Particle-cluster aggregation on a small-world network.
To describe the aggregation behaviors on substrates with long-range jump paths, a model of particle-cluster aggregation on a two-dimensional small-world network is presented. This model is characterized by two parameters: the clustering exponent alpha and the long-range connection rate phi. The results show that there exists an asymptotic fractal dimension D(max)(f) that depends upon alpha. With decrement of alpha, D(max)(f) varies from 1.7 to 2.0, which corresponds to a crossover from diffusion-limited-aggregation-like to dense growth. The change of the aggregation pattern results from the long-range connection in the network, which reduces the effect of screening during the aggregation. When the system size is not large enough, the effective fractal dimension D(f) depends upon phi because of the finite-size effect. With primitive analysis, we obtain the expression of the effective fractal dimension D(f) with the network parameters alpha and phi.
Huang
Sheng-You
SY
Department of Physics, Wuhan University, Wuhan 430072, People's Republic of China.
Zou
Xian-Wu
XW
Shao
Zhi-Gang
ZG
Tan
Zhi-Jie
ZJ
Jin
Zhun-Zhi
ZZ