Modeling and Scaling of Material Processing Systems

该奖项支持的项目涉及开发和应用数学方法来制定、分析和解决材料加工系统模型。具体来说，目的是检查时间依赖的尖锐界面凝固模型，相场模型和化学气相沉积（CVD）模型。项目的总体目标是检查简单的模型问题，以确定过程对操作条件的敏感性，描述系统内热、质量和动量传输的科学现象，并阐明这些传输机制的耦合动力学。这将包括在二维结构中研究凝固锋和浓度分布的时变演变，研究相场模型的多参数渐近展开方法，研究停滞流动CVD反应器的渐近方法以及沉积膜的气/固界面演化方程的发展。该奖项将支持与工业材料加工相关的数学模型验证相关的研究。凝固是工业环境中常见的现象。它描述了从液体到固体的状态变化。在实验中，已经观察到凝固过程产生的凝固表面是枝晶（指状）。计算机模拟也显示了这些结构。这些模拟的正确性还缺乏验证。工作的前两部分将在严格的数学基础上解决这个问题。本工作的第三部分关注与高性能材料设计相关的薄膜形成。制作这种薄膜的一种方法被称为化学气相沉积（CVD）。沉积反应器的数学模型通常是复杂的，计算机模拟通常用于从数学模型中提取有用的信息。这项研究将产生更简单的模型，可以更详细地研究。然后可以用简单的模型来验证复杂的计算机代码的正确性。

The project that is supported by this award concerns the development and application of mathematical methods for the formulation, analysis and solution of material processing system models. Specifically, the aims are to examine time-dependent sharp-interface solidification models, phase-field models, and chemical vapor deposition (CVD) models. The general goals of the projects are to examine simple model problems to determine the process sensitivity to the operating conditions, describe the scientific phenomena of heat, mass, and momentum transport within the system, and to elucidate the coupled dynamics of these transport mechanisms. This will include the investigation of time varying evolution of solidifying fronts and concentration profiles in a two-dimensional configuration, a multi-parameter asymptotic expansion approach for investigation of phase-field models, and an asymptotic approach for the investigation of a stagnation flow CVD reactor and development of an evolution equation for the gas/solid interface of the deposited film. This award will support research that deals with the verification of mathematical modelsthat are pertinent to industrial material processing. Solidification isa common phenomenon in an industrial setting. It describes the state change from liquid to solid. Experimentally, it has been observed that the solidification process yields solidified surfaces which aredendritic (finger-like) in nature. Computer simulations also show these structures.The correctness of these simulations still lacks verification. Thefirst two parts of the work will address this very issue on a mathematically rigorous basis. The third part of this work concerns thin film formation as related todesigning high performance materials. One such process for making thisfilm is called Chemical Vapor Deposition (CVD). Mathematical models for the deposition reactors are often complex, and computer simulations are typically used to extract useful information from the mathematical models. The research willresult in simpler models which can be studied in more detail. A complex computer code can then be verified against the simpler models for correctness.