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

摘要

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.