Nearest-neighbor distance distributions and self-ordering in diffusion-controlled reactions. I. A+A simulations.

Abstract

Monte Carlo simulation of transient, diffusion-controlled annihilation (A+A\ensuremath{\rightarrow}0) and fusion (A+A\ensuremath{\rightarrow}A) reactions have been performed on one- and two-dimensional lattices and on the fractal, critical percolation cluster of a square lattice (applying a breadth-first search algorithm). Fast self-ordering is demonstrated via analyses of the interparticle distributions and the nearest-neighbor distance distributions (NNDD). Good agreement is obtained with the few existing analytical results in one dimension. For the higher dimensions (where there are no analytical results and where the interparticle distances are not uniquely defined), we find the NNDD via a ``taxicab'' approach. We obtain the kinetically self-ordered particle distributions and relate them to the global rate laws.