Autocatalytic reaction on low-dimensional substrates

Abstract

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.

15 pages

References in corpus (4)

• Trapping Reactions with Randomly Moving Traps: Exact Asymptotic Results for Compact Exploration
• Efficiency of Information Spreading in a population of diffusing agents
• Universal features of information spreading efficiency on $d$-dimensional lattices
• Fluctuation Effects on Quadratic Autocatalysis Fronts

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