Complex dynamics in initially separated reaction-diffusion systems

We review recent developments in the study of the diffusion reaction systems of the type A + B → C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x > 0 and x < 0, respectively. We find that whereas for d ⩾ 2 the mean field exponent characterizes the width of the reaction zone, fluctuations are relevant in the one-dimensional system. We present analytical and numerical results for the reaction rate on fractals and percolation systems at criticality.We also study the case where the particles are Lévy flights in d = 1. Finally, we consider experimentally, analytically, and numerically the reaction A + Bstatic → C, where species A diffuses from a localized source.