Here we present the results from two sets of simulations, in two and three
spatial dimensions. In two dimensions, the simulations include multifrequency
flux-limited diffusion neutrino transport in the "ray-by-ray-plus"
approximation, two-dimensional self gravity in the Newtonian limit, and nuclear
burning through a 14-isotope alpha network. The three-dimensional simulations
are model simulations constructed to reflect the post stellar core bounce
conditions during neutrino shock reheating at the onset of explosion. They are
hydrodynamics-only models that focus on critical aspects of the shock stability
and dynamics and their impact on the supernova mechanism and explosion. In two
dimensions, we obtain explosions (although in one case weak) for two
progenitors (11 and 15 Solar mass models). Moreover, in both cases the
explosion is initiated when the inner edge of the oxygen layer accretes through
the shock. Thus, the shock is not revived while in the iron core, as previously
discussed in the literature. The three-dimensional studies of the development
of the stationary accretion shock instability (SASI) demonstrate the
fundamentally new dynamics allowed when simulations are performed in three
spatial dimensions. The predominant l=1 SASI mode gives way to a stable m=1
mode, which in turn has significant ramifications for the distribution of
angular momentum in the region between the shock and proto-neutron star and,
ultimately, for the spin of the remnant neutron star. Moreover, the
three-dimensional simulations make clear, given the increased number of degrees
of freedom, that two-dimensional models are severely limited by artificially
imposed symmetries.Comment: 9 pages, 3 figure