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

Gabriel Morgado, Bogdan Nowakowski and Annie Lemarchand

Physica A: Statistical Mechanics and its Applications, 2020, vol. 558, issue C

Abstract: 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.

Keywords: Wave front; Stochastic description; Master equation; Cross-diffusion (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120304982

DOI: 10.1016/j.physa.2020.124954

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