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

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

1996-01-22

arxiv.org/abs/cond-mat/9601096v1

Physics

Condensed Matter

11 pages, revtex, 4 separate PostScript figures

Scientific paper

10.1103/PhysRevE.53.R2017

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, 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.

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