| 薄板热扩散分形生长的环境干扰控制 |
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| 引用本文： | 张丽,刘树堂. 薄板热扩散分形生长的环境干扰控制[J]. 物理学报, 2010, 59(11): 7708-7712 |
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| 作者姓名： | 张丽 刘树堂 |
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| 作者单位： | 山东大学控制科学与工程学院,济南 250061 |
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| 基金项目： | 国家自然科学基金(批准号: 60874009, 10971120),全国百篇优秀博士论文专项基金(批准号: 200444)资助的课题. |
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| 摘 要： | 研究了薄板热扩散中分形生长的控制,给出了生长概率与干扰项之间的数量关系,预测了热扩散分形生长表面在干扰作用区域内的凝聚情况,并随着干扰项的制约而达到控制的目的.其中以三角函数形式的非线性项与定义域为圆域的源项构成的环境干扰项为例,验证了该控制方法的有效性.另外,生长表面的标度维数变化显示了环境干扰项对实际生长复杂度的影响.
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| 关 键 词： | 薄板热扩散 分形 环境干扰 控制 |
| 收稿时间： | 2010-01-12 |
| 修稿时间： | 2010-03-05 |
Control of thermal diffusion fractal growth of thin plate under environmental disturbance |
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| Zhang Li,Liu Shu-Tang. Control of thermal diffusion fractal growth of thin plate under environmental disturbance[J]. Acta Physica Sinica, 2010, 59(11): 7708-7712 |
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| Authors: | Zhang Li Liu Shu-Tang |
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| Affiliation: | School of Control Science and Engineering, Shandong University, Jinan 250061, China;School of Control Science and Engineering, Shandong University, Jinan 250061, China |
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| Abstract: | 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 |
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