Nonclassical kinetics in three dimensions: Simulations of elementary A+B and A+A reactions

Monte Carlo simulations are employed to study the rate laws of A + A --> 0 and A + B --> 0 diffusion-limited elementary reactions in three dimensions (3D). Using reflective instead of cyclic boundary conditions, we do observe the Zeldovich regime in 3D for the A + B reaction. The time and density values for the crossover into the Zeldovich regime in 3D agree with the existing scaling laws and provide the hitherto missing scaling coefficient. We show that the behavior of the A + A reaction rates and the early time behavior of the A + B reaction rates in 1D, 2D, and 3D map the rate of distinct sites visited by a single random walker, giving nonclassical kinetics at early times in all cases. We also determine a simple scaling law for crossover to finite size effects, which depends only on the linear lattice length, except when the crossover to finite size effects and the crossover to the Zeldovich regime are concomitant.