Abstract
The “method of compounding moments” devised by Van Kampen is used to study the spatial fluctuations in a model describing the irreversible formation of clusters. The reaction and diffusion constants in this model are chosenindependent of the cluster sizes. For a monodisperse initial distribution explicit expressions are calculated for the equal-time and two-time correlation functions of the concentrations ofm- andn-mers. For general initial conditions the fluctuations in the mass density are considered and a scaling theory is presented for the fluctuations at large times. Extensions to more general models are discussed.
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van Dongen, P.G.J. Fluctuations in reaction-diffusion systems: A new exactly soluble growth model. J Stat Phys 53, 221–232 (1988). https://doi.org/10.1007/BF01011554
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DOI: https://doi.org/10.1007/BF01011554