Diffusion-Limited Aggregation Processes with 3-Particle Elementary Reactions

Abstract

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-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 $t$, $c(m,t)m^{-1/2}(log(t)/t{)}^{3/4}$, for $1<<m<<\sqrt{t/log(t)}$. The total concentration of clusters, $c(t)$, decays as $c(t)\sqrt{log(t)/t}$ at $t-->\infty$. We also investigate the problem with a localized steady source of monomers and find that the steady-state concentration $c(r)$ scales as $r^{-1}(log(r){)}^{1/2}$, $r^{-1}$, and $r^{-1}(log(r){)}^{-1/2}$, respectively, for the spatial dimension $d$ equal to 1, 2, and 3. The total number of clusters, $N(t)$, grows with time as $(log(t){)}^{3/2}$, $t^{1/2}$, and $t(log(t){)}^{-1/2}$ for $d$ = 1, 2, and 3. Furthermore, in three dimensions we obtain an asymptotic solution for the steady state cluster-mass distribution: $c(m,r)\sim r^{-1}(log(r){)}^{-1}\Phi (z)$, with the scaling function $\Phi (z)=z^{-1/2}\exp (-z)$ and the scaling variable $zm/\sqrt{log(r)}$.

12 pages, plain TeX

References in corpus (1)

• Fast-diffusion mean-field theory for k-body reactions in one dimension

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