Efficiency of encounter-controlled reactions in regular and disordered networks
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Using a Markov chain formulation, we study the efficiency of an encounter-controlled reaction for a pair of walkers diffusing through both regular and disordered networks. The efficiency is determined by the mean number of steps the walkers perform before meeting. Ordinarily, the efficiency is expected to increase monotonically as the effective size of the network diminishes, e.g. as a result of increasing the relative mobility between particles or introducing shortcuts by randomly rewiring connections between nodes. However, we show that the efficiency can display nontrivial nonmonotonic behavior within a proper parameter range. An explanation of this behavior is proposed in terms of a competition between the increase of the relative diffusion coefficient and the increase in the probability of escaping from the typical interaction zone.