Mathematical modeling of polymerization reactors

聚合物用于日常用品，如塑料容器和纺织品，也用于专门的医疗应用。生产聚合物所需的化学反应是在聚合反应器中进行的。数学方程式（模型）可以用来描述聚合反应器条件（温度和不同化学物质的浓度）如何影响所生产的聚合物的性质。我的大部分研究都是针对聚合反应器的数学建模。公司使用我的模型来提高对聚合过程的理解，提高产品质量，并提高生产率。近年来，我扩大了我的工作范围，包括聚合物凝胶剂量计的数学建模，用于校准癌症放疗设备提供的辐射剂量。这些模型帮助医学物理学家了解在他们的剂量计中发生的化学和物理过程，并将帮助他们确保将正确的辐射剂量输送到患者体内的正确位置。我还开发数学建模和统计技术，以帮助其他建模者。在本提案中，要求为五个研究课题提供资金。首先，将利用我们实验室的实验数据，开发模型来预测工业尼龙反应器的产品质量。第二，建立不同类型凝胶剂量计的模型，以便更好地评估其优点和不足，设计改进的剂量计。第三，将开发模型来预测支链聚合物的性能，以协助设计用于生物医学应用的新材料。在第四和第五部分，将开发统计工具，以协助建模者找到适当的参数值，这些参数值是使用模型进行预测时所需要的。这些统计工具将导致更有效地利用实验数据和更可靠的模型预测。所要求的大部分预算将用于研究生的工资，他们将接受聚合反应工程、数学建模和应用统计方面的宝贵培训。

Polymers are used in everyday products such as plastic containers and textiles, and also in specialized medical applications. Chemical reactions required to produce polymers are carried out in polymerization reactors. Mathematical equations (a model) can be used to describe how polymerization reactor conditions (temperature, and the concentrations of different chemicals) affect the properties of the polymers that are produced. Most of my research is aimed at mathematical modeling of polymerization reactors. Companies use my models to gain improved understanding of their polymerization processes, to improve product quality, and to increase production rates. In recent years, I have expanded my work to include mathematical modeling of polymer gel dosimeters, which are used to calibrate radiation doses delivered by cancer radiotherapy equipment. These models help medical physicists to understand chemical and physical processes that occur in their dosimeters, and will help them to ensure that the correct radiation doses are being delivered to the correct locations in patients' bodies. I also develop mathematical modeling and statistical techniques that assist other modelers. In this proposal, funds are requested for five research topics. In the first, models will be developed to predict product quality in industrial nylon reactors, using experimental data from our lab. In the second, models will be developed for different types of gel dosimeters, so that benefits and short-comings can be better assessed, and improved dosimeters can be designed. In the third, models will be developed to predict the properties of branched polymers, to assist in the design of new materials for biomedical applications. In the fourth and fifth, statistical tools will be developed to assist modelers in finding appropriate values of parameters, which are required when models are used to make predictions. These statistical tools will result in more effective use of experimental data and more reliable model predictions. Most of the budget requested will be spent on salaries for graduate students, who will receive valuable training in polymerization reaction engineering, mathematical modeling and applied statistics.