关键词: kinetic scaling behaviour, aggregation growth, catalyzed birth and death, rate equation

Abstract: An aggregation growth model of three species $A$, $B$ and $C$ with the competition between catalyzed birth and catalyzed death is proposed. Irreversible aggregation occurs between any two aggregates of the like species with the constant rate kernels $I_{n} (n=1,2,3)$. Meanwhile, a monomer birth of an $A$ species aggregate of size $k$ occurs under the catalysis of a $B$ species aggregate of size $j$ with the catalyzed birth rate kernel $K(k,j)=Kkj^{\upsilon}$, and a monomer death of an $A$ species aggregate of size $k$ occurs under the catalysis of a $C$ species aggregate of size $j$ with the catalyzed death rate kernel $L(k,j)=Lkj^{\upsilon}$, where $\upsilon$ is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate. The kinetic evolution behaviours of the three species are investigated by the rate equation approach based on the mean-field theory. The form of the aggregate size distribution of $A$ species $a_k(t)$ is found to be dependent crucially on the competition between the catalyzed birth and death of $A$ species, as well as the irreversible aggregation processes of the three species: (1) In the $\upsilon<0$ case, the irreversible aggregation dominates the process, and $a_k(t)$ satisfies the conventional scaling form; (2) In the $\upsilon\geq 0$ case, the competition between the catalyzed birth and death dominates the process. When the catalyzed birth controls the process, $a_k(t)$ takes the conventional or generalized scaling form. While the catalyzed death controls the process, the scaling description of the aggregate size distribution breaks down completely.

Key words: kinetic scaling behaviour, aggregation growth, catalyzed birth and death, rate equation