Autocatalytic reaction on low-dimensional substrates

TL;DR

This paper models autocatalytic reactions on low-dimensional substrates where reactants explore space compactly, analyzing how reaction completion time scales with system size and concentration, with implications for various applications.

Contribution

It introduces a mean-field model for autocatalytic reactions on low-dimensional lattices with spectral dimension less than 2, highlighting different scaling regimes for reaction time.

Findings

Reaction time scales differently at high and low reactant concentrations.

Mean-field approximation describes the dependence of reaction time on system volume and concentration.

Potential applications in systems with low-dimensional reactive environments.

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.