Asymptotic Behavior of Densities in Diffusion-Dominated Annihilation Reactions
Nov 21, 1988Citations per year
Abstract: (APS)
We obtain rigorous bounds on the long-time behavior of the densities ρA(t) and ρB(t) of species A and B, which diffuse and annihilate upon meeting, i.e., A+B→inert. For equal initial densities ρA(0)=ρB(0), the density goes to zero asymptotically as t−d4 for dimensions d≤4 and as t−1 for d≥4. When ρA(0)<ρB(0), ρA(t)∼exp(−λ1t), ρA(t)∼exp(−λ2tInt) for d=1,2, respectively,andρA(t)∼exp(−λdt) for d≥3.- 82.20.-w
- 05.20.-y
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