相关论文: Estimating the Number of Stable Configurations for…
We conducted a comprehensive numerical investigation of the energy landscape of the Thomson problem for systems up to $N=150$. Our results show the number of distinct configurations grows exponentially with $N$, but significantly faster…
We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of…
Determination of \emph{optimal} arrangements of $N$ particles on a sphere is a well-known problem in physics. A famous example of such is the Thomson problem of finding equilibrium configurations of electrical charges on a sphere. More…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
We investigate the classical ground state of a large number of charges confined inside a disk and interacting via the Coulomb potential. By realizing the important role that the peripheral charges play in determining the lowest energy…
We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable…
In an earlier paper \cite{yu2021Finiteness}, we showed that there are finitely many stationary configurations (consisting of equilibria, rigidly translating configurations, relative equilibria and collapse configurations) in the planar…
We describe an algorithm to compute the stable multiplicity of a family of irreducible representations in the cohomology of ordered configuration space of the plane. Using this algorithm, we compute the stable multiplicities of all families…
In this article we consider the distribution of $N$ points on the unit sphere $\mathbb{S}^{d-1}$ in $\mathbb{R}^d$ interacting via logarithmic potential. A characterization theorem of the stationary configurations is derived when $N=d+2$…
We study a numerical instability of direct simulations with truncated equation chains for the "circular cumulant" representation and two approaches to its suppression. The approaches are tested for a chimera-bearing hierarchical population…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
A popular method for selecting the number of clusters is based on stability arguments: one chooses the number of clusters such that the corresponding clustering results are "most stable". In recent years, a series of papers has analyzed the…
Thomson problem is a classical problem in physics to study how $n$ number of charged particles distribute themselves on the surface of a sphere of $k$ dimensions. When $k=2$, i.e. a 2-sphere (a circle), the particles appear at equally…
The stability of a system of $N$ equal sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the "Euler Resting" configurations previously…
We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
The finiteness problem of stationary configurations for the planar five-vortex problem is considered in this paper. The numbers of equilibria and rigidly translating configurations are shown to be at most 6 and 24 respectively. The numbers…