相关论文: Spiderweb central configurations

This article intends to provide a concise overview, from an observational point-of-view, of the current state of our knowledge of the most relevant properties of the Milky Way's nuclear star cluster (MWNSC). The MWNSC appears to be a…

Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations on representations correspond to…

Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…

We study the indices of the geodesic central configurations on $\H^2$. We then show that central configurations are bounded away from the singularity set. With Morse's inequality, we get a lower bound for the number of central…

The odd-even mass staggering in nuclei is analyzed in the context of self-consistent mean-field calculations, for spherical as well as for deformed nuclei. For these nuclei, the respective merits of the energy differences $\Delta^{(3)}$ and…

The purpose of this article is to \begin{enumerate} \item define $M(t,k)$ the $t$-fold center of mass arrangement for $k$ points in the plane, \item give elementary properties of $M(t,k)$ and \item give consequences concerning the space…

Using the Einstein cluster models, we construct a fully relativistic, spherically symmetric, spiky structure of matter distribution near a supermassive black hole. We introduce and discuss three simple toy models, together with a more…

Highly accurate numerical solutions to the problem of Black Holes surrounded by uniformly rotating rings in axially symmetric, stationary spacetimes are presented. The numerical methods developed to handle the problem are discussed in some…

Let $S_n$ denote the symmetric group of permutations acting on $n$ elements. We investigate the double sequence $\{N_{\ell}(n)\}$ counting the number of $\ell$ tuples of elements of the symmetric group $S_n$, where the components commute,…

We study singularities of the n-body problem in spaces of constant curvature and generalize certain results due to Painleve, Weierstrass, and Sundman. For positive curvature, some of our proofs use the correspondence between total collision…

In this paper, we first consider a flat plate (called a lamina) with uniform density $\rho$ that occupies a region $\mathfrak R$ of the plane. We show that the location of the center of mass, also known as the centroid, of the region equals…

In the $n$-body problem, when a~cluster of bodies tends to a collision, then its normalized shape curve converges to the set of normalized central configurations, which has $SO(2)$ symmetry in the planar case. This leaves a possibility that…

We investigate many-body localization in the chain of interacting spins with a transverse power-law interaction, $J_{0}/r^{\alpha}$, and random on-site potentials, $\phi_i \in \left(-W/2,W/2\right)$, in the long-range limit, $\alpha< 3/2$,…

We show that there exist an upper bound and a lower bound for the number of non-degenerate central configurations of the n-body problem in the plane with a homogeneous potential. In particular, both bounds are independent of the homogeneous…

Abridged: In one widely discussed model for the formation of nuclear star clusters (NSCs), massive globular clusters spiral into the center of a galaxy and merge to form the nucleus. It is now known that at least some NSCs coexist with…

This paper introduces the problem of passive control of a chain of N identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The problem arises in the…

We establish, in the framework of the theory of nested figures, the expressions for the gravitational moments $J_{2n}$ of a systems made of ${\cal L}$ homogeneous layers separated by spheroidal surfaces and in relative rotational motion. We…

We investigate rigidity-type problems on the real line and the circle in the non-generic setting. Specifically, we consider the problem of uniquely determining the positions of $n$ distinct points $V = {v_1, \ldots, v_n}$ given a set of…

In fully-dynamic consistent clustering, we are given a finite metric space $(M,d)$, and a set $F\subseteq M$ of possible locations for opening centers. Data points arrive and depart, and the goal is to maintain an approximately optimal…

We subject to an N-body numerical investigation our analysis of Paper I on the survival of stellar clusters undergoing rapid mass loss. We compare analytical tracks of bound mass-fraction {\it vs} star formation efficiency $\epsilon$ to…