Matthias Raives et al. studied transition from accretion to explosion in highly idealized setting of the neutrino mechanism of core-collapse supernovae and in relation to the critical neutrino luminosity of Burrows & Goshy (1993) and extending the previous work of Pejcha & Thompson (2012). Interestingly, in order to properly resolve the vicinity of the critical transition, high simulation resolution is needed.
The full paper is available at astro-ph.