Mathematical Sciences: Modeling of Material Processing Systems

小行星9532021 拟议的项目将研究钢的连续铸造， 纯纤维和带芯纤维的水平Ohno连续铸造， 将多种单体体系光共聚合成光纤。 这些模型的一般目标是确定工艺对下列因素的敏感性： 操作条件，描述热，溶质， 和动量输运的系统，并阐明耦合 这些运输机制的动力学。 一个渐进的组合 技术结合实际的计算方法将被用来 模拟这些系统。 主要重点将放在 方程组近似解析解的发展 控制这些处理技术。 如果这不是 实际上，将使用渐近方法来减少控制集 一组简单的演化方程。 数值模拟 这些方程将被执行。 拟议的项目将研究几种材料的数学模型 和制造工艺。 特别是钢的连续铸造， 纯纤维和带芯纤维的水平Ohno连铸， 将多种单体体系光共聚合成光纤将 追究 建议的解决方案方法使人们能够 代表材料和系统参数对 系统性能 这种方法还允许人们调查各种 的模型，以应对不断变化的技术，并可以修改为新的 应用领域。 进一步，设计了实时控制器， 用于复杂、多阶段、制造过程的优化方法， 以及快速评估大量替代工艺的需求 设计，需要捕捉系统趋势的模型， 计算密集型。

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.