Abstract
The spatial structure of reactants in the two-species annihilation reaction A+B→0 is described. In one dimension, we investigate the distribution of domain sizes and the distributions of nearest-neighbor distances between particles of the same and of opposite species. The latter two quantities are characterized by a new length scale which is intermediate to the domain size t1/2 and the typical interparticle spacing t1/4. A scaling argument suggests that the typical distance between particles of opposite species, or equivalently the gaps between domains, grows ast ζ, with ζ = 3/8 and 1/3, respectively, in spatial dimensiond=1 and 2. The average density profile of a single domain is spatially nonuniform, with the density decaying to zero linearly as the domain edge is approached. This behavior permits a determination of the distribution of nearest-neighbor distances of same-species reactants. The corresponding moments of this distribution exhibit multiscaling which involves geometric averages of different powers of the domain size and the interparticle spacing.
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Redner, S., Leyvraz, F. Spatial organization in two-species annihilation. J Stat Phys 65, 1043–1056 (1991). https://doi.org/10.1007/BF01049597
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DOI: https://doi.org/10.1007/BF01049597