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 K_n(k,j)=K_nkj (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)=Ikj^v and J(k,j)=Jkj^v, respectively. The kinetic behavior is investigated by means of the mean-field rate equation approach. The form of the aggregate size distribution a_k(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, a_k(t) satisfies the conventional scaling form; (ii) when catalyzed birth dominates the process, a_k(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.