Simulation of Self-sustained Relaxation of a Two-dimensional Metastable Medium by Means of a Traveling Wave

Abstract

The traveling wave mode of self-sustained relaxation of a metastable medium, such as combustion and annealing of radiation-induced defects in solids, is studied. The mechanism of self-sustained relaxation and propagation of the traveling wave is a positive thermal-concentration feedback and heat transfer. The thermal-concentration feedback develops because the relaxation rate depends strongly on temperature, and the energy of the metastable state transforms into thermal energy in the process of relaxation. Hence, the relaxation leads to an increase in the medium temperature and, consequently, to further support of the relaxation. In this work, traveling waves are considered, and their features are investigated by computer simulation. The shape and speed of the traveling wave are investigated as a function of the medium properties, and the way of its initiation. We examined the shapes of wavefronts as they propagate on a plane, and observed two different regimes of traveling wave propagation. Sometimes the front of the traveling wave spreads as a whole and velocity of propagation is perpendicular to the wavefront. Sometimes small perturbations arise on the wavefront, and then grow by virtue of relaxation along the front, thus, the new area of the relaxed medium has the form of a narrow strip that propagates along the line of the front and maintains a constant width in the direction perpendicular to the front. We observe the appearance of one or more small perturbations, which arise in a symmetric way. The influence of boundaries on the traveling waves was also investigated.