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Multicomponent reaction-diffusion processes on complex networks

Sebastian Weber·Markus Porto
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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.

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Sebastian Weber, Markus Porto. 2006-08-17. Multicomponent reaction-diffusion processes on complex networks. https://doi.org/10.1103/physreve.74.046108

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