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

doi:10.1088/1674-1056/22/9/096802

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 a_k(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 a_k(t) satisfies the conventional scaling form. When the catalyzed replication process dominates the system, a_k(t) takes the generalized scaling form. When the catalyzed decline process dominates the system, a_k(t) approaches the modified scaling form.

Keywords: aggregation catalytically activated reaction replication decline

Received: 30 December 2012
Revised: 01 March 2013
Accepted manuscript online:

PACS:	68.43.Jk	(Diffusion of adsorbates, kinetics of coarsening and aggregation)
	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)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10875086 and 11145004).

Corresponding Authors: Wang Hai-Feng
E-mail: whfeng@shzu.edu.cn; hfwang11@126.com

Cite this article:

Gao Yan (高艳), Wang Hai-Feng (王海锋), Zhang Ji-Dong (张吉东), Yang Xia (杨霞), Sun Mao-Zhu (孙茂珠), Lin Zhen-Quan (林振权) Evolution behavior of catalytically activated replication–decline in a coagulation process 2013 Chin. Phys. B 22 096802

[1]	Stockmayer W H 1943 J. Chem. Phys. 11 45
[2]	Flory P J 1953 Principles of Polymer Chemistry (Ithaca: Cornell University Press)
[3]	Leyvraz F 2003 Phys. Rep. 383 95
[4]	Ben-Naim E and Krapivsky P L 2005 J. Phys.: Condens. Matter 17 S4249
[5]	Ben-Naim E and Krapivsky P L 2007 Phys. Rev. E 75 011103
[6]	Ben-Naim E and Krapivsky P L 2008 Phys. Rev. E 77 061132
[7]	Yu J and Hu G 1989 Phys. Rev. B 39 4659
[8]	Yu J, Hu G and Ma B K 1990 Phys. Rev. B 41 9424
[9]	Yang S Y, Zhu S Q and Ke J H 2009 Phys. Rev. E 80 031114
[10]	Smoluchowski M V 1916 Phys. Z 17 557
[11]	Leyvraz F and Redner S 2002 Phys. Rev. Lett. 88 068301
[12]	Ke J H, Lin Z Q, Zheng Y Z, Chen X S and Lu W 2006 Phys. Rev. Lett. 97 028301
[13]	Bond G C 1987 Heterogeneous Catalysis: Principles and Applications (Oxford: Clarendon)
[14]	Oshanin G and Burlatsky S F 2002 J. Phys. A: Math. Theory 35 L695
[14]	Benichou O, Coppey M, Moreau M and Oshanin G 2005 J. Chem. Phys. 123 194506
[16]	Wu Y G, Lin Z Q and Ke J H 2012 Chin. Phys. B 21 068201
[17]	Lin Z Q, Ke J H and Ye G X 2006 Phys. Rev. E 74 046113
[18]	Wang H F, Lin Z Q and Ke J H 2007 Phys. Rev. E 75 046108
[19]	Lipps H J 1980 Proc. Natl. Acad. Sci. USA 77 4104
[20]	Cairns J 1962 Nature 194 1274
[21]	Yang S Y, Zhu S Q Ke J H and Lin Z Q 2008 Commun. Theor. Phys. 50 787
[22]	Hao X J, Wang S and Huang J F 2012 Journal of Shihezi University (Natural Science) 5 582
[23]	Family F, Meakin P and Deutch J M 1986 Phys. Rev. Lett. 57 727
[24]	Ke J H and Lin Z Q 2002 Phys. Rev. E 66 062101
[25]	Ke J H, Zheng Y Z, Lin Z Q and Chen X S 2007 Phys. Lett. A 368 188
[26]	Ziff R M, Ernst M H and Hendriks E M 1983 J. Phys. A: Math. Gen. 16 2293
[27]	Ben-Naim E and Krapivsky P L 2003 Phys. Rev. E 68 031104
[28]	Wang H F, Lin Z Q and Gao Y 2008 Chin. Phys. B 17 1490

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

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