Computer simulations of diffusion-limited reactions

In many situations, it is possible to model a system by entities that diffuse and occasionally react upon encounter. Examples include chemical reactions, electron-hole recombination, annealing of defects in crystals, interacting excitons (solitons, photoexcited states, and so on), predator-prey models, and the spreading of ideas through social intercourse. For concreteness and without loss of generality, we refer to the interacting entities as particles. We discuss various ways to simulate diffusion-reaction systems. For simplicity, we restrict our discussion to simple reaction schemes, such as coalescence and annihilation, and to the case where the particles occupy a 1D lattice. It turns out that diffusion-limited kinetics deviates the most from the classical reaction-limited regime in d=1, so the focus on one dimension is reasonable. The generalization of the techniques discussed to more realistic models (off-lattice, higher dimensions, and so on), is straightforward.