The fragmentation of expanding shells III: Oligarchic accretion and the
  mass spectrum of fragments
  We use SPH simulations to investigate the gravitational fragmentation of
expanding shells through the linear and non--linear regimes. The results are
analysed using spherical harmonic decomposition to capture the initiation of
structure during the linear regime; the potential-based method of Smith et al.
(2009) to follow the development of clumps in the mildly non-linear regime; and
sink particles to capture the properties of the final bound objects during the
highly non-linear regime. In the early, mildly non--linear phase of
fragmentation, we find that the clump mass function still agrees quite well
with the mass function predicted by the analytic model. However, the sink mass
function is quite different, in the sense of being skewed towards high-mass
objects. This is because, once the growth of a condensation becomes non-linear,
it tends to be growing non-competitively from its own essentially separate
reservoir; we call this Oligarchic Accretion.
