Directional region control of the thermalfractal diffusion of a space body

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

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.

Keywords: thermal diffusion fractal growth directional region control

Received: 24 October 2014
Revised: 10 December 2014
Accepted manuscript online:

PACS:	05.45.Df	(Fractals)
	61.43.Hv	(Fractals; macroscopic aggregates (including diffusion-limited Aggregates))

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61273088, 61473173, and 61473174).

Corresponding Authors: Sun Jie
E-mail: sunj@sdu.edu.cn

About author: 05.45.Df; 61.43.Hv

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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 2015 Chin. Phys. B 24 050504

[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

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Directional region control of the thermalfractal diffusion of a space body

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