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Aggregation processes with catalysis-driven monomer birth/death
陈 玉, 韩安家, 柯见洪, 林振权
2006 (8):
1896-1902.
doi: 10.1088/1009-1963/15/8/045
摘要
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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.
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