中国物理B ›› 2006, Vol. 15 ›› Issue (8): 1896-1902.doi: 10.1088/1009-1963/15/8/045
陈 玉, 韩安家, 柯见洪, 林振权
Chen Yu(陈玉), Han An-Jia(韩安家), Ke Jian-Hong(柯见洪)†, and Lin Zhen-Quan(林振权)
摘要: 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 \le 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 \ge 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 \ge 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 \ge 0 case.
中图分类号: (Disperse systems; complex fluids)