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。是一个新兴的数学研究领域，重点关注由非线性偏微分方程描述的动态和随机、多尺度波浪现象，这些现象在物理上涵盖了长尺度、流体动力学和流体之间的复杂相互作用。自 2012 年以来，这将是第一个关于分散流体动力学的扩展项目，以至少 6 个专门研讨会和多次会议小型研讨会为基础，每年都会吸引至少 25 名长期驻场参观者。为期 5 周的研讨会每次都有 40 名或更多参与者，参与者包括应用数学科学领域的顶尖研究人员。来自美国的学生将被鼓励参加研讨会和长期项目，这种支持将提供与世界各地领先研究人员互动的持续机会。初级研究人员，既可以激发研究，也可以促进专业发展，从而帮助培养最优秀的年轻研究人员，这些研究人员将成为推动这一领域和其他应用数学领域研究的下一代应用数学家。统一的数学框架来描述色散介质中的多尺度非线性波现象，包括波传播的动态和随机方面，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学的研究主题结合在一起。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应用包括流体力学和远远超出了非线性光学、超流体（玻色-爱因斯坦凝聚体）、凝聚态物质和粒状晶体。这反映了 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。