Pregelation Behaviour of Coagulation Processes with the Constant-Reaction-Number Kernel
KE Jian-Hong1,2, LIN Zhen-Quan1, CHEN Xiao-Shuang2
1School of Physics and Electronic Information, Wenzhou University, Wenzhou 325027
2National Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083
Pregelation Behaviour of Coagulation Processes with the Constant-Reaction-Number Kernel
KE Jian-Hong1,2;LIN Zhen-Quan1;CHEN Xiao-Shuang2
1School of Physics and Electronic Information, Wenzhou University, Wenzhou 325027
2National Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083
Abstract： We propose an irreversible binary coagulation model with a constant-reaction-number kernel, in which, among all the possible binary coagulation reactions, only p reactions are permitted to take place at every time. By means of the generalized rate equation we investigate the kinetic behaviour of the system with the reaction rate kernel K(i;j)=(ij)ω (0≤ ω <1/2), at which an i-mer and a j-mer coagulate together to form a large one. It is found that for such a system there always exists a gelation transition at a finite time tc, which is in contrast to the ordinary binary coagulation with the same rate kernel. Moreover, the pre-gelation behaviour of the cluster size distribution near the gelation point falls in a scaling regime and the typical cluster size grows as (tc-t)-1/(1-2ω). On the other hand, our model can also provide some predictions for the evolution of the cluster distribution in multicomponent complex networks.
KE Jian-Hong;LIN Zhen-Quan;CHEN Xiao-Shuang. Pregelation Behaviour of Coagulation Processes with the Constant-Reaction-Number Kernel[J]. 中国物理快报, 2006, 23(3): 720-723.
KE Jian-Hong, LIN Zhen-Quan, CHEN Xiao-Shuang. Pregelation Behaviour of Coagulation Processes with the Constant-Reaction-Number Kernel. Chin. Phys. Lett., 2006, 23(3): 720-723.
2006, Vol. 23 
