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I will present a series of models for the explosion mechanism of Type-II (core collapse) supernovae. These models are based on general relativistic radiation-hydrodynamic numerical simulations of stellar core collapse and the subsequent evolution of the proto-neutron star. The simulations employ various models for the equation of state (EOS) of hot, dense matter and various models for the pre-supernova progenitor. I will discuss the proposed late-time neutrino reheating mechanism, as well as the role of both the progenitor model and the EOS in this mechanism. Additionally, I will address the problem of the accuracy and consistency of the numerical radiation-hydrodynamic techniques used to model supernovae. Both the shortcomings of the existing generation of models and the improvments that will be provided by the next generation will be discused.
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