Multicomponent reaction-diffusion processes on complex networks

TL;DR

This paper analytically investigates reaction-diffusion processes on complex networks, deriving expressions for particle correlations and densities, and analyzing the impact of jamming effects in multicomponent reactions.

Contribution

The study provides new analytical insights into reaction-diffusion dynamics on scale-free networks, especially regarding the jamming effect and its long-term behavior.

Findings

Jamming effects diminish over time in low-density regimes.

Hubs attract particles but do not sustain jamming effects long-term.

Analytical expressions for particle correlations and densities are derived.

Abstract

We study the reaction-diffusion process $A + B \to \emptyset$ on uncorrelated scale-free networks analytically. By a mean-field ansatz we derive analytical expressions for the particle pair-correlations and the particle density. Expressing the time evolution of the particle density in terms of the instantaneous particle pair-correlations, we determine analytically the `jamming' effect which arises in the case of multicomponent, pair-wise reactions. Comparing the relevant terms within the differential equation for the particle density, we find that the `jamming' effect diminishes in the long-time, low-density limit. This even holds true for the hubs of the network, despite that the hubs dynamically attract the particles.