Mathematical Sciences: Modeling of Material Processing Systems

拟议的项目将研究钢的连续铸造，纯纤维和芯纤维的水平大野连续铸造，以及多单体系统光共聚成光纤。这些模型的总体目标是确定过程对操作条件的敏感性，描述系统内热、溶质和动量输运的科学现象，并阐明这些输运机制的耦合动力学。渐近技术与实际计算方法的结合将用于模拟这些系统。主要的重点将放在对控制这些处理技术的方程组的近似解析解的发展上。在不实际的情况下，将使用渐近方法将控制方程集简化为更简单的演化方程集。本文将对这些方程进行数值模拟。拟议的项目将检查几种材料和制造过程的数学模型。特别是，将研究钢的连续铸造、纯纤维和芯纤维的水平大野连续铸造以及多单体体系的光共聚成光纤。所提出的解决方法使人们能够表示材料和系统参数对系统性能的一般趋势。这种方法还允许研究各种模型以响应不断变化的技术，并且可以修改到新的应用领域。此外，实时控制器的设计、复杂、多阶段制造过程的实时优化方法，以及对大量替代过程设计的快速评估的愿望，都需要能够捕捉系统趋势且不需要计算密集型的模型。

9532021 Young The proposed project will examine the continuous casting of steel, the horizontal Ohno continuous casting of pure and cored fibers, and the photocopolymerization of multiple monomer systems into optical fibers. The general goals of the models are to determine the process sensitivity to the operating conditions, describe the scientific phenomena of heat, solute, and momentum transport within the system, and to elucidate the coupled dynamics of these transport mechanisms. A combination of asymptotic techniques coupled with practical computational methods will be used to simulate these systems. Primary emphasis will be placed upon the development of approximate analytical solutions to the systems of equations governing these processing techniques. In instances where this is not practical, an asymptotic approach will be used to reduce the governing set of equations to a simpler set of evolution equations. Numerical simulation of these equations will be conducted. The proposed project will examine mathematical models of several material and manufacturing processes. In particular, the continuous casting of steel, the horizontal Ohno continuous casting of pure and cored fibers, and the photocopolymerization of multiple monomer systems into optical fibers will be investigated. The proposed solution methodologies enable one to represent the general trends that material and system parameters have on the system performance. This approach also allows one to investigate a variety of models in response to changing technologies, and can be modified to new areas of application. Further, the design of real-time controllers, real-time optimization methods for complex, multi-stage, manufacturing processes, and the desire for quick evaluation of a large number of alternative process designs, require models which capture system trends and are not computationally intensive.