Characteristics of reaction-diffusion on scale-free networks

TL;DR

This study investigates reaction-diffusion processes on scale-free networks, revealing how annihilation events shift from low to high connectivity nodes over time, leading to faster reaction rates compared to lattice systems.

Contribution

It provides new insights into the spatial-temporal dynamics of reaction-diffusion on scale-free networks, highlighting the role of network heterogeneity in accelerating reactions.

Findings

Annihilations initially occur on low-connectivity nodes.

Over time, reactions concentrate on high-connectivity hubs.

Reaction rates are faster on scale-free networks than on regular lattices.

Abstract

We examine some characteristic properties of reaction-diffusion processes of the A+A->0 type on scale-free networks. Due to the inhomogeneity of the structure of the substrate, as compared to usual lattices, we focus on the characteristics of the nodes where the annihilations occur. We show that at early times the majority of these events take place on low-connectivity nodes, while as time advances the process moves towards the high-connectivity nodes, the so-called hubs. This pattern remarkably accelerates the annihilation of the particles, and it is in agreement with earlier predictions that the rates of reaction-diffusion processes on scale-free networks are much faster than the equivalent ones on lattice systems.