Kinetic roughening and bifurcations in reaction-diffusion systems

We study the dynamics of two reaction-diffusion phenomena driven by chemical activation and thermal dissipation and evolving, respectively, on a randomly distributed or continuous medium. The first system describes the process of slow combustion of a randomly distributed reactant. It is studied by a phase-field model built up from first principles and describes the evolution of thermal and reactant concentration fields. Our combustion model incorporates thermal diffusion, activation and dissipation. We examine it in a manner which makes a connection between the propagation of combustion fronts, their kinetic roughening and the percolation transition. In so doing, we examine slow combustion in the context phase transitions. The second system describes propagation of reaction fronts arising in transformations obeying the Arrhenius law of chemical reactions. It too is modelled by a set of phase-field equations describing the dynamics of both thermal and concentration fields. A typical example of this transformation is the crystallization of an amorphous material. In addition to the features of our combustion model, this model also incorporated a realistic treatment of mass diffusion. Front propagation of our model is shown to undergo period doubling bifurcations as one varies the background temperature at which the system is maintained. The signature of these bifurcations is the same as those of the logistics map. We study how the bifurcation structure changes as a function mass diffusion, focusing on changes of the background temperature for which period doubling first emerges. This temperature is the most easily obtained experimentally