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公式、分析和求解的数学方法的开发和应用。具体地说，其目的是检验与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。这将包括研究二维构型中凝固前沿和浓度分布的随时间变化的演化，研究相场模型的多参数渐近展开方法，以及研究停滞流动CVD反应器和建立沉积膜气/固界面演化方程的渐近方法。该奖项将支持涉及验证与工业材料加工有关的数学模型的研究。凝固是工业环境中的一种常见现象。它描述了从液体到固体的状态变化。在实验上，已经观察到凝固过程产生的凝固表面本质上是树枝状(指状)。计算机模拟也显示了这些结构，但这些模拟的正确性还有待验证。这项工作的前两部分将在严格的数学基础上解决这个问题。这项工作的第三部分涉及与设计高性能材料相关的薄膜形成。制作这种薄膜的一种工艺称为化学气相沉积(CVD)。沉积反应堆的数学模型通常很复杂，通常使用计算机模拟来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，可以进行更详细的研究。然后，可以用较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.