Modeling and Scaling of Material Processing Systems

该奖项支持的项目涉及材料加工系统模型的制定，分析和解决方案的数学方法的开发和应用。具体而言，其目的是研究时间相关的尖锐界面凝固模型，相场模型和化学气相沉积（CVD）模型。这些项目的总体目标是研究简单的模型问题，以确定对操作条件的过程敏感性，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。 这将包括在一个二维的配置，多参数渐近展开的相场模型的调查方法，和一个渐进的方法调查的滞止流CVD反应器和发展的气体/固体界面的沉积膜的演化方程随时间变化的演变的凝固前沿和浓度分布的调查。 该奖项将支持与工业材料加工相关的数学模型验证有关的研究。凝固伊萨工业环境中的一种普遍现象。它描述了从液体到固体的状态变化。实验上，已经观察到，凝固过程产生本质上为树枝状（指状）的凝固表面。计算机模拟也显示了这些结构，但这些模拟的正确性尚缺乏验证。前两部分的工作将解决这个问题上的数学严格的基础。本工作的第三部分涉及薄膜形成与设计高性能材料。其中一种制造这种薄膜的方法叫做化学气相沉积（CVD）。沉积反应器的数学模型通常是复杂的，并且计算机模拟通常用于从数学模型提取有用的信息。这项研究将导致更简单的模型，可以更详细地研究。一个复杂的计算机代码，然后可以验证对简单的模型的正确性。

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.