The Reaction-Diffusion Front for $A+B\to \varnothing$ in One Dimension

Abstract

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\to \varnothing$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal diffusion constants $D$, we find that when $\lambda J^{-1/2}{D}^{-1/2}\ll 1$ the reaction front is well described by mean field theory. However, for $\lambda J^{-1/2}{D}^{-1/2}\gg 1$, the front acquires a Gaussian profile - a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (non-wandering) front width and find results consistent with scaling and field theoretic predictions.

11 pages, revtex, 4 separate PostScript figures

References in corpus (4)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• 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

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