2002/01/31 by Richard Battye, Gary Gibbons, Paul Sutcliffe · 2 citations
Physics and Astronomy · Mathematics · #hep-th #astro-ph #cond-mat #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1098/rspa.2002.1061
published as Proc.Roy.Soc.Lond.A459:911-943,2003 · 37 pages, 18 figures, 3 as colour jpg files. References added. Version to appear in Proceedings of the Royal Society
arxiv created 2002/10/02 · arxiv updated 2009/11/30
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in particular as homothetic time-dependent solutions to Newton's equations of motion and as stationary states in the One Component Plasma model. Concentrating mainly on the case of an inverse square law balanced by a linear force, we compute numerically equilibria and their statistical properties. When all the masses (or charges) of the particles are equal, for small numbers of points they are regular convex deltahedra, which on increasing the number of points give way to a multi-shell structure. In the limit of a large number of points we argue using an analytic model that they form a homogeneous spherical distribution of points, whose spatial distribution appears, from our preliminary investigation, to be similar to that of a Bernal hard-sphere liquid.