RTG: Analysis and Applications

RTG：分析与应用

• 批准号: 1147523
• 负责人: Andreas Seeger
• 金额: $ 179.66万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1147523&HistoricalAwards=false
• 关键词: RTG; Analysis; Applications

The University of Wisconsin Research and Training Groups (RTG) project in Analysis and Applications consists of a variety of initiatives with the aim of increasing the number of US citizens and permanent residents who study mathematics and then pursue teaching and research careers in mathematics. The project will significantly increase both the intensity and range of activities at UW Madison, and create a culture of broad education and intensive well-rounded training, for trainees at the postdoctoral, graduate and undergraduate level. The research scope of the proposal is both broad and coherent, interwoven by common themes and ideas. The harmonic analysis research topics include classical questions on Fourier multipliers, restriction of Fourier transforms and the interplay of sub-Riemannian geometry and analysis. In mathematical fluid dynamics, the research will focus on regularity and blow up problems for active scalars, on investigating realistic models of atmospheric dynamics building upon the classical Boussinesq system, and on mixing problems that lie on the interface of partial differential equations, dynamical systems and probability. In mathematical biology, we will work on reaction networks that model a broad range of processes in biochemistry, systems biology and ecology, and on applications of chemotaxis to enhancement of biological reactions. The research of this project will be focused on analysis and applications. The applied problems will come from a variety of areas and sciences. There will be applications that involve models used in atmospheric science for weather and climate studies. There will be problems on efficiency of mixing in fluids, of interest in applications ranging from internal combustion modeling to food processing. Finally, there will be problems on reaction networks of interest in biochemistry, and problems on sensing of chemicals by living organisms of interest in ecology and oceanography. The project is designed to give young participants experience and depth necessary to adapt to a variety of career paths and to pursue the most promising directions available. It offers a wide range of teaching and research activities, including summer training programs for incoming graduate students, annual research seminars for graduate students and postdocs, annual research experience programs for undergraduates, research workshops and outreach opportunities. The research experience programs for undergraduates seek to early acquaint students with the excitement of mathematics research and provide leadership training opportunities for graduate students and postdocs. Those activities will have a large innovative teaching component during the academic year, and will be followed by intensive research programs in the summer. The graduate research seminars will cover a diverse range of active topics, exposing researchers and students to a mix of advanced analysis techniques along with concrete applied problems where these techniques can be used. The research workshops will serve to broaden the perspective of the trainees and suggest new directions of research. Outreach activities sponsored by the project will include regular mathematics seminars for high-school students, with the participation of RTG trainees. The activities supported by the RTG grant will significantly strengthen the UW mathematics department's research and training programs which contribute to the effort of creating a mathematically skilled workforce. This contribution represents the national and statewide effect of this project.

威斯康星大学研究和培训小组（RTG）的分析和应用项目包括各种举措，目的是增加美国公民和永久居民学习数学，然后从事数学教学和研究工作的人数。该项目将显著增加威斯康星大学麦迪逊分校的活动强度和范围，并为博士后、研究生和本科生的受训者创造一种广泛的教育和密集的全面培训文化。提案的研究范围既广泛又连贯，由共同的主题和思想交织在一起。谐波分析的研究课题包括傅里叶乘子的经典问题、傅里叶变换的限制以及亚黎曼几何与分析的相互作用。在数学流体动力学方面，研究将集中在活动标量的正则性和爆炸问题，研究基于经典Boussinesq系统的大气动力学的现实模型，以及位于偏微分方程，动力系统和概率界面上的混合问题。在数学生物学中，我们将研究模拟生物化学、系统生物学和生态学中广泛过程的反应网络，并研究趋化性在增强生物反应中的应用。本课题的研究将集中在分析和应用方面。应用的问题将来自不同的领域和科学。将会有一些应用涉及到用于天气和气候研究的大气科学模型。在从内燃建模到食品加工的应用中，将会有关于流体混合效率的问题。最后，将会有生物化学中感兴趣的反应网络问题，以及生态学和海洋学中感兴趣的生物体对化学物质的感知问题。该项目旨在为年轻的参与者提供必要的经验和深度，以适应各种职业道路，并追求最有前途的方向。它提供广泛的教学和研究活动，包括为即将入学的研究生提供夏季培训计划，为研究生和博士后提供年度研究研讨会，为本科生提供年度研究体验计划，研究研讨会和外展机会。本科生研究体验项目旨在让学生尽早了解数学研究的兴奋，并为研究生和博士后提供领导力培训机会。这些活动将在学年期间包含大量的创新教学内容，随后将在夏季进行密集的研究项目。研究生研究研讨会将涵盖各种活跃的主题，向研究人员和学生展示先进的分析技术，以及这些技术可以使用的具体应用问题。研究讲习班将有助于拓宽受训者的视野，并提出新的研究方向。该项目赞助的外联活动将包括定期为高中生举办数学研讨会，RTG学员也将参加。RTG资助的活动将大大加强西澳大学数学系的研究和培训计划，为培养数学熟练的劳动力做出贡献。这一贡献代表了该项目在全国和全州的影响。

项目成果

Atmospheric rivers and water fluxes in precipitating quasi‐geostrophic turbulence

准地转湍流中的大气河流和水通量

• DOI: 10.1002/qj.3777
• 发表时间: 2020
• 期刊: Quarterly Journal of the Royal Meteorological Society
• 影响因子: 8.9
• 作者: Edwards, Thomas K.;Smith, Leslie M.;Stechmann, Samuel N.
• 通讯作者: Stechmann, Samuel N.

Spectra of atmospheric water in precipitating quasi-geostrophic turbulence

准地转湍流中大气水的光谱

• DOI: 10.1080/03091929.2019.1692205
• 发表时间: 2019
• 期刊: Geophysical & Astrophysical Fluid Dynamics
• 影响因子: 1.3
• 作者: Edwards, Thomas K.;Smith, Leslie M.;Stechmann, Samuel N.
• 通讯作者: Stechmann, Samuel N.