Dynamic Multiscaling of the Reaction-Diffusion Front for mA+nB ->0

Abstract

We consider the reaction zone that grows between separated regions of diffusing species $A$ and $B$ that react according to $mA+nB\to 0$, within the framework of the mean-fieldlike reaction-diffusion equations. For distances from the centre of the reaction zone much smaller than the diffusion length $X_D\equiv \sqrt{Dt}$, the particle density profiles are described by the scaling forms predicted by a quasistatic approximation, whereas they have a diffusive cutoff at a distance of order $X_D$. This cutoff, and the power-law decay of the quasistatic profiles, give rise to multiscaling behaviour, with anomalous values for the exponents describing the moments of the density and reaction profiles. Numerical solutions of the reaction-diffusion equations are in good quantitative agreement with the predictions of this theory.

11 pages, Revtex 3.0, 7 figures (uuencoded Postscript)

References in corpus (3)

• Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
• FLUCTUATION EFFECTS AND MULTISCALING OF THE REACTION-DIFFUSION FRONT FOR A+B->0
• Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension

Cited by in corpus (4)

• The long time behavior of initially separated A+B->0 reaction-diffusion systems with arbitrary diffusion constants
• Asymptotics of Reaction-Diffusion Fronts with One Static and One Diffusing Reactant
• Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall
• Asymptotic expansion for reversible A + B <-> C reaction-diffusion process