Critical detonation shock curvature and failure dynamics developments in theory of detonation shock dynamics

We report on recent developments in the theory of detonation shock dynamics (DSD). In particular we discuss the normal detonation shock velocity, Dn, curvature, K, relation for a near-Chapman-Jouguet detonation, for a material with Arrhenius kinetics and a large activation energy. An explicit formula for a multi-valued Dn - K relation, that shows a turning point with a critical curvature Ker such that for K > Ker, the possibility of detonation extinction, is obtained. We also outline a new asymptotic analysis when Dn is far below its Chapman-Jouguet value, which give rise to a new evolution equation and new dynamics that can describe failing and accelerating detonation