Self-similar behavior for multicomponent coagulation

doi:10.1007/s10483-014-1872-7

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (11): 1353-1360.doi: https://doi.org/10.1007/s10483-014-1872-7

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Self-similar behavior for multicomponent coagulation

杨曼丽^1,2, 卢志明¹, 刘宇陆¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University, Shanghai 200444, P. R. China;
2. Tianmu College, Zhejiang Agriculture and Forestry University, Zhuji 311800, Zhejiang Province, P. R. China

收稿日期:2013-05-30 修回日期:2014-02-15 出版日期:2014-11-01 发布日期:2014-11-01
通讯作者: Zhi-ming LU, Professor, Ph.D., E-mail: zmlu@shu.edu.cn E-mail:zmlu@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11272196 and 11222222) and the Zhejiang Association of Science and Technology of Soft Science Research Project (No. ZJKX14C-34)

Self-similar behavior for multicomponent coagulation

Man-li YANG^1,2, Zhi-ming LU¹, Yu-lu LIU¹

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University, Shanghai 200444, P. R. China;
2. Tianmu College, Zhejiang Agriculture and Forestry University, Zhuji 311800, Zhejiang Province, P. R. China

Received:2013-05-30 Revised:2014-02-15 Online:2014-11-01 Published:2014-11-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11272196 and 11222222) and the Zhejiang Association of Science and Technology of Soft Science Research Project (No. ZJKX14C-34)

摘要/Abstract

摘要： Self-similar behavior for the multicomponent coagulation system is investigated analytically in this paper. Asymptotic self-similar solutions for the constant kernel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel (gelling kernel) is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coagulation.

关键词: multicomponent coagulation, generating function, self-similar solution

Abstract: Self-similar behavior for the multicomponent coagulation system is investigated analytically in this paper. Asymptotic self-similar solutions for the constant kernel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel (gelling kernel) is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coagulation.

Key words: multicomponent coagulation, self-similar solution, generating function

中图分类号:

O175.2

杨曼丽;卢志明;刘宇陆. Self-similar behavior for multicomponent coagulation[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1353-1360.

Man-li YANG;Zhi-ming LU;Yu-lu LIU. Self-similar behavior for multicomponent coagulation[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1353-1360.

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Self-similar behavior for multicomponent coagulation

Self-similar behavior for multicomponent coagulation

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