中国物理B ›› 2013, Vol. 22 ›› Issue (9): 96802-096802.doi: 10.1088/1674-1056/22/9/096802

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

Evolution behavior of catalytically activated replication–decline in a coagulation process

高艳a, 王海锋a, 张吉东a, 杨霞a, 孙茂珠a, 林振权b   

  1. a Key Laboratory of Ecophysics and Department of Physics, School of Science, Shihezi University, Shihezi 832003, China;
    b Department of Physics, Wenzhou University, Wenzhou 325027, China
  • 收稿日期:2012-12-30 修回日期:2013-03-01 出版日期:2013-07-26 发布日期:2013-07-26
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 11145004).

Evolution behavior of catalytically activated replication–decline in a coagulation process

Gao Yan (高艳)a, Wang Hai-Feng (王海锋)a, Zhang Ji-Dong (张吉东)a, Yang Xia (杨霞)a, Sun Mao-Zhu (孙茂珠)a, Lin Zhen-Quan (林振权)b   

  1. a Key Laboratory of Ecophysics and Department of Physics, School of Science, Shihezi University, Shihezi 832003, China;
    b Department of Physics, Wenzhou University, Wenzhou 325027, China
  • Received:2012-12-30 Revised:2013-03-01 Online:2013-07-26 Published:2013-07-26
  • Contact: Wang Hai-Feng E-mail:whfeng@shzu.edu.cn; hfwang11@126.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 11145004).

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摘要： We propose a catalytically activated replication-decline model of three species, in which two aggregates of the same species can coagulate themselves, an A aggregate of any size can replicate itself with the help of B aggregates, and the decline of A aggregate occurs under the catalysis of C aggregates. By means of mean-field rate equations, we derive the asymptotic solutions of the aggregate size distribution ak(t) of species A, which is found to depend strongly on the competition among three mechanisms: the self-coagulation of species A, the replication of species A catalyzed by species B, and the decline of species A catalyzed by species C. When the self-coagulation of species A dominates the system, the aggregate size distribution ak(t) satisfies the conventional scaling form. When the catalyzed replication process dominates the system, ak(t) takes the generalized scaling form. When the catalyzed decline process dominates the system, ak(t) approaches the modified scaling form.

关键词: aggregation, catalytically activated reaction, replication, decline

Abstract: We propose a catalytically activated replication-decline model of three species, in which two aggregates of the same species can coagulate themselves, an A aggregate of any size can replicate itself with the help of B aggregates, and the decline of A aggregate occurs under the catalysis of C aggregates. By means of mean-field rate equations, we derive the asymptotic solutions of the aggregate size distribution ak(t) of species A, which is found to depend strongly on the competition among three mechanisms: the self-coagulation of species A, the replication of species A catalyzed by species B, and the decline of species A catalyzed by species C. When the self-coagulation of species A dominates the system, the aggregate size distribution ak(t) satisfies the conventional scaling form. When the catalyzed replication process dominates the system, ak(t) takes the generalized scaling form. When the catalyzed decline process dominates the system, ak(t) approaches the modified scaling form.

Key words: aggregation, catalytically activated reaction, replication, decline

中图分类号:  (Diffusion of adsorbates, kinetics of coarsening and aggregation)

  • 68.43.Jk
05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 82.20.-w (Chemical kinetics and dynamics) 89.75.Da (Systems obeying scaling laws)