Spatial structure in diffusion-limited two-particle reactions |
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Authors: | Maury Bramson Joel L Lebowitz |
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Institution: | (1) Department of Mathematics, University of Wisconsin, 53706 Madison, Wisconsin;(2) Departments of Mathematics and Physics, Rutgers University, 08903 New Brunswick, New Jersey |
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Abstract: | We analyze the limiting behavior of the densities
A(t) and
B(t), and the random spatial structure (r) = (
A(t).,
B(t)), for the diffusion-controlled chemical reaction A+B inert. For equal initial densities
B(0) = b(0) there is a change in behavior fromd 4, where A(t) =
B(t) C/td/4, tod 4, where A(t) =
b(t) C/t ast ; the termC depends on the initial densities and changes withd. There is a corresponding change in the spatial structure. Ind < 4, the particle types separate with only one type present locally, and , after suitable rescaling, tends to a random Gaussian process. Ind >4, both particle types are, after large times, present locally in concentrations not depending on type or location. Ind=4, both particle types are present locally, but with random concentrations, and the process tends to a limit. |
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Keywords: | Diffusion-limited reaction annihilating random walks asymptotic densities spatial structure exact results |
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