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.

为期 6 个月的研究密集型项目，题为“分散流体动力学：数学、模拟和实验，以及在非线性波中的应用”将于 2020 年 7 月 6 日至 12 月 18 日在英国剑桥大学艾萨克牛顿研究所举行。分散流体动力学是一个新兴的数学研究领域，重点关注非线性偏微分描述的动态和随机、多尺度波动现象 物理上包含长尺度流体动力学效应和短尺度色散效应之间复杂相互作用的方程。 自 2012 年以来，该主题至少举办了六次专门研讨会和无数次会议小型研讨会，这将是第一个关于色散流体动力学的扩展项目。 它将在任何特定时间吸引至少 25 名长期居住访客，并在每次为期 5 周的研讨会中吸引 40 名或更多参与者。 多元化的国际参与者名单包括应用数学科学领域的领先研究人员。该国家科学基金会奖项为来自美国的早期职业应用数学家提供参加研讨会和长期项目的旅费支持。传统上应用数学领域代表性不足的群体将被鼓励申请。这种支持提供了与世界各地领先研究人员互动的持续机会。这种互动和接触对于刚起步的研究人员来说非常宝贵，既可以激发研究灵感，也可以促进专业发展，从而有助于培养最优秀的年轻研究人员。这些研究人员将成为下一代应用数学家，推动这一领域和其他应用数学领域的研究。 色散流体动力学已成为描述色散介质中多尺度非线性波现象的统一数学框架，涵盖波传播的动态和随机方面。理论和实验的发展催生了应用数学研究的新领域。该数学程序将可积和不可积色散偏微分方程、凸和非凸色散流体动力系统、多维波、渐近分析、数值分析、非线性色散波中的随机性和湍流等研究主题编织在一起。应用范围包括流体力学，并远远超出非线性光学、超流体（玻色-爱因斯坦凝聚体）、凝聚态物质和粒状晶体。该计划的网站可以在 http://www.newton.ac.uk/event/hyd 上找到，其中包含研讨会和其他活动的链接。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。