REU Site: Applied Mathematics Research Experience -- Theory, Applications, and Numerics

该奖项支持休斯顿市中心大学举办一项面向本科生的跨学科研究体验(REU)项目，该项目旨在为具有数学背景的学生和对工程和生物科学感兴趣的学生之间架起桥梁。学生将进行协作研究项目，需要在跨学科研究团队中广泛应用数学技能。该课程由三个主要部分组成：理论、实验和数值，旨在为学生提供完整和平衡的研究体验。该项目将在为期8周的时间里，每年夏天接待10名本科生。研究体验的设计有三个具体目标：(1)增加本科生，特别是代表不足的群体，参与需要科学中定量方法的项目的合作研究；(2)培训和教育学生在科学和数学领域有效地交流研究成果；(3)鼓励学生利用其REU经验中所具有的智力和计算技能从事职业。这个REU项目的学生将学习和参与应用数学研究领域，包括固体力学和植物运输系统的问题。中心主题是控制偏微分方程式，包括线弹性方程式、传输方程式和扩散方程式。所有项目还包括实验室和/或实地工作部分，让学生在收集模型背后的数据方面有第一手经验。这些模型将通过定性分析和数值模拟相结合的方法进行研究。将调查参数变化的影响，以解释结果并得出切实可行的结论。所有学生参与者将应用完整的科学方法循环。

This award provides support to the University of Houston-Downtown to host an interdisciplinary research experience for undergraduates (REU) program developed to build bridges between students with mathematical backgrounds and students interested in engineering and biological sciences. Students will conduct collaborative research projects requiring extensive application of mathematical skills in interdisciplinary research teams. The program consists of three major components: theory, experiments, and numerics, and it aims to provide students a complete and balanced research experience. The program will host ten undergraduate students each summer for eight weeks. The research experience has been designed with three specific aims: (1) increase the number of undergraduates, particularly under-represented groups, engaged in collaborative research on projects that require quantitative methods in the sciences; (2) train and educate students to communicate research findings effectively across both the sciences and mathematics; (3) encourage students to pursue careers employing the intellectual and computational skills featured in their REU experience. The students in this REU program will learn and participate in the applied mathematics research fields that include problems in solid mechanics and plant transport systems. The central theme is on the governing partial differential equations, which include equations of linear elasticity, transport equations, and diffusion equations. All projects also include a laboratory and/or fieldwork component that gives students a firsthand experience in collecting data underlying the models. These models will be studied through a combination of qualitative analysis and numerical simulation. Effects of parameter variation will be surveyed to interpret the results and to formulate practical conclusions. All student participants will apply a complete cycle of the scientific method.