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Two-loop calculation of anomalous kinetics of the reaction A + A → Ø in randomly stirred fluid

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Abstract

The single-species annihilation reaction A + A → Ø is studied in the presence of a random velocity field generated by the stochastic Navier-Stokes equation. The renormalization group is used to analyze the combined influence of the density and velocity fluctuations on the long-time behavior of the system. The direct effect of velocity fluctuations on the reaction constant appears only from the two-loop order, therefore, all stable fixed points of the renormalization group and their regions of stability are calculated in the two-loop approximation in the two-parameter (ε, Δ) expansion. A renormalized integro-differential equation for the number density is put forward which takes into account the effect of density and velocity fluctuations at next-to-leading order. Solution of this equation in perturbation theory is calculated in a homogeneous system.

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Correspondence to Juha Honkonen.

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Hnatič, M., Honkonen, J. & Lučivjanský, T. Two-loop calculation of anomalous kinetics of the reaction A + A → Ø in randomly stirred fluid. Eur. Phys. J. B 86, 214 (2013). https://doi.org/10.1140/epjb/e2013-30982-9

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  • DOI: https://doi.org/10.1140/epjb/e2013-30982-9

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