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Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with…
The Kuzmin-Toomre family of discs is used to construct potential-density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a…
Some formulae are presented for finding two-integral distribution functions (DFs) which depends only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar…
We consider a spherical thick shell immersed in two different spherically symmetric space-times. Using the fact that the boundaries of the thick shell with two embedding space-times must be nonsingular hypersurfaces, we develop a scheme to…
Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric…
The problem of one-dimensional randomly forced Burgers turbulence is considered in terms of (1+1) directed polymers. In the limit of strong turbulence (which corresponds to the zero temperature limit for the directed polymer system) using…
The effect of ring stiffness and pressure on the glassy dynamics of a thermal assembly of two-dimensional ring polymers is investigated using extensive coarse-grained molecular dynamics simulations. In all cases, dynamical slowing down is…
The rotation dynamics of spiral galaxies is modeled using a sum of two mass distributions: a spherical bulge and a thin disk. The density functions representing these mass distributions are calculated from the total angular momentum of the…
In this work, we study a particular system of coagulation equations characterized by two values, namely volume $v$ and surface area $a$. Compared to the standard one-dimensional models, this model incorporates additional information about…
We discuss the nature of the velocity dispersion vs. size relation for molecular clouds. In particular, we add to previous observational results showing that the velocity dispersions in molecular clouds and cores are not purely functions of…
In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability…
The nanoscale cylindrical Couette flow is investigated by means of molecular dynamics simulations, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. We find that the tangential velocity of the low is…
For disc galaxies, a close relation exists between the distribution of light and the shape of the rotation curve. We quantify this relation by measuring the inner circular-velocity gradient d_{R}V(0) for spiral and irregular galaxies with…
Turbophoresis in inhomogeneous turbulent flows leads to the formation of large-scale nonuniform particle number density distributions of inertial particles. This effect is associated with an effective drift velocity directed toward regions…
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of $\sigma_B/\sigma_A=0.1$ and a mass ratio of $m_B/m_A=0.001$ are investigated using event driven molecular dynamics. The contact value of the pair…
We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions…
Given the dimensions (including thickness) and rotation speeds for an axisymmetric galaxy, a closed-loop iterative method is designed to find the total mass, density, and surface-mass density (SMD)distributions. There is no need for…
We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set…
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…