FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0

TL;DR

This paper analyzes the steady-state reaction front in a diffusion-controlled A+B->0 system, revealing universal fluctuation-induced power law tails in densities and reaction rates, with implications for multiscaling and front wandering.

Contribution

The study provides explicit asymptotic forms of the reaction front and densities using renormalisation group methods, including fluctuation effects and multiscaling behavior in various dimensions.

Findings

Universal power law tails in minority species densities for d<2

Asymptotic power law profiles for reaction rate R

Negligible fluctuation-induced front wandering in large systems

Abstract

We consider the properties of the diffusion controlled reaction A+B->0 in the steady state, where fixed currents of A and B particles are maintained at opposite edges of the system. Using renormalisation group methods, we explicitly calculate the asymptotic forms of the reaction front and particle densities as expansions in (JD^{-1}|x|^{d+1})^{-1}, where J are the (equal) applied currents, and D the (equal) diffusion constants. For the asymptotic densities of the minority species, we find, in addition to the expected exponential decay, fluctuation induced power law tails, which, for d<2, have a universal form A|x|^{-omega}, where omega=5+O(epsilon), and epsilon=2-d. A related expansion is derived for the reaction rate profile R, where we find the asymptotic power law R \sim B|x|^{-omega -2}. For d>2, we find similar power laws with omega=d+3, but with non-universal coefficients. Logarithmic corrections occur in d=2. These results imply that, in the time dependent case, with segregated initial conditions, the moments \int |x|^{q}R(x,t)dx fail to satisfy simple scaling for q>omega+1. Finally, it is shown that the fluctuation induced wandering of the position of the reaction front centre may be neglected for large enough systems.