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具有凝固平直界面的温度场的扰动分析
引用本文:刘竞,陈明文,孙仁济,王自东.具有凝固平直界面的温度场的扰动分析[J].贵州师范大学学报(自然科学版),2005,23(4):77-81.
作者姓名:刘竞  陈明文  孙仁济  王自东
作者单位:1. 北京科技大学,数学力学系,北京,100083
2. 北京科技大学,材料科学与工程学院,北京,100083
基金项目:国家重大基础研究项目(No.G20000672061).
摘    要:考虑具有凝固平直界面的二维非稳态晶体生长过程,由于凝固过程中溶质原子的吸附作用,电磁搅拌等诸多因素的干扰,在固液平直界面会产生扰动,从而影响界面的形态。本文研究凝固过程中具有固液平直界面的温度场扰动分析,用多重尺度法求出一阶渐近解,指出在扰动条件下,温度变化沿晶体生长方向呈指数衰减,提出扰动条件下固液平直界面晶体生长的稳定性条件。这为晶体生长的理论研究及实验工作提供了理论依据。

关 键 词:晶体生长  偏微分方程  多重尺度法  可解性条件
文章编号:1004-5570(2005)04-0077-05
收稿时间:2005-09-08
修稿时间:2005年9月8日

The Perturbation analysis of the temperature field to straight interface solidifying
LIU Jing,CHEN Ming-wen,SUN Ren-ji,WANG Zi-dong.The Perturbation analysis of the temperature field to straight interface solidifying[J].Journal of Guizhou Normal University(Natural Sciences),2005,23(4):77-81.
Authors:LIU Jing  CHEN Ming-wen  SUN Ren-ji  WANG Zi-dong
Institution:1. Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, China; 2. Material Science and Engineering School, University of Science and Technology Beijing, Beijing 100083, China
Abstract:Consider the two-dimentional non-stable crystal growth question under the straight interface solidifying. The straight interface of firm liquid will produce the perturbation, thus it will influence the shape of the interface because of the adsorption of the solute and atom in the course, the interference of a great deal of factors that mix electromagnetically, etc. in the solidifying course. This paper studies the perturbation analysis of temperature field with straight interface of solid liquid in the solidifying course and use the MVE method to solve the one step question. Then the paper points out the temperature change presents the index and decays along the crystal growth direction, and proposes the stability condition of straight interface crystal growth of the solid liquid under the perturbation condition, which has offered theoretical foundation for theoretical research of crystal growth and experimental work.
Keywords:crystal growth  partial differential equation  MVE method  solvability condition
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