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

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 aggrega...

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Published inChinese physics B Vol. 22; no. 9; pp. 547 - 553
Main Author 高艳 王海锋 张吉东 杨霞 孙茂珠 张振权
Format Journal Article
LanguageEnglish
Published 01.09.2013
Subjects
Activated
Aggregates
Asymptotic properties
Catalysis
Coagulation
Evolution
Mathematical models
Replication
Size distribution
催化活化
凝血
演变
粒径分布
自我复制
行为
递减模型
速率方程
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Summary: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 a~（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.
Bibliography: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 a~（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.
aggregation, catalytically activated reaction, replication, decline
11-5639/O4
Gao Yan, Wang Hai-Feng, Zhang Ji-Dong, Yang Xia, Sun Mao-Zhu, and Lin Zhen-Quan（ 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
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/9/096802