Annihilation reaction A+A→0 with diffusion and interaction between particles in disordered structures

We performed numerical simulations of the bimolecular annihilation reaction A+A→0 with diffusion and short range interactions. We used the two-dimensional percolation cluster at probability p (p_c≤p≤1, where p_c is the critical probability) as the substratum over which the particles diffuse and studied the particle density ρ as a function of the time t. We analyzed the effects of (i) repulsive nearest neighbor interaction and (ii) repulsive nearest neighbor with attractive next nearest neighbor interactions. These effects become relevant at short times. We propose a crude approximation for ρ(t) for each case and for p≥p_c, which works reasonable well at short times. The crossover from short times to asymptotic regimes is analyzed for case (i). Asymptotic behaviors for ρ(t), which are independent of the interactions, are expected at very long times.