Absence of Kinetic Effects in Reaction-Diffusion Processes in Scale-Free Networks

摘要

We show that the chemical reactions of the model systems of A + A → 0 and A + B → 0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A + A) and the segregation of the reactants (A + B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A + A reaction) and of mixed A and B (A + B reaction) around the hubs of the network Only at the limit of very sparse networks is the usual behavior recovered.