Kang-Redner Anomaly in Cluster-Cluster Aggregation

Details Kang-Redner Anomaly in Cluster-Cluster Aggregation Kang-Redner Anomaly in Cluster-Cluster Aggregation

2002-09-06

arxiv.org/abs/cond-mat/0209174v1

Phys. Rev. E, Vol 66, 066118 (2002)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 6 figures, Revtex 4

Scientific paper

10.1103/PhysRevE.66.066118

The large time, small mass, asymptotic behavior of the average mass distribution $\pb$ is studied in a $d$-dimensional system of diffusing aggregating particles for $1\leq d \leq 2$. By means of both a renormalization group computation as well as a direct re-summation of leading terms in the small reaction-rate expansion of the average mass distribution, it is shown that $\pb \sim \frac{1}{t^d} (\frac{m^{1/d}}{\sqrt{t}})^{e_{KR}}$ for $m \ll t^{d/2}$, where $e_{KR}=\epsilon +O(\epsilon ^2)$ and $\epsilon =2-d$. In two dimensions, it is shown that $\pb \sim \frac{\ln(m) \ln(t)}{t^2}$ for $ m \ll t/ \ln(t)$. Numerical simulations in two dimensions supporting the analytical results are also presented.

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