical evolution. In particular, we consider the quasi-equilibrium behaviors of the N -body systems in the setup of the so-called Antonov problem, i.e., self-gravitating N -body system confined in an adiabatic wal...

Free and constrained equilibrium states in a variational problem on a surface

We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman's and Skrypnik's variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik's method, described in [P. Vyridis, {it Bifurcation in...

The Antonov problem for rotating systems

We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum λ c (or, in the canonical language, a critical angular velocity ω c) exists, such that for λ < λ c the system's beha...

Non-equilibrium quasi-stationary states in a magnetized plasma

Non-equilibrium quasi-stationary states resulting from curvature driven interchange instabilities and driftwave instabilities in a low beta, weakly ionized, magnetized plasma are investigated in the context of laboratory experiments in a toroidal configuration. Analytic modelling, numerical simulations and experimental results are discussed with emphasis on identifying the unstable modes and un...

The N-body Problem