Some properties of the diffusion-limited reaction nA + mB → C with homogeneous and inhomogeneous initial conditions

The diffusion-limited reaction nA +mB → C is studied both for homogeneous and inhomogeneous initial conditions. For the homogeneous case, microscopic arguments are given which allow one to decide when the kinetics is anomalous. These predictions are confirmed by numerical simulations. For the inhomogeneous case, a front is formed, whose properties can be described by scaling theory. Numerical simulations show that the fluctuations play an important role only in one dimension, provided that n+m ⩽ 3 and play a marginal role in two dimensions for n = m = 1