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

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

2004-02-10

arxiv.org/abs/cond-mat/0402269v1

Phys. Rev. Lett. 92, 138301 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures, to be published in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.92.138301

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.

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