The Spatial Structure in Diffusion Limited Two-Particle Reactions

Maury Bramson and Joel L. Lebowitz
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Maury Bramson: University of Wisconsin, Department of Mathematics
Joel L. Lebowitz: Rutgers University, Departments of Mathematics and Physics

A chapter in Mathematical Physics X, 1992, pp 364-369 from Springer

Abstract: Abstract We analyze the limiting behavior of the densities ρ A (t) and ρ B (t) and the random spatial structure ξ(t) = (ξ A (t), (ξ B (t)) for the diffusion controlled chemical reaction A + B → inert with equal initial densities. There is a change in behavior from d ≤ 4, where ρ A (t) = ρ B (t) ≈ c d /t d/4 , to d ≥ 4, where ρ A (t) = ρ B (t) ≈ c d /t as t → ∞. There is a corresponding change in the spatial structure. In d 4, both particle types are, after large times, present locally in concentrations not depending on type or location. In d = 4, both particle types are present locally but with random concentrations, and the process tends to a limit.

Keywords: Spatial Structure; Initial Configuration; Gaussian Random Field; Opposite Type; Diffusion Control Chemical Reaction (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-77303-7_37

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DOI: 10.1007/978-3-642-77303-7_37

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