Scaling in Aggregation with Breakup Simulations and Mean-Field Theory

An extended scaling description of the cluster size distribution Nₛ(t,k) in time-dependent coagulation-fragmentation processes (k is a small breakup rate constant) is presented as Nₛ(t,k)~s^-2h(skʸ,tkˣ)) and its validity is confirmed by computer simulations. This scaling form includes the scaling description of irreversible and steady-state processes as limiting cases for both short and long times compared to a crossover time τ(k)~k^-x. A mean-field theory is analyzed and its limits of validity are explored.