One-dimensional lattice dynamics of the diffusion-limited reaction A+A -> A+S: Transient behavior

We use a Boolean cellular automaton model to describe the diffusion-limited dynamics of the irreversible reaction A + A --> A + S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilit ies from which explicit expressions for the particle concentration and the two-point correlation can be obtained. It is shown that the long-time dynam ics is in agreement with the off-lattice solution. The early-time behavior, however, predicts a slower decay of the concentration.