STOCHASTIC SIMULATION OF THE REACTION-DIFFUSION SYSTEM A-]INERT IN INTEGER AND FRACTAL DIMENSIONS(B)

We present a stochastic simulation of the reaction-diffusion system A + B -->inert based upon the algorithm of the minimal process method. I n order to overcome the well known problems of this algorithm when sel ecting a reaction or diffusion event according to its rate contributio n we introduce the concept of logarithmic classes which accelerates th e algorithm by an order of magnitude. We simulate the system A + B --> inert for integer dimensions d = 1,2,3,4 and confirm the predictions o f the scaling theory by Kang and Redner. We extend our simulations to fractal structures, namely the Sierpinski carpet, triangle, the Menger sponge and HLA-clusters. Again we find agreement with the scaling the ory if the fractal dimensions are defined as the spectral dimension.