Abstract We propose two solvable cluster growth models, in which an irreversible aggregation spontaneously occurs between any two clusters of the same species; meanwhile, monomer birth or death of species A occurs with the help of species B. The system with the size-dependent monomer birth/death rate kernel $K(i,j) = Jij^v$ is then investigated by means of the mean-field rate equation. The results show that the kinetic scaling behaviour of species A depends crucially on the value of the index $v$. For the model with catalysis-driven monomer birth, the cluster-mass distribution of species $A$ obeys the conventional scaling law in the $v \leq 0$ case, while it satisfies a generalized scaling form in the $v > 0$ case; moreover, the total mass of species A is a nonzero value in the $v < 0$ case while it grows continuously with time in the $v \geq 0$ case. For the model with catalysis-driven monomer death, the cluster-mass distribution also approaches the conventional scaling form in the $v < 0$ case, while the conventional scaling description of the system breaks down in the $v \geq 0$ case. Additionally, the total mass of species A retains a nonzero quantity in the $v < 0$ case, but it decreases to zero with time in the $v \geq 0$ case.
Received: 16 December 2005
Revised: 24 February 2006
Accepted manuscript online:
(Specific chemical reactions; reaction mechanisms)
Fund: Project supported by the National Natural Science
Foundation of China (Grant Nos 10305009 and 10275048) and the
Zhejiang Provincial Natural Science Foundation, China (Grant No
102067).
Cite this article:
Chen Yu(陈玉), Han An-Jia(韩安家), Ke Jian-Hong(柯见洪), and Lin Zhen-Quan(林振权） Aggregation processes with catalysis-driven monomer birth/death 2006 Chinese Physics 15 1896
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