中国物理B ›› 2003, Vol. 12 ›› Issue (4): 443-451.doi: 10.1088/1009-1963/12/4/318

• 8000 CROSSDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇    

Kinetic behaviour of two-species-group aggregation process with complete annihilation

柯见洪, 林振权, 王向红   

  1. Department of Physics and Electronic Information Science, Wenzhou Normal College, Wenzhou 325027, China
  • 收稿日期:2002-09-18 修回日期:2002-12-24 出版日期:2005-03-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10175008 and 10275048) and by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos 102067 and 101002).

Kinetic behaviour of two-species-group aggregation process with complete annihilation

Ke Jian-Hong (柯见洪), Lin Zhen-Quan (林振权), Wang Xiang-Hong (王向红)   

  1. Department of Physics and Electronic Information Science, Wenzhou Normal College, Wenzhou 325027, China
  • Received:2002-09-18 Revised:2002-12-24 Online:2005-03-16 Published:2005-03-16
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10175008 and 10275048) and by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos 102067 and 101002).

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摘要： We propose a two-species-group aggregation-annihilation model in which an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible joint annihilation reaction occurs between two distinct species groups. Based on the mean-field theory, we have investigated the rate equations of the process with constant reaction rates to obtain the asymptotic descriptions of the cluster-mass distributions. The results indicate that for the symmetrical initial cases the kinetic behaviour of the system depends crucially on the ratio of the equivalent aggregation rate to the annihilation rate. The cluster-mass distribution of each species always obeys a conventional or modified scaling law in each individual case. Moreover, all the species cannot finally survive except for the cases in which at least one equivalent aggregation rate is less than twice the annihilation rate.

Abstract: We propose a two-species-group aggregation-annihilation model in which an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible joint annihilation reaction occurs between two distinct species groups. Based on the mean-field theory, we have investigated the rate equations of the process with constant reaction rates to obtain the asymptotic descriptions of the cluster-mass distributions. The results indicate that for the symmetrical initial cases the kinetic behaviour of the system depends crucially on the ratio of the equivalent aggregation rate to the annihilation rate. The cluster-mass distribution of each species always obeys a conventional or modified scaling law in each individual case. Moreover, all the species cannot finally survive except for the cases in which at least one equivalent aggregation rate is less than twice the annihilation rate.

Key words: kinetic behaviour, aggregation-annihilation, scaling law

中图分类号:  (Rate constants, reaction cross sections, and activation energies)

  • 82.20.Pm
82.60.-s (Chemical thermodynamics) 82.70.-y (Disperse systems; complex fluids)