Please wait a minute...
Chinese Physics, 2004, Vol. 13(5): 772-777    DOI: 10.1088/1009-1963/13/5/034
CROSS DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY Prev   Next  

Dynamic scaling of migration-driven aggregate growth

Ke Jian-Hong (柯见洪), Wang Xiang-Hong (王向红), Lin Zhen-Quan (林振权), Zhuang You-Yi (庄友谊)
School of Physics and Electronic Information, Wenzhou Normal College, Wenzhou 325027, China
Abstract  We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate $K(i;j)=K^′(i;j)\varpropto i^uj^v$ at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with $u+v\leq3$ and $u<2$ approaches a conventional scaling form, which reduces to the Smoluchovski form in the $u=1$ case. On the other hand, for the system with $u<2$, the average aggregate size $S(t)$ grows exponentially in the $u+v=3$ case and as $(t\ln t)^{1/(5-2u)}$ in another special case of $v=u-2$. Moreover, this typical size $S(t)$ grows as $t^{1/(3-u-v)}$ in the general $u-2<v<3-u$ case; while it always grows as $t^{1/(5-2v)}$ in the $v<u-2$ case.
Keywords:  kinetic behaviour      migration      aggregate growth      scaling law  
Received:  11 July 2003      Revised:  30 October 2003      Accepted manuscript online: 
PACS:  05.60.-k (Transport processes)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos 10305009, 10275048 and 10175008) and by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos 102067 and 101002).

Cite this article: 

Ke Jian-Hong (柯见洪), Wang Xiang-Hong (王向红), Lin Zhen-Quan (林振权), Zhuang You-Yi (庄友谊) Dynamic scaling of migration-driven aggregate growth 2004 Chinese Physics 13 772

[1] Ion migration in metal halide perovskite QLEDs and its inhibition
Yuhui Dong(董宇辉), Danni Yan(严丹妮), Shuai Yang(杨帅), Naiwei Wei(魏乃炜),Yousheng Zou(邹友生), and Haibo Zeng(曾海波). Chin. Phys. B, 2023, 32(1): 018507.
[2] Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence
Mu-Hong Hu(胡木宏), Nan Wang(王楠), Pin-Jun Ouyang(欧阳品均),Xin-Jie Feng(冯新杰), Yang Yang(杨扬), and Chen-Sheng Wu(武晨晟). Chin. Phys. B, 2022, 31(9): 093101.
[3] Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow
Pei-Feng Lin(林培锋), Xiao Hu(胡箫), and Jian-Zhong Lin(林建忠). Chin. Phys. B, 2022, 31(8): 080501.
[4] Coherence migration in high-dimensional bipartite systems
Zhi-Yong Ding(丁智勇), Pan-Feng Zhou(周攀峰), Xiao-Gang Fan(范小刚),Cheng-Cheng Liu(刘程程), Juan He(何娟), and Liu Ye(叶柳). Chin. Phys. B, 2022, 31(6): 060308.
[5] Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy
Zeyu Zhang(张泽宇), Qiang Zhang(张强), and Wenbo Mi(米文博). Chin. Phys. B, 2022, 31(4): 047305.
[6] Nonlinear dynamics of cell migration in anisotropic microenvironment
Yanping Liu(刘艳平), Da He(何达), Yang Jiao(焦阳), Guoqiang Li(李国强), Yu Zheng(郑钰), Qihui Fan(樊琪慧), Gao Wang(王高), Jingru Yao(姚静如), Guo Chen(陈果), Silong Lou(娄四龙), and Liyu Liu(刘雳宇). Chin. Phys. B, 2021, 30(9): 090505.
[7] Migration and shape of cells on different interfaces
Xiaochen Wang(王晓晨), Qihui Fan (樊琪慧), and Fangfu Ye(叶方富). Chin. Phys. B, 2021, 30(9): 090502.
[8] Effect of strain on electrochemical performance of Janus MoSSe monolayer anode material for Li-ion batteries: First-principles study
Guoqing Wang(王国庆), Wenjing Qin(秦文静), and Jing Shi(石晶). Chin. Phys. B, 2021, 30(4): 046301.
[9] Prediction of epidemics dynamics on networks with partial differential equations: A case study for COVID-19 in China
Ru-Qi Li(李汝琦), Yu-Rong Song(宋玉蓉), and Guo-Ping Jiang(蒋国平). Chin. Phys. B, 2021, 30(12): 120202.
[10] Taking snapshots of a moving electron wave packet in molecules using photoelectron holography in strong-field tunneling ionization
Mingrui He(何明睿), Yang Fan(樊洋), Yueming Zhou(周月明), and Peixiang Lu(陆培祥). Chin. Phys. B, 2021, 30(12): 123202.
[11] Suppression of ion migration in perovskite materials by pulse-voltage method
Xue-Yan Wang(王雪岩), Hu Wang(王虎), Luo-Ran Chen(陈烙然), Yu-Chuan Shao(邵宇川), and Jian-Da Shao(邵建达). Chin. Phys. B, 2021, 30(11): 118104.
[12] Influence of matrix-metalloproteinase inhibitor on the interaction between cancer cells and matrigel
Teng Ye(叶腾), Fangfu Ye(叶方富), Feng Qiu(邱峰). Chin. Phys. B, 2020, 29(6): 068701.
[13] Shock-induced migration of asymmetry tilt grain boundary in iron bicrystal: A case study of Σ3 [110]
Xueyang Zhang(张学阳), Kun Wang(王昆), Jun Chen(陈军), Wangyu Hu(胡望宇), Wenjun Zhu(祝文军), Shifang Xiao(肖时芳), Huiqiu Deng(邓辉球), Mengqiu Cai(蔡孟秋). Chin. Phys. B, 2019, 28(12): 126201.
[14] Influence of matrigel on the shape and dynamics of cancer cells
Teng Ye(叶腾), Feng Qiu(邱峰). Chin. Phys. B, 2019, 28(10): 108704.
[15] Effect of elasticity mismatch on cell deformation and migration: A phase-field study
Yuanfeng Yin(尹元枫), Hui Xing(邢辉), Duyang Zang(臧渡洋), Kexin Jin(金克新). Chin. Phys. B, 2018, 27(11): 116201.
No Suggested Reading articles found!