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Kinetic Anomalies in Addition-Aggregation Processes

M. Mobilia·P. L. Krapivsky·S. Redner
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Abstract

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*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma >= 2.

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M. Mobilia, P. L. Krapivsky, S. Redner. 2003-01-15. Kinetic Anomalies in Addition-Aggregation Processes. https://doi.org/10.1088/0305-4470%2F36%2F16%2F304

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