Dispersive Hydrodynamics Program at the Isaac Newton Institute

艾萨克·牛顿研究所的分散流体动力学项目

• 批准号: 1941489
• 负责人: Mark Hoefer
• 金额: $ 3.5万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1941489&HistoricalAwards=false
• 关键词: Dispersive; Hydrodynamics; Program; Isaac; Newton

A 6-month research-intensive program titled "Dispersive hydrodynamics: mathematics, simulations and experiments, with applications in nonlinear waves" will be held at the Isaac Newton Institute, University of Cambridge, UK from July 6–December 18, 2020. Dispersive hydrodynamics is an emergent mathematical field of research focusing on dynamic and stochastic, multiscale wave phenomena described by nonlinear partial differential equations that physically encompass the complex interplay between long-scale, hydrodynamic, and short-scale, dispersive, effects. Building upon at least six dedicated workshops and numerous conference minisymposia on the subject since 2012, this will be the first extended program on dispersive hydrodynamics. It will attract at least 25 long-term, residential visitors at any given time and 40 or more participants in each of 5 week-long workshops. The diverse, international roster of participants includes leading researchers in the applied mathematical sciences. This National Science Foundation award provides travel support for early career applied mathematicians from the United States to participate in the workshops and the long-term program. Traditionally underrepresented groups in applied mathematics will be encouraged to apply. This support enables sustained opportunities to interact with leading researchers from across the world. Such interactions and contacts are invaluable to beginning researchers, both to inspire research, and for professional development, thereby helping to cultivate the very best young researchers. These researchers will be the next generation of applied mathematicians who advance this and other applied mathematical fields of research. Dispersive hydrodynamics has emerged as a unified mathematical framework for the description of multiscale nonlinear wave phenomena in dispersive media, encompassing both dynamic and stochastic aspects of wave propagation. Theoretical and experimental developments have spawned new areas of applied mathematical research. The mathematical program weaves together research topics on integrable and nonintegrable dispersive PDEs, convex and nonconvex dispersive hydrodynamic systems, multidimensional waves, asymptotic analysis, numerical analysis, randomness and turbulence in nonlinear dispersive waves. Applications include fluid mechanics and go well beyond, to nonlinear optics, superfluids (Bose-Einstein condensates), condensed matter, and granular crystals. The program website can be found at http://www.newton.ac.uk/event/hyd, with links to the workshops and other activities.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.

一个为期6个月的研究密集型计划，标题为“分散流体动力学：数学，模拟和实验，在非线性波浪中的应用”将在英国剑桥市的艾萨克·牛顿研究所（Isaac Newton Institute）举行物理上包含长尺度，流体动力和短尺度，分散效应之间的复杂相互作用的方程式。自2012年以来，基于至少六个专门的研讨会和许多关于该主题的会议迷你典礼的基础，这将是第一个关于分散流体动力学的扩展计划。它将在任何给定时间至少吸引25个长期的居民，为期5周的讲习班中的每一个。潜水员国际参与者的名册包括应用数学科学领域的主要研究人员。这项国家科学基金会奖为来自美国的早期职业应用数学家提供了旅行支持，以参加研讨会和长期计划。传统上，将鼓励应用数学中代表性不足的群体应用。这种支持使持续的机会与来自世界各地的主要研究人员进行互动。这种互动和接触对启发研究和专业发展的初学者研究人员都是无价的，从而有助于培养最好的年轻研究人员。这些研究人员将是下一代应用数学家，他们推进了这一研究和其他应用数学领域的研究。分散流体动力学已成为一个统一的数学框架，用于描述分散介质中多尺度非线性波现象，涵盖了波传播的动态和随机方面。理论和实验发展催生了应用数学研究的新领域。数学程序将有关集成和不可集成的分散PDE，凸和非凸形分散流体动力系统，多维波，非对称分析，数值分析，随机分析，随机性和湍流在非线性分散波中编织在一起的研究主题。应用包括流体力学，并远远超出了非线性光学，超级流体（Bose-Einstein冷凝物），冷凝物质和颗粒状晶体。可以在http://www.newton.ac.uk/event/hydr上找到该计划网站，并链接到讲习班和其他活动。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛的审查标准通过评估来通过评估来获得的。