Related papers: A Roche Model for Uniformly Rotating Rings
An analytical method is presented for treating the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity. The method is based on an expansion about the thin ring limit, where the cross-section of…
An iterative method is presented for solving the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to…
In this paper, we describe an analytical method for treating uniformly rotating homogeneous rings without a central body in Newtonian gravity. We employ series expansions about the thin ring limit and use the fact that in this limit the…
In this paper uniformly rotating relativistic rings are investigated analytically utilizing two different approximations simultaneously: (1) an expansion about the thin ring limit (the cross-section is small compared with the size of the…
Some exact analytical formulas are presented for the generalized Roche model of rotating star. The gravitational field of the central core is described by the model of two equal-mass point centers placed symmetrically at rotation axis with…
This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical…
An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported…
In this paper, we discuss general relativistic, self-gravitating and uniformly rotating perfect fluid bodies with a toroidal topology (without central object). For the equations of state describing the fluid matter we consider polytropic as…
We show that the solutions obtained in the paper `An exact solution for arbitrarily rotating gaseous polytropes with index unity' by Kong, Zhang, and Schubert represent only approximate solutions of the free-boundary Euler-Poisson system of…
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 remarkable appearance of self-organized regular and peaked polygonal rotating patterns in shallow Leidenfrost rings is investigated as a balance between surface tension geometry and nonlinear terms of Euler equation. Using the…
We examine bound orbits of particles around singly rotating black rings. We show that there exist stable bound orbits in toroidal spiral shape near the axis of the ring, and also exist stable circular orbits on the axis as special cases.…
In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe…
In the article the Fourier series analytical solutions of uniformly loaded rectangular thin plates with symmetrical boundary conditions are considered. For all the cases the numerical values are tabulated.
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We propose a generic mechanism for the formation of narrow rings in rotating systems. For this purpose we use a system of discs rotating about a common center lying well outside the discs. A discussion of this system shows that narrow rings…
We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable…
We introduce a novel type of surface waves that form at the edge of guiding structures consisting of several concentric rings. Such surface waves rotate steadily upon propagation and, in contrast to nonrotating waves, for high rotation…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…