Absence of kinetic effects in reaction-diffusion processes in scale-free networks

TL;DR

This paper demonstrates that reaction-diffusion processes on scale-free networks behave differently from normal spaces, with faster reactions and cluster formations around hubs, due to the absence of typical depletion zones and segregation effects.

Contribution

It reveals that kinetic effects like depletion zones and segregation are absent in scale-free networks, leading to faster reaction dynamics and cluster formations around hubs.

Findings

Reactions occur faster on scale-free networks with higher density exponents.

Depletion zones and segregation effects are absent in scale-free networks.

Normal reaction behavior is recovered only in very sparse networks.

Abstract

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.