Diffusion-limited-aggregation processes with three-particle elementary reactions

P. L. Krapivsky
Phys. Rev. E 49, 3233 – Published 1 April 1994
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Abstract

A diffusion-limited-aggregation process, in which clusters coalesce by means of a three-particle reaction, A+A+AA, 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, Cm(t)∼m1/2[ln(t)/t]3/4, 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 r1[ln(r)]1/2, r1, and r1[ln(r)]1/2, respectively, for the spatial dimension d=1, 2, and 3. The total number of clusters, N(t), grows with time as [ln(t)]3/2, t1/2, and t[ln(t)]1/2 for d=1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady-state cluster-mass distribution, Cm(r)∼r1[ln(r)]1Φ(z), with the scaling function Φ(z)=z1/2exp(-z) and the scaling variable zm/ √ln(r) .

  • Received 16 December 1993

DOI:https://doi.org/10.1103/PhysRevE.49.3233

©1994 American Physical Society

Authors & Affiliations

P. L. Krapivsky

  • Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215

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Vol. 49, Iss. 4 — April 1994

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