Fluctuation Effects on Quadratic Autocatalysis Fronts
Mikhail V. Velikanov, Raymond Kapral (Chemical Physics Theory, Group, Dept. of Chemistry, Univ. of Toronto)
TL;DR
This paper investigates how fluctuations influence the behavior of chemical wave fronts in autocatalytic systems with quadratic reactions, using a Markov chain model and comparing analytical results with simulations.
Contribution
It introduces an approximate Markov chain model for autocatalytic fronts and analyzes fluctuation effects on wave propagation and concentration profiles.
Findings
Fluctuations cause deviations from deterministic wave velocity predictions.
The approximate distribution aligns well with lattice-gas automaton simulations.
Diffusion speed impacts the significance of fluctuation effects.
Abstract
A Markov chain model for spatially distributed autocatalytic systems with a quadratic reaction rate is considered. An approximate solution for the local probability distribution is obtained in the form of a perturbation expansion for the regimes where diffusion is relatively fast. Using this approximate distribution, properties of the chemical wave fronts found in these autocatalytic systems are studied, and deviations of the minimum propagation velocity and the concentration profile from deterministic predictions are analyzed. A comparison with numerical results from lattice-gas automaton simulations is also provided.
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