Renormalization Group Study of Two-Species Reaction-Diffusion System: Influence of Random Velocity Fluctuations

We investigate the influence of random velocity field on the kinetics of a two-species reaction-diffusion system \(A+A \rightarrow (\emptyset , A),\ A+B \rightarrow A\) near its upper critical dimension \(d_c = 2\) . The random velocity field is modeled by a stochastically forced Navier-Stokes equation and the analysis is performed with the aid of field-theoretic renormalization group formalism and two-parameter \((\epsilon , \Delta )\) expansion. Here \(\epsilon \) denotes deviation from Kolmogorov scaling and \(\Delta \) is the deviation from the upper critical dimension \(d=2\) . All permissible macroscopic regimes corresponding to stable fixed points of the renormalization group and their regions of stability are calculated to the first order of the perturbation scheme.