Discreteness effects on the front propagation in the A + B → 2 A reaction in 3 dimensions

We consider numerically the front propagation in a three-dimensional, diffusion-controlled A + B → 2A autocatalytic reaction. We show that the interplay between local and global ordering phenomena strongly affects the reaction kinetics, and that it leads to the breakdown of the classical continuous scheme (described by the Fisher equation) even at quite small concentrations of reactants. Discreteness aspects lead to considerable deviations of the simulated behavior of chemical fronts from the continuous scheme predictions, especially in what the fronts' structure and their propagation velocities are concerned.