Abstract
A diffusion-limited-aggregation process, in which clusters coalesce by means of a three-particle reaction, A+A+A→A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic behavior for the concentration of clusters of mass m at time t, (t)∼[ln(t)/t, for 1≪m≪ √t/ln(t) . The total concentration of clusters, C(t), decays as C(t)∼ √ln(t)/t at t→∞. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration C(r) scales as [ln(r), , and [ln(r), respectively, for the spatial dimension d=1, 2, and 3. The total number of clusters, N(t), grows with time as [ln(t), , and t[ln(t) for d=1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady-state cluster-mass distribution, (r)∼[ln(r)Φ(z), with the scaling function Φ(z)=exp(-z) and the scaling variable z∼m/ √ln(r) .
- Received 16 December 1993
DOI:https://doi.org/10.1103/PhysRevE.49.3233
©1994 American Physical Society