Related papers: An Asymptotic Matching Method for Analyzing Non-Pl…
In order to identify the exact criteria for the formation of two-ring structures in galaxies, we studied the issue of gravitational instability of the corresponding structural vibration modes against the background of a composite disk model…
We review the available methods for estimating actions, angles and frequencies of orbits in both axisymmetric and triaxial potentials. The methods are separated into two classes. Unless an orbit has been trapped by a resonance, convergent,…
We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…
A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in…
We develop a model for spiral galaxies based on a nonlinear realization of the Newtonian dynamics starting from the momentum and mass conservations in the phase space. The radial solution exhibits a rotation curve in qualitative accordance…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
Galactic accretion interacts in complex ways with gaseous halos, including galactic winds. As a result, observational diagnostics typically probe a range of intertwined physical phenomena. Because of this complexity, cosmological…
Spatially-resolved emission line kinematics are invaluable to investigating fundamental galaxy properties and have become increasingly accessible for galaxies at $z\gtrsim0.5$ through sensitive near-infrared imaging spectroscopy and…
We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e.,…
The model of a geometrically thin gaseous disk in the external gravitational potential is considered. The dinamics of small nonaxisymmetric perturbations in the plane of the accretion disk with dissipative effects is investigated. It is…
We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method.…
Discretized numerical simulations are a powerful tool for investigation of nonlinear MHD turbulence in accretion disks. However, confidence in their quantitative predictions requires a demonstration that further refinement of the spatial…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
The observed velocities of the gas in barred galaxies are a combination of the azimuthally-averaged circular velocity and non-circular motions, primarily caused by gas streaming along the bar. These non-circular flows must be accounted for…
Using three-dimensional stellar kinematic data from simulated galaxies, we examine the efficacy of a Jeans equation analysis in reconstructing the total disk surface density, including the dark matter, at the "Solar" radius. Our simulation…
We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface…
Astrophysical discs which are sufficiently massive and cool are linearly unstable to the formation of axisymmetric structures. In practice, linearly stable discs of surface density slightly below the threshold needed for this instability…
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…