Directional region control of the thermalfractal diffusion of a space body

doi:10.1088/1674-1056/24/5/050504

中国物理B ›› 2015, Vol. 24 ›› Issue (5): 50504-050504.doi: 10.1088/1674-1056/24/5/050504

Directional region control of the thermalfractal diffusion of a space body

乔威^{a b}, 孙洁^b, 刘树堂^a

a School of Control Science and Engineering, Shandong University, Jinan 250061, China;
b School of Mechanical and Electrical Engineering, Shandong University at Weihai, Weihai 264209, China

收稿日期:2014-10-24 修回日期:2014-12-10 出版日期:2015-05-05 发布日期:2015-05-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61273088, 61473173, and 61473174).

Directional region control of the thermalfractal diffusion of a space body

Qiao Wei (乔威)^{a b}, Sun Jie (孙洁)^b, Liu Shu-Tang (刘树堂)^a

a School of Control Science and Engineering, Shandong University, Jinan 250061, China;
b School of Mechanical and Electrical Engineering, Shandong University at Weihai, Weihai 264209, China

Received:2014-10-24 Revised:2014-12-10 Online:2015-05-05 Published:2015-05-05
Contact: Sun Jie E-mail:sunj@sdu.edu.cn
About author:05.45.Df; 61.43.Hv
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61273088, 61473173, and 61473174).

摘要/Abstract

摘要： We present a directional region control (DRC) model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.

关键词: thermal diffusion, fractal growth, directional region control

Abstract: We present a directional region control (DRC) model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.

Key words: thermal diffusion, fractal growth, directional region control

中图分类号: (Fractals)

05.45.Df

61.43.Hv (Fractals; macroscopic aggregates (including diffusion-limited Aggregates))

乔威, 孙洁, 刘树堂. Directional region control of the thermalfractal diffusion of a space body[J]. 中国物理B, 2015, 24(5): 50504-050504.

Qiao Wei (乔威), Sun Jie (孙洁), Liu Shu-Tang (刘树堂). Directional region control of the thermalfractal diffusion of a space body[J]. Chin. Phys. B, 2015, 24(5): 50504-050504.

参考文献 27

[1]	Wang L and Zheng D Z 2000 Control Theory and Applications 17 139 (in Chinese)
[2]	Sun J, Liu S T and Qiao W 2011 Acta Phys. Sin. 60 70510 (in Chinese)
[3]	Wang X Y and Jin T 2013 Nonlinear Dynamics 73 843
[4]	Wang X Y and Yu X J 2007 Applied Mathematics and Computation 189 1186
[5]	Wang X Y, Jia R H and Zhang Z F 2009 Applied Mathematics and Computation 210 107
[6]	Wang X Y and Wang Y X 2011 Chin. Phys. B 20 104202
[7]	Yu S M and Chen G 2012 Communications in Nonlinear Science and Numerical Simulation 17 2617
[8]	Yu S M and Yu Z D 2008 Acta Phys. Sin. 57 6859 (in Chinese)
[9]	Yu S M, Lin Q H and Qiu S S 2004 Acta Phys. Sin. 53 2084 (in Chinese)
[10]	Witten T A and Sander L M 1981 Phys. Rev. Lett. 47 1400
[11]	Witten T A and Sander L M 1983 Phys. Rev. B 27 5686
[12]	Suemi R R and Antonio S H 2013 Physica A: Statistical Mechanics and its Applications 392 3316
[13]	Suemi R R and Roberto M 2014 Chaos Soliton. Fract. 66 31
[14]	Kolesnikov N N and Borisenko E B 2008 Journal of Crystal Growth 310 3287
[15]	Argoul F and Arneodo A 1988 Phys. Rev. Lett. 61 2558
[16]	Shiny and Kamz S H 2010 Computer Graphics Forum 29 675
[17]	Shen S L 2008 Analysis and Control of Diffusion Limited Aggregation Growth (Ji Nan: Shandong University) (in Chinese)
[18]	Zhang L 2011 Control and Application of Fractal Growth (Ji Nan: Shandong University) (in Chinese)
[19]	Katyal N, Banerjee V and Puri S 2014 Journal of Quantitative Spectroscopy and Radiative Transfer 146 290
[20]	He Q J and Huang Z L 2007 Journal of Crystal Growth 300 460 (in Chinese)
[21]	Dias E O 2013 Phys. Rev. E 88 063007
[22]	Evans P, Pemble M E and Sheel D W 2006 Chemistry of Materials 18 5750
[23]	Qiao W, Liu S T and Sun J 2014 Control Theory & Applications 31 361 (in Chinese)
[24]	Qi M Y and Wu F T 1999 Generalized Functions and Equations of Mathematical Physics (Beijing: Higher Education Press) (in Chinese)
[25]	Lv H X and Wang T M 2011 Applied Functional Analysis (Da Lian: Dalian University of Technology Press) (in Chinese)
[26]	Falconer K 2003 Fractal Geometry (New York: Wiley)
[27]	Qiao W, Liu S T and Sun J 2014 Mathematical Problems in Engineering 2014 672547

Directional region control of the thermalfractal diffusion of a space body

Directional region control of the thermalfractal diffusion of a space body

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 27

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	兰瑞君, 阳光, 王正平. Single, composite, and ceramic Nd:YAG 946-nm lasers[J]. 中国物理B, 2015, 24(6): 64210-064210.
[2]	王晓东, 欧阳洁, 苏进, 周文. Phase field modeling of the ring-banded spherulites of crystalline polymers: The role of thermal diffusion[J]. 中国物理B, 2014, 23(12): 126103-126103.