Reaction-diffusion front for A+B→∅ in one dimension

Abstract

We study theoretically and numerically the steady state diffusion controlled reaction A+B→∅, where currents J of A and B particles are applied at opposite boundaries. For a reaction rate λ, and equal diffusion constants D, we find that when λJ−12D−12≪1 the reaction front is well described by mean-field theory. However, for λJ−12D−12≫1, the front acquires a Gaussian profile—a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (nonwandering) front width and find results consistent with scaling and field theoretic predictions.