  We have performed fully 3D simulations of the collapse of molecular cloud
cores which obey the logatropic equation of state. By following the collapse of
these cores from states of near hydrodynamic equilibrium, we are able to
produce accretion histories which closely resemble those of observed cores. The
accretion proceeds in four distinct stages: an initial period of very slow
accretion; a period of vigorous accretion following the development of a
central density singularity, with a mass accretion rate proportional to t^3, as
predicted by self-similar models; a period of relatively stable, vigorous
accretion; and finally a gradual decrease in the accretion rate once about 50%
of the available mass of the molecular cloud core has been accreted. These
results may explain the accretion histories of cores as they pass through the
pre-protostellar, Class 0, and Class I stages.
