Autocatalytic reaction on low-dimensional substrates

Details Autocatalytic reaction on low-dimensional substrates Autocatalytic reaction on low-dimensional substrates

2007-08-24

arxiv.org/abs/0708.3314v1

Physics

Condensed Matter

Statistical Mechanics

15 pages

Scientific paper

10.1007/s00214-007-0323-5

We discuss a model for the autocatalytic reaction $A+B\to 2A$ on substrates where the reactants perform a compact exploration of the space, i.e., on lattices whose spectral dimension $\tilde{d}$ is $< 2$. For finite systems, the total time $\tau$ for the reaction to end scales according to two different regimes, for high and low concentrations of reactants. The functional dependence of $\tau$ on the volume of the substrate and the concentration of reactants is discussed within a mean-field approximation. Possible applications are discussed.

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