  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.
