Asymptotic behavior of densities in diffusion dominated two-particle reactions

Maury Bramson; Joel L. Lebowitz

doi:10.1016/0378-4371(90)90360-5

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

Original language	English (US)
Pages (from-to)	88-94
Number of pages	7
Journal	Physica A: Statistical Mechanics and its Applications
Volume	168
Issue number	1
DOIs	https://doi.org/10.1016/0378-4371(90)90360-5
State	Published - Sep 1 1990
Externally published	Yes

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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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.",

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N2 - 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.

AB - 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.

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Asymptotic behavior of densities in diffusion dominated two-particle reactions

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