Propagation and ignition of fast gasless detonation waves of phase or chemical transformation in condensed matter

Fast self sustained waves of chemical or phase transformations, observed in several contexts in condensed matter effectively result in "gasless detona tion". The phenomenon is modelled by coupling the reaction diffusion equati on, describing chemical or phase transformations, and the wave equation, de scribing elastic perturbations. The coupling considered in this work involv es (i) a dependence of the sound velocity on the chemical (phase) field, an d (ii) the destruction of the initial chemical equilibrium when the strain exceeds a critical value (strain induced phase transition). Both the case o f an initially unstable state (first order kinetics) and metastable state ( second order kinetics) are considered. An exhaustive analytic and numerical study of travelling waves reveals the existence of supersonic modes of tra nsformations. The practically important problem of ignition of fast waves b y mechanical perturbation is investigated. With the present model, the crit ical strain necessary to ignite gasless detonation by local perturbations i s determined.