Analytical Solution of Governing Equations for Three-dimension Steady State Crystal Growth
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摘要: 研究了一類關于濃度的三維穩態晶體生長控制方程.這類問題由于帶有遠場條件,無法按常規方法給出其解析解或數值解.在復數域內利用分離變量法,得到了這類方程的級數形式的解析解,而最后的解是實數形式.結果表明,固液界面前沿濃度是指數震蕩衰減的.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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