Mathematical Sciences: Presidential Young Investigator Award

该项目的研究涉及对大型高质量晶体生产中由热应力和机械应力以及熔体重量引起的与生长相关的缺陷进行建模和分析。 目标是描述决定晶体结构和成分的热、溶质和熔体传输的科学现象，并阐明这些传输机制的耦合动力学。 这项研究的结果将通过定义最佳温度分布和冷冻速率来帮助材料加工技术的设计，以控制凝固界面并最大限度地减少晶体中的热应力。 将实施耦合渐近/数值方法，以利用与这些问题相关的长度和时间尺度的差异。 该方法是将控制方程简化为一个更易于分析的系统，但保留了过程的大部分物理原理。 更简单的系统可以是描述自由凝固界面形状的单个演化方程，或者是耦合的一组场以及任何可变形界面的一致描述。 要达到生长晶体的指定标准，需要确定系统参数解流形的位置，以产生最佳的生长条件。 这些分析技术将针对定向凝固、浮区、晶体片和纤维生长系统而开发。

The research in this project is concerned with the modeling and analysis of growth-related defects induced by thermal and mechanical stresses and melt weight in the production of large high quality crystals. The goals are to describe the scientific phenomena of heat, solute, and melt transport determining the crystal structure and composition, and to elucidate the coupled dynamics of these transport mechanisms. The results of this study will aid the design of material processing technique by defining optimal temperature profiles and freezing rates to gain control over the solidifying interface and to minimize thermal stresses in the crystal. Coupled asymptotic/numerical methods will be implemented to take advantage of the disparity in length and time scales associated with these problems. The approach is to reduce the governing equations to a system which is simpler for analysis, but which retains much of the physics of the process. The simpler system may be a single evolution equation describing the shape of free solidifying interface, or a coupled set of fields together with a consistent description of any deformable interfaces. The achievement of specified criteria for the grown crystal will require the location of a system parameter solution manifold yielding the optimal growth conditions. These techniques of analysis will be developed for directional solidification, float-zone, crystal sheet, and fiber growth systems.