Universal properties of the mA + nB → Ø diffusion-limited reaction

The mA + nB → Ø diffusion limited reaction with homogeneous initial condition is studied analytically and numerically. Through renormalization group arguments, it is shiown that the system exhibits the anomalous kinetic behavior below the critical dimension dc∗ ≡ 4/(m + n − 1). Asymptotic behavior of the density below the critical dimension is universal and is predicted to be t−d/4 in d dimensions irrespective of the reaction type (m, n). These predictions are compared with the numerical simulations in one dimensions.