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The control of thermal diffusion fractal growth of thin plate in reality under the environmental disturbance is introduced. The quantitative relationship between growth probability and environmental disturbance is obtained. According to the relationship, we predict that the growth surface will aggregate in the region of the environmental disturbance and be controlled by restricting the disturbance. The simulations show that the environmental disturbance, which is composed of a trigonometric function as a nonlinear term and a source term having a round region, controls the growth variation effectively. In addition, the change in fractal dimension of surface growth illustrates that the complexity of the growth increases as the environmental disturbance increases.
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Keywords:
- thermal diffusion of the thin plate /
- fractal /
- environmental disturbance /
- control
[1] Yang Z R 1996 Fractal physics (Shanghai: Scientific and Technological Education) p209 (in Chinese) [杨展如 1996 分形物理学 (上海: 科技教育) 第209页]
[2] Meakin P 2001 Fractal, scaling and growth far from equilibrium (United Kingdom: Cambridge University Press) p183
[3] Witten T A, Sander L M 1981 Phys. Rev. Lett. 47 1400
[4] Zhang D P, Qi H J, Shao J D, Fan R Q, Fan Z X 2005 Acta Phys. Sin. 54 1385 (in Chinese) [张东平、 齐红基、 邵建达、 范瑞瑛、 范正修 2005 物理学报 54 1385]
[5] Murcio R, Rodríguez-Romo S 2009 Physica A 388 2689
[6] Yan L F, Iwasaki H 2004 Chaos Soliton Fract 20 877
[7] Zeng J L, Zhao G, Yuan J M 2006 Chin. Phys. Lett. 23 660
[8] Jin F T, Yuan J M 2003 Chin. Phys. Lett. 22 2324
[9] Su Y F, Li P X, Chen P, Xu Z F, Zhang X L 2009 Acta Phys. Sin. 58 4531 (in Chinese) [苏亚凤、 李普选、 陈 鹏、 徐忠锋、 张孝林 2009 物理学报 58 4531]
[10] Xu X J, Wang F F, Cai P G, Wei G R, Sui C H 2007 Acta Phys. Sin. 56 6881 (in Chinese) [许晓军、 王凤飞、 蔡萍根、 魏高尧、 隋成华 2007 物理学报 56 6881]
[11] Zang J C, Tian Z K, Liu Y X, Chi J, Zou Y L, Wei J Z, Ye J P 2006 Acta Phys. Sin. 55 1358 (in Chinese) [臧竞存、 田战魁、 刘燕行、 迟 静、 邹玉林、 魏建忠、 叶建萍 2006 物理学报 55 1358]
[12] Xie G F, Wang D W, Ying C T 2005 Acta Phys. Sin. 54 2212 (in Chinese) [谢国锋、 王德武、 应纯同 2005 物理学报 54 〖13] Wei H L, Liu Z L, Yao K L 2000 Acta Phys. Sin. 49 791 (in Chinese) [魏合林、 刘祖黎、 姚凯伦 2000 物理学报 49 791]
[13] Lu H J, Wu F M, Yun Z 2004 Chin. Phys. 13 2038
[14] Tang Q, Tian J P, Yao K L 2006 Chin. Phys. Lett. 23 3033
[15] Yang L, Pei W J, Li T, Cheung Y M, He Z Y 2008 Chin. Phys. Lett. 25 1153
[16] Gu C H, Li D Q, Chen S X, Zheng S M, Tan Y J 2002 Equations of Mathematical Physics (Higher Education Press) p48 (in Chinese) [谷超豪、 李大潜、 陈恕行、 郑宋穆、 谭永基 2002 数学物理方程 (高等教育出版社) 第48页]
[17] Haemers T A M, Rickerby D G, Mittemeijer E 1999 Modelling Simul.Mater.Sci.Eng. 7 233
[18] Tél T, Fülp á, Vicsek T 1989 Physica A 159 155
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[1] Yang Z R 1996 Fractal physics (Shanghai: Scientific and Technological Education) p209 (in Chinese) [杨展如 1996 分形物理学 (上海: 科技教育) 第209页]
[2] Meakin P 2001 Fractal, scaling and growth far from equilibrium (United Kingdom: Cambridge University Press) p183
[3] Witten T A, Sander L M 1981 Phys. Rev. Lett. 47 1400
[4] Zhang D P, Qi H J, Shao J D, Fan R Q, Fan Z X 2005 Acta Phys. Sin. 54 1385 (in Chinese) [张东平、 齐红基、 邵建达、 范瑞瑛、 范正修 2005 物理学报 54 1385]
[5] Murcio R, Rodríguez-Romo S 2009 Physica A 388 2689
[6] Yan L F, Iwasaki H 2004 Chaos Soliton Fract 20 877
[7] Zeng J L, Zhao G, Yuan J M 2006 Chin. Phys. Lett. 23 660
[8] Jin F T, Yuan J M 2003 Chin. Phys. Lett. 22 2324
[9] Su Y F, Li P X, Chen P, Xu Z F, Zhang X L 2009 Acta Phys. Sin. 58 4531 (in Chinese) [苏亚凤、 李普选、 陈 鹏、 徐忠锋、 张孝林 2009 物理学报 58 4531]
[10] Xu X J, Wang F F, Cai P G, Wei G R, Sui C H 2007 Acta Phys. Sin. 56 6881 (in Chinese) [许晓军、 王凤飞、 蔡萍根、 魏高尧、 隋成华 2007 物理学报 56 6881]
[11] Zang J C, Tian Z K, Liu Y X, Chi J, Zou Y L, Wei J Z, Ye J P 2006 Acta Phys. Sin. 55 1358 (in Chinese) [臧竞存、 田战魁、 刘燕行、 迟 静、 邹玉林、 魏建忠、 叶建萍 2006 物理学报 55 1358]
[12] Xie G F, Wang D W, Ying C T 2005 Acta Phys. Sin. 54 2212 (in Chinese) [谢国锋、 王德武、 应纯同 2005 物理学报 54 〖13] Wei H L, Liu Z L, Yao K L 2000 Acta Phys. Sin. 49 791 (in Chinese) [魏合林、 刘祖黎、 姚凯伦 2000 物理学报 49 791]
[13] Lu H J, Wu F M, Yun Z 2004 Chin. Phys. 13 2038
[14] Tang Q, Tian J P, Yao K L 2006 Chin. Phys. Lett. 23 3033
[15] Yang L, Pei W J, Li T, Cheung Y M, He Z Y 2008 Chin. Phys. Lett. 25 1153
[16] Gu C H, Li D Q, Chen S X, Zheng S M, Tan Y J 2002 Equations of Mathematical Physics (Higher Education Press) p48 (in Chinese) [谷超豪、 李大潜、 陈恕行、 郑宋穆、 谭永基 2002 数学物理方程 (高等教育出版社) 第48页]
[17] Haemers T A M, Rickerby D G, Mittemeijer E 1999 Modelling Simul.Mater.Sci.Eng. 7 233
[18] Tél T, Fülp á, Vicsek T 1989 Physica A 159 155
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