Conference: Emergent Phenomena in Nonlinear Dispersive Waves

会议：非线性色散波中的涌现现象

• 批准号: 2339212
• 负责人: Mark Hoefer
• 金额: $ 1.5万
• 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: 2024
• 资助国家: 美国
• 起止时间: 2024-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2339212&HistoricalAwards=false
• 关键词: Conference; Emergent; Phenomena; Nonlinear; Dispersive

A one-month research-intensive satellite program by the Isaac Newton Institute, Cambridge, UK titled "Emergent phenomena in nonlinear dispersive waves" (PDW) will be held at Northumbria University and the University of Newcastle in Newcastle Upon Tyne, UK from July 22–August 16, 2024 (see the program website https://www.newton.ac.uk/event/pdw/). The concept of emergence will be explored in the context of dynamic and stochastic, multiscale dispersive wave phenomena described by nonlinear partial differential equations. This program will host approximately 35 long-term, residential visitors at any given time and 60 or more participants in a one-week workshop. 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 workshop and the program. Traditionally underrepresented groups in applied mathematics will be encouraged to apply. This support enables sustained opportunities to interact with leading researchers from around 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.Emergence is a powerful concept that plays a fundamental role in many areas of theoretical and mathematical physics. In a system composed of a very large number of elementary constituents, e.g. classical or quantum particles, the observable macroscopic behavior can be highly nontrivial. This transition from short-to-large scales is at the heart of hydrodynamic theories for inhomogeneous, dynamic many-body states. A very different kind of hydrodynamics arises when the microscopic constituents are waves. The subject of dispersive hydrodynamics—the theory of multiscale phenomena in nonlinear dispersive waves—has attracted much attention recently and was the focus of the 2022 "Dispersive Hydrodynamics" (HYD2) program held at the Isaac Newton Institute, Cambridge, UK. The satellite PDW program aims to capitalize on the successful HYD2 program to explore new frontiers of dispersive hydrodynamics in relation to the overarching theme of emergent phenomena in nonlinear waves. In particular, PDW will focus on three highly synergistic themes: (i) emergent hydrodynamics in integrable and nonintegrable systems; (ii) stability of nonlinear dispersive waves and emergent phenomena in unstable wave systems; (iii) soliton gas, generalized hydrodynamics and statistical mechanics of integrable systems.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.

英国剑桥市艾萨克·牛顿研究所（Isaac Newton Institute）的一个月研究密集型卫星计划，名为“非线性色散波的新兴现象”（PDW）（PDW）将在诺森比亚大学和纽卡斯尔的纽卡斯尔在英国纽卡斯尔的纽卡斯尔，英国，7月22日至2024年7月22日至2024年（请参阅2024年7月22日） https://www.newton.ac.uk/event/pdw/）。出现的概念将在动态和随机，多尺度分散波现象的背景下进行探讨。该计划将在任何给定时间举办大约35个长期的居民，在为期一周的研讨会中举办60名或更多参与者。参与者的多样性，国际阵容包括应用数学科学领域的主要研究人员。该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。这种互动和联系对于开始研究人员的启发和专业发展是无价的，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，他们推进了这一目标，而其他研究人员则应用了数学研究领域。杰出是一个有力的概念，在理论和数学物理学的许多领域都起着基本作用。在由大量基本宪法组成的系统中，例如经典或量子颗粒，可观察到的宏观行为可能是高度不平凡的。从短到大尺度的过渡是不均匀，动态多体状态的流体动力学理论的核心。当微观构成是波浪时，就会出现一种非常不同的流体动力。分散流体动力学的主题 - 非线性分散波中的多尺度现象的理论 - 最近引起了很多关注，并且是2022年在英国坎布里奇Isaac Newton Institute举行的2022年“分散流体动力学”计划（HYD2）计划的重点。卫星PDW计划旨在利用成功的HYD2计划，以探索与非线性波中新兴现象的总体主题有关的分散流体动力学的新领域。特别是，PDW将专注于三个高度协同的主题：（i）在可集成和不可整合系统中的新兴流体动力学； （ii）在不稳定波系统中非线性色散波和新兴现象的稳定性； （iii）孤子气体，广泛的流体力学和可集成系统的统计力学。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准通过评估来支持的。