REU Site: Undergraduate Research in Applied Analysis at West Virginia University

REU 网站：西弗吉尼亚大学应用分析本科生研究

• 批准号: 2349040
• 负责人: Charis Tsikkou
• 金额: $ 37.2万
• 依托单位: West Virginia University Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2027-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2349040&HistoricalAwards=false
• 关键词: REU; Site; Undergraduate; Research; Applied

This project is jointly funded by the Workforce program in the Division of Mathematical Sciences and the Established Program to Stimulate Competitive Research (EPSCoR). This Research Experiences for Undergraduates (REU) site award will support the mathematical training of ten students per year at West Virginia University in Morgantown, WV, for eight weeks during the summers of 2024, 2025, and 2026. The program will engage participants in applied analysis and partial differential equations research. While recruiting from a nationwide pool, special consideration will be given to underrepresented groups, students attending baccalaureate degree programs at colleges and universities in the Appalachian region and beyond, and, in general, institutions with limited research opportunities. Through weekly interactions, training, and mentoring, participants are expected to complete an independent research project, obtain first-hand experience with the rigors of and best practices in mathematical research, and familiarize themselves with mainstream expectations for graduate school and pursuing a career in mathematics. This program will also help strengthen STEM education and attract talent to West Virginia, thereby enhancing the region’s workforce and development. Participants' research projects will focus on utilizing tools from analysis and PDEs to address practical issues arising from physics and materials science. The projects include a diverse collection of topics based on the research interests of the faculty mentors: systems of conservation and balance laws with singular solutions, asymptotics for a basic cosmological model, and the director field model with electromagnetic waves. Research in hyperbolic conservation laws will focus on solving equations with special initial conditions and employ the characteristic method and, in general, various dynamical systems ideas with geometric flavor. These methods will help us gain quantitative and qualitative insights into more general problems with many applications, such as fluid mechanics, biosciences, and cosmology. The analysis of the director field model will advance our understanding of the interaction between elastic and electromagnetic waves in liquid crystals. Research on the sticky particles model will enhance our comprehension of the formation of large-scale structures in the universe by accretion of matter; more specifically, this part of the project will involve a discrete particle evolution approach to gain insight into the long-time behavior of stellar and galactic clusters. The proposed projects for this REU are based on interesting open problems and are designed to be accessible, while highly intellectually stimulating, for talented undergraduates. Additional information will be provided on the webpage: https://mathanddata.wvu.edu/students/undergraduate/applied-analysis-reu.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目是由数学科学部和刺激竞争研究（EPSCOR）的劳动力计划共同资助的。在2024年，2025年和2026年的夏季，该计划将为参与者参与应用分析和部分微分方程研究，在西弗吉尼亚州摩根镇的西弗吉尼亚大学，在西弗吉尼亚大学的西弗吉尼亚大学进行十项学生的数学培训八周。在全国范围内招募的招聘时，将特别考虑代表性不足的团体，参加阿巴拉契亚地区及其他地区学院和大学的学士学位课程的学生，总的来说，研究机会有限的机构。通过每周的互动，培训和心理，参与者有望完成一个独立的研究项目，以数学研究的严格和最佳实践获得第一手的经验，并熟悉对研究生院的主流期望以及从事数学职业。该计划还将有助于增强西弗吉尼亚州的STEM教育和吸引力人才，从而增强该地区的劳动力和发展。参与者的研究项目将专注于利用分析和PDE的工具来解决物理和材料科学引起的实际问题。这些项目包括基于教师导师的研究兴趣的潜水员集合：具有奇异解决方案的保护和平衡法，基本宇宙学模型的渐近学以及带有电磁波的导演现场模型。双曲线保护法的研究将集中于解决具有特殊初始条件的方程式，并使用特征性方法，并且通常是各种具有几何风味的动态系统思想。这些方法将有助于我们获得许多应用程序，例如流体力学，生物科学和宇宙学的定量和定性见解。对导演现场模型的分析将提高我们对液晶中弹性波和电磁波之间相互作用的理解。对粘性颗粒模型的研究将通过物质的积聚来增强我们对宇宙中大规模结构形成的理解。更具体地说，该项目的这一部分将涉及一种离散的粒子演化方法，以深入了解恒星和银河簇的长期行为。此REU的拟议项目是基于有趣的开放问题，旨在为才华横溢的本科生而高度智能刺激。网页上将提供其他信息：https：//mathanddata.wvu.edu/students/undergraduate/applied-analysis-reu.this Award反映了NSF的法定任务，并被认为是通过使用该基金会的知识分子和更广泛影响的评估来通过评估来获得支持的珍贵的。