Cold uniform spherical collapse revisited
  We report results of a study of the Newtonian dynamics of N self-gravitating
particles which start in a quasi-uniform spherical configuration, without
initial velocities. These initial conditions would lead to a density
singularity at the origin at a finite time when N \rightarrow \infty, but this
singularity is regulated at any finite N (by the associated density
fluctuations). While previous studies have focussed on the behaviour as a
function of N of the minimal size reached during the contracting phase, we
examine in particular the size and energy of the virialized halo which results.
We find the unexpected result that the structure decreases in size as N
increases, scaling in proportion to N^{-1/3}, a behaviour which is associated
with an ejection of kinetic energy during violent relaxation which grows in
proportion to N^{1/3}. This latter scaling may be qualitatively understood, and
if it represents the asymptotic behaviour in N implies that this ejected energy
is unbounded above. We discuss also tests we have performed which indicate that
this ejection is a mean-field phenomenon (i.e. a result of collisionless
dynamics).
