Competition between the catalyzed birth and death in the exchange-driven growth

We propose a three-species ( A , B , and C ) exchange-driven aggregate growth model with competition between catalyzed birth and catalyzed death. In the system, exchange-driven aggregation occurs between any two aggregates of the same species with the size-dependent rate kernel Kn(k,j)=Knkj (n=1,2,3) , and, meanwhile, monomer birth and death of species A occur under the catalysis of species B and C with the catalyzed birth and catalyzed death rate kernels I(k,j)=Ikjv and J(k,j)=Jkjv , respectively. The kinetic behavior is investigated by means of the mean-field rate equation approach. The form of the aggregate size distribution ak(t) of species A is found to depend crucially on the competition between species- B -catalyzed birth of species A and species- C -catalyzed death of species A , as well as the exchange-driven growth. The results show that (i) when exchange-driven aggregation dominates the process, ak(t) satisfies the conventional scaling form; (ii) when catalyzed birth dominates the process, ak(t) takes the conventional or generalized scaling form; and (iii) when catalyzed death dominates the process, the aggregate size distribution of species A evolves only according to some modified scaling forms.