相关论文: Nested spheroidal figures of equilibrium I. Approx…

For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solutions) in which each body moves along a Keplerian orbit and the…

We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…

The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…

In this paper we classify the free boundary associated to equilibrium configurations of compressible, self-gravitating fluid masses, rotating with constant angular velocity. The equilibrium configurations are all critical points of an…

For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, $d\ge 2$, the simplest possible periodic solutions are provided by circular relative equilibria, (RE) for short, namely solutions in which each body…

We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…

We consider thin spherical shells of matter in both Newtonian gravity and general relativity, and examine their equilibrium configurations and dynamical stability. Thin-shell models are admittedly a poor substitute for realistic stellar…

Rotation is ubiquitous in the Universe, and recent kinematic surveys have shown that early type galaxies and globular clusters are no exception. Yet the linear response of spheroidal rotating stellar systems has seldom been studied. This…

Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is…

Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme mass-ratio, one can model these systems using…

The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric fluid under the additional assumption that it is incompressible and stratified. In this setting we show that the…

The pure traction problem of elasticity appears frequently in engineering applications, and its complexity stems from the fact that its solution is unique only up to (infinitesimal) rigid body motions. When finite elements are employed to…

Ellipse and ellipsoid fitting has been extensively researched and widely applied. Although traditional fitting methods provide accurate estimation of ellipse parameters in the low-noise case, their performance is compromised when the noise…

The hydrostatic equilibrium of multi-layer bodies lacks a satisfactory theoretical treatment despite its wide range of applicability. Here we show that by using the exact analytical potential of homogeneous ellipsoids we can obtain…

Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…

The binodals and the non-ergodicity lines of a binary mixture of hard sphere-like particles with large size ratio are computed for studying the interplay between dynamic arrest and phase separation in depletion-driven colloidal mixtures.…

The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of…

In this paper we investigate gravitationally bound, spherically symmetric equilibrium configurations consisting of ordinary (polytropic) matter nonminimally coupled to an external chameleon scalar field. We show that this system has static,…

Stable assemblages of localized vortices exist which have particle-like properties, such as mass, and which can interact with one another when they closely approach. In this article I calculate the mass of these localized states and…

We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the…