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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 |
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| Cite this article: |
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KE Jian-Hong, LIN Zhen-Quan, CHEN Xiao-Shuang 2006 Chin. Phys. Lett. 23 720-723 |
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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.
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82.20.-w
68.43.Jk
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Published: 01 March 2006
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| PACS: |
82.20.-w
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(Chemical kinetics and dynamics)
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68.43.Jk
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(Diffusion of adsorbates, kinetics of coarsening and aggregation)
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89.75.Da
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(Systems obeying scaling laws)
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