Kinetic Anomalies in Addition-Aggregation Processes
摘要
We investigate irreversible aggregation in which monomer-monomer, monomer-cluster, and cluster-cluster reactions occur with constant but distinct rates K_{MM}, K_{MC}, and K_{CC}, respectively. The dynamics crucially depends on the ratio gamma=K_{CC}/K_{MC} and secondarily on epsilon=K_{MM}/K_{MC}. For epsilon=0 and gamma<2, there is conventional scaling in the long-time limit, with a single mass scale that grows linearly in time. For gamma >= 2, there is unusual behavior in which the concentration of clusters of mass k, c_k decays as a stretched exponential in time within a boundary layer k<k* propto t^{1-2/gamma} (k* propto ln t for gamma=2), while c_k propto t^{-2} in the bulk region k>k*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma >= 2.
引用
@article{arxiv.cond-mat/0301276,
title = {Kinetic Anomalies in Addition-Aggregation Processes},
author = {M. Mobilia and P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/0301276},
year = {2009}
}
备注
6 pages, 2 column revtex4 format, for submission to J. Phys. A