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 (1)

• Universal features of information spreading efficiency on $d$-dimensional lattices

Cited by in corpus (1)

• Exact mean first-passage time on the T-graph