A microscopic model for the propagation of detonations in solids

We present a simple one-dimensional microscopic model for the propagation of a detonation which is specially adapted to solids. It couples a non-linear equation for the dynamics of the crystal lattice to an equation describing the molecular dissociations. Analytical calculations in the continuum limit and numerical solutions of the discrete model show that it yields the essential features of a detonation wave. Moreover, the model exhibits the existence of two detonation regimes, in agreement with recent molecular dynamics simulations.