Physics and Astronomy, Mathematics, Chemistry, Ames Laboratory
Journal or Book Title
Physical Review A
We consider processes where the sites of an infinite, uniform, one-dimensional lattice are filled irreversibly and cooperatively, with the rates ki, depending on the number i=0,1,2 of filled nearest neighbors. Furthermore, we suppose that filling of sites with both neighbors already filled is forbidden,so k2=0. Thus, clusters can nucleate and grow, but cannot coalesce. Exact truncation solutions of the corresponding infinite hierarchy of rate equations for subconfiguration probabilities are possible. For the probabilities of filled s-tuples fs as a function of coverage, θ≡f1, we find that fs/fs+1=D(θ)s+C(θ,s), where C(θ,s)/s→0 as s→∞. This corresponds to faster than exponential decay. Also, if ρ≡k1/k0, then one has D(θ)∼(2ρθ)−1 as θ→0. The filled-cluster-size distribution ns has the same characteristics. Motivated by the behavior of these families of fs/fs+1-vs-s curves, we develop the natural extension of fs to s≤0. Explicit values for fs and related quantities for ‘‘almost random’’ filling, k0=k1, are obtained from a direct statistical analysis.
American Physical Society
Evans, James W. and Nord, R. S., "Cluster-size distributions for irreversible cooperative filling of lattices. II. Exact one-dimensional results for noncoalescing clusters" (1985). Physics and Astronomy Publications. 442.