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

Abstract

The single-species annihilation reaction $A+A\to \varnothing$ 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 $(\epsilon ,\Delta )$ 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.

arXiv admin note: substantial text overlap with arXiv:1212.1025

References in corpus (2)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions

Cited by in corpus (3)

• Master equations and the theory of stochastic path integrals
• Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time
• Numerical Solution of a Nonlinear Integro-Differential Equation