| 控制熔体浓度三维稳定态方程的精确解 |
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| 引用本文： | 廖福成, 祖翠娥, 郑连存, 王自东, 李为东. 控制熔体浓度三维稳定态方程的精确解[J]. 工程科学学报, 2004, 26(1): 53-55. DOI: 10.13374/j.issn1001-053x.2004.01.015 |
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| 作者姓名： | 廖福成 祖翠娥 郑连存 王自东 李为东 |
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| 作者单位： | 北京科技大学应用科学学院,北京,100083;北京科技大学材料学院,北京,100083 |
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| 基金项目： | 国家重点基础研究发展计划（973计划）;北京市科技新星计划 |
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| 摘 要： | 研究了一类关于浓度的三维稳态晶体生长控制方程.这类问题由于带有远场条件,无法按常规方法给出其解析解或数值解.在复数域内利用分离变量法,得到了这类方程的级数形式的解析解,而最后的解是实数形式.结果表明,固液界面前沿浓度是指数震荡衰减的.
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| 关 键 词： | 晶体生长 分离变量法 偏微分方程 Fourier级数 |
| 收稿时间： | 2003-03-28 |
Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth |
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| LIAO Fucheng, ZU Cuie, ZHENG Liancun, WANG Zidong, LI Weidong. Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth[J]. Chinese Journal of Engineering, 2004, 26(1): 53-55. DOI: 10.13374/j.issn1001-053x.2004.01.015 |
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| Authors: | LIAO Fucheng ZU Cuie ZHENG Liancun WANG Zidong LI Weidong |
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| Abstract: | A class of partial differential equations (PDE) which describe three-dimension steady state crystal growth for concentration were studied. Because there exists far-field condition, their exact solution or numerical solution can not be derived based on known results about PDE. By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained. The result shows that the concentration in the solid-liquid interface is exponentially damped oscillation. |
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| Keywords: | crystal growth detached variable method partial differential equation Fourier series |
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