Front propagation in A+B -> 2A reaction under subdiffusion

TL;DR

This paper investigates how subdiffusion affects the propagation of reaction fronts in an autocatalytic reaction, revealing that unlike normal diffusion, subdiffusion leads to a zero minimal propagation velocity, implying potential propagation failure.

Contribution

It extends the understanding of reaction front dynamics to subdiffusive systems, showing that the classical FKPP velocity concept does not hold under subdiffusion.

Findings

Minimal propagation velocity is zero under subdiffusion.

Propagation failure is possible in subdiffusive reactions.

Classical FKPP results do not apply to subdiffusive systems.

Abstract

We consider an irreversible autocatalytic conversion reaction A+B -> 2A under subdiffusion described by continuous time random walks. The reactants' transformations take place independently on their motion and are described by constant rates. The analog of this reaction in the case of normal diffusion is described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation leading to the existence of a nonzero minimal front propagation velocity which is really attained by the front in its stable motion. We show that for subdiffusion this minimal propagation velocity is zero, which suggests propagation failure.