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.

威斯康星州的研究和培训组（RTG）的分析和应用项目的大学包括各种举措，目的是增加美国公民和永久居民谁学习数学，然后追求数学教学和研究事业的数量。该项目将显着增加在UW麦迪逊的活动的强度和范围，并创造广泛的教育和密集的全面培训的文化，在博士后，研究生和本科层次的学员。该提案的研究范围既广泛又连贯，由共同的主题和想法交织在一起。调和分析的研究课题包括傅里叶乘子、傅里叶变换的限制以及次黎曼几何与分析的相互作用等经典问题。在数学流体动力学，研究将集中在规律性和爆破问题的积极标量，在调查现实模型的大气动力学建设的经典Boussinesq系统，并在混合问题上的偏微分方程，动力系统和概率的接口。在数学生物学中，我们将研究反应网络，这些网络模拟了生物化学，系统生物学和生态学中的各种过程，以及趋化性在增强生物反应中的应用。本项目的研究将侧重于分析和应用。应用问题将来自不同的领域和科学。将有涉及用于天气和气候研究的大气科学模型的应用。在流体中的混合效率将存在问题，这在从内燃机建模到食品加工的应用中是令人感兴趣的。最后，还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。它提供了广泛的教学和研究活动，包括即将到来的研究生暑期培训计划，研究生和博士后的年度研究研讨会，本科生的年度研究经验计划，研究研讨会和推广机会。本科生的研究经验计划旨在尽早让学生熟悉数学研究的兴奋点，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有一个很大的创新教学组成部分，并将在夏季进行密集的研究计划。研究生研究研讨会将涵盖各种活跃的主题，使研究人员和学生接触到先进的分析技术沿着与具体应用问题的组合，这些技术可以使用。研究讲习班将有助于拓宽学员的视野，并提出新的研究方向。该项目赞助的推广活动将包括定期为高中学生举办数学研讨会，RTG受训人员将参加研讨会。由RTG赠款支持的活动将大大加强华盛顿大学数学系的研究和培训计划，这有助于创造一个数学熟练的劳动力的努力。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.