  The nature of type Ia supernovae (SNIa) - thermonuclear explosions of white
dwarf stars - is an open question in astrophysics. Virtually all existing
theoretical models of normal, bright SNIa require the explosion to produce a
detonation in order to consume all of stellar material, but the mechanism for
the deflagration-to-detonation transition (DDT) remains unclear. We present a
unified theory of turbulence-induced DDT that describes the mechanism and
conditions for initiating detonation both in unconfined chemical and
thermonuclear explosions. The model is validated using experiments with
chemical flames and numerical simulations of thermonuclear flames. We use the
developed theory to determine criteria for detonation initiation in the single
degenerate Chandrasekhar-mass SNIa model, and show that DDT is almost
inevitable at densities 10^7 - 10^8 g/cc.
