Eur. Phys. J. B (2013) 86: 214
https://doi.org/10.1140/epjb/e2013-30982-9

Regular Article

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

¹ Institute of Experimental Physics, SAS, 040 01 Košice, Slovakia
² Faculty of Sciences, P.J. Šafarik University, 041 54 Košice, Slovakia
³ Department of Military Technology, National Defence University, FI-00861 Helsinki, Finland

^a e-mail: juha.honkonen@helsinki.fi

Received: 26 October 2012
Received in final form: 1 March 2013
Published online: 16 May 2013

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.