Asymptotic behavior of densities in diffusion dominated two-particle reactions

Maury Bramson, Joel L. Lebowitz

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Abstract

We analyze the limiting behavior of the densities ρA(t) and ρB(t) for the diffusion controlled chemical reaction A + B → inert. We prove that for equal initial densities ρA(0)=ρB(0) there is a change in behavior from d ≤4, where ρA(t)=ρB(t)∼ C t d 4, to d≥4, where ρA(t)=ρB(t)∼ C t as t→∞. For unequal initial densities ρA(t)(0)<ρB(0), ρA(t)∼e -C t in d=1, ρA(t)∼e-Ct/log t in d=2, ρA(t)∼e-Ct in d≥3. The term C depends on the initial densities and changes with d.

Original languageEnglish (US)
Pages (from-to)88-94
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume168
Issue number1
DOIs
StatePublished - Sep 1 1990
Externally publishedYes

Bibliographical note

Funding Information:
Supported in part by NSF Grant DMS 89-01545. 2 Supported in part by NSF Grant DMR 89-18903.

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