Stochastic approach to Fisher and Kolmogorov, Petrovskii, and Piskunov wave fronts for species with different diffusivities in dilute and concentrated solutions

• Published in: Physica A 2020-11, Vol.558, p.124954, Article 124954
• Main Authors: Morgado, Gabriel, Nowakowski, Bogdan, Lemarchand, Annie
• Format: Article
• Language: English
• Subjects: Chemical Physics; Cross-diffusion; Master equation; Physics; Stochastic description; Wave front
• ISSN: 0378-4371; 1873-2119; 0378-4371
• DOI: 10.1016/j.physa.2020.124954

A wave front of Fisher and Kolmogorov, Petrovskii, and Piskunov type involving two species A and B with different diffusion coefficients DA and DB is studied using a master equation approach in dilute and concentrated solutions. Species A and B are supposed to be engaged in the autocatalytic reaction A+B → 2A. Contrary to the results of a deterministic description, the front speed deduced from the master equation in the dilute case sensitively depends on the diffusion coefficient of species B. A linear analysis of the deterministic equations with a cutoff in the reactive term cannot explain the decrease of the front speed observed for DB>DA. In the case of a concentrated solution, the transition rates associated with cross-diffusion are derived from the corresponding diffusion fluxes. The properties of the wave front obtained in the dilute case remain valid but are mitigated by cross-diffusion which reduces the impact of different diffusion coefficients. •Stochastic description of FKPP wave front for 2 species with different diffusivities.•Unexpected decrease of propagation speed for larger diffusivity of consumed species.•Non-standard master equation for reaction and cross-diffusion processes.•Cross-diffusion mitigates the impact of different diffusivities.