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.
Categories: cond-mat.stat-mech