Kang-Redner small-mass anomaly in cluster-cluster aggregation.
The large-time small-mass asymptotic behavior of the average mass distribution P(m,t) is studied in a d-dimensional system of diffusing aggregating particles for 1< or =d< or =2. By means of both a renormalization group computation as well as a direct resummation of leading terms in the small-reaction-rate expansion of the average mass distribution, it is shown that P(m,t) approximately (1/t(d))(m(1/d)/sqrt[t])(e(KR)) for m<<t(d/2), where e(KR)=epsilon+O(epsilon(2)) and epsilon=2-d. In two dimensions, it is shown that P(m,t) approximately ln(m)ln(t)/t(2) for m<<t/ln(t). Numerical simulations in two dimensions supporting the analytical results are also presented.
Krishnamurthy
Supriya
S
Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA. supriya@santafe.edu
Rajesh
R
R
Zaboronski
Oleg
O