Encounter-controlled reactions between interacting walkers in finite lattices: Complex kinetics and many-body effects

Montroll's approach to diffusion-controlled annihilation reactions recently generalized by the present authors to account for the simultaneous displacement of two walkers, is extended by including more complex kinetic schemes and many-body effects. The mean walklength to reaction and the spatial organization of the reactants in a finite planar lattice is evaluated analytically and by Monte Carlo simulations in two representative schemes involving, respectively, a single autocatalytic reaction and an autocatalytic reaction coupled to isomerization. While in the first scheme the results are in qualitative (though not quantitative) accord with mean-field predictions, marked qualitative differences with mean-field behavior are found in the second scheme. (C) 2001 American Institute of Physics.