Dimensional crossovers and anomalous scaling of single and reacting random walkers in baguettelike lattices: Monte Carlo simulations of the number of distinct sites visited and of bimolecular A+A and A+B reactions.

Abstract

We performed Monte Carlo simulations on baguettelike lattices of random-walk-based bimolecular $A+A$ and $A+B$ reactions, and of the number of distinct sites visited. The emphasis is on the crossover times, from high (two- or three-) dimensional behavior to one-dimensional behavior, and their scaling laws with respect to tube width. We find that these dimensional crossovers deviate significantly from a mean square displacement law and are specific to both tube dimensionality (2 or 3) and reaction type (e.g., $A+A$ or $A+B$), instead of an expected power of 2, the exponents range between 1 and 4. Thus, the global information propagation is either faster or slower than single particle diffusion. The fractional densities of the $A+B$ reactions at the dimensional crossover are compared to the fractional densities at the segregation crossover in nonconfined media. The time evolutions of the $A+A$ reactions approximately mimic those of the average number of distinct sites visited. All asymptotic time behaviors exhibit one-dimensional character.