SPATIAL FLUCTUATIONS IN REACTION-DIFFUSION SYSTEMS - A MODEL FOR EXPONENTIAL-GROWTH

The spatial fluctuations in an exactly soluble model for the irreversible aggregation of clusters are treated. The model is characterized by rate constants Kij=i+j for the clustering of an i- and a j-mer, and diffusion constants Dj=D. It is assumed that D≫1 (reaction-limited aggregation). Explicit expressions for the correlation functions at equal and at different times are calculated. The equal-time correlation functions show scaling behavior in the scaling limit. The correlation length remains finite as t→∞, and the fluctuations become large at large times (t≥tD) in any dimension. The crossover time tD, at which the mean field theory (Smoluchowski's equation) breaks down, is given by tD≃In D. These exact results imply that the upper critical dimension of this model is dc=∞ and, hence, that there is no unique upper critical dimension in models for the irreversible aggregation of clusters. © 1990 Plenum Publishing Corporation.