Related papers: A Roche Model for Uniformly Rotating Rings
The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…
We describe the trajectories of circular orbits of spinless and spinning test particles around of rotating bodies in equatorial and non-equatorial planes via the Mathisson-Papapetrou-Dixon equations which include the Ricci rotation…
Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
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…
In this work, we study and solve the normalized Ricci flow equation for circle bundles over surfaces. Moreover, we study the asymptotic behavior of the solutions and their connections to some model geometries.
The scattering of spinning test particles by a Schwarzschild black hole is studied. The motion is described according to the Mathisson-Papapetrou-Dixon model for extended bodies in a given gravitational background field. The equatorial…
We propose a new class of space-filling designs called rotated sphere packing designs for computer experiments. The approach starts from the asymptotically optimal positioning of identical balls that covers the unit cube. Properly scaled,…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…
We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear beam…
Although intersection homology lacks a ring structure, certain expressions (called uniform) in the intersection homology of an irreducible projective variety $X$ always give the same value, when computed via the decomposition theorem on any…
This paper studies the problem of using a robot arm to manipulate a uniformly rotating chain with its bottom end fixed. Existing studies have investigated ideal rotational shapes for practical applications, yet they do not discuss how these…
Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by {\it overfitting}, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the…
We prove optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles.
The asymptotic structure of outflows from rotating magnetized objects confined by a uniform external pressure is calculated. The flow is assumed to be perfect MHD, polytropic, axisymmetric and stationary. The well known associated first…
Several observational pieces of evidence indicate that specific evolutionary channels which involve Roche lobe overflow are not correctly accounted for by the classical Roche model. We generalize the concept of Roche lobe in the presence of…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
We solve the inverse spectral problem for rotationally symmetric manifolds, which include the class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…