Propagation of stationary exothermic transition front with nonstationary oscillatory tail

摘要

We consider a propagation of exotermic transition front in a discreteconservative oscillatory chain. Adequate description of such fronts is a keypoint in prediction of important transient phenomena, including phasetransitions and topochemical reactions. Due to constant energy supply, thetransition front can propagate with high velocities, precluding anycontinuum-based considerations. Stationary propagation of the front isaccompanied by formation of a non-stationary oscillatory tail with complicatedinternal structure. We demonstrate that the structure of the oscillatory tailis related to a relationship between phase and group velocities of theoscillations. We suggest also an approximate analytic procedure, which allowsone to determine all basic characteristics of the propagation process: velocityand width of the front, frequency and amplitude of the after-frontoscillations, as well as the structure of the oscillatory tail. As an example,we consider a simple case of biharmonic double-well on-site potential. Numericresults nicely conform to the analytic predictions.