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arXiv · 1512.05935

Two-loop calculation of anomalous kinetics of the reaction $A + A \rightarrow\varnothing$ in randomly stirred fluid

Michal Hnatič·Juha Honkonen·Tomáš Lučivjanský
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Abstract

The single-species annihilation reaction $A + A \rightarrow\varnothing$ 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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Michal Hnatič, Juha Honkonen, Tomáš Lučivjanský. 2015-12-18. Two-loop calculation of anomalous kinetics of the reaction $A + A \rightarrow\varnothing$ in randomly stirred fluid. https://doi.org/10.1140/epjb%2Fe2013-30982-9

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