Conference: Emergent Phenomena in Nonlinear Dispersive Waves

2024年7月22日至8月16日，英国剑桥艾萨克·牛顿研究所（Isaac Newton Institute）将在诺森比亚大学（Northumbria University）和位于泰恩河畔纽卡斯尔（Newcastle Upon Tyne）的纽卡斯尔大学（University of Newcastle）进行为期一个月的研究密集型卫星项目，名为“非线性色散波中的新兴现象”（Emergent phenomena in nonlinear dispersion waves， PDW）（参见项目网站https://www.newton.ac.uk/event/pdw/）。涌现的概念将在由非线性偏微分方程描述的动态、随机、多尺度色散波现象的背景下进行探讨。该计划将在任何给定时间接待大约35名长期住宿访客，并在为期一周的研讨会上接待60名或更多的参与者。多样化的国际参与者名单包括应用数学科学领域的主要研究人员。美国国家科学基金会奖为美国早期职业应用数学家参加研讨会和项目提供旅费支持。传统上在应用数学中代表性不足的群体将被鼓励申请。这种支持使我们有机会与来自世界各地的顶尖研究人员进行持续的互动。这样的互动和接触对于刚起步的研究人员来说是无价的，既可以激发研究，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，他们将推动这一领域和其他应用数学领域的研究。涌现是一个强大的概念，在理论和数学物理的许多领域起着重要作用。在一个由大量基本成分组成的系统中，例如经典粒子或量子粒子，可观察到的宏观行为可能是高度非平凡的。这种从短尺度到大尺度的转变是非均匀、动态多体状态的水动力理论的核心。当微观成分是波时，就会出现一种非常不同的流体力学。近年来，色散流体力学（非线性色散波中的多尺度现象理论）备受关注，是英国剑桥牛顿研究所2022年“色散流体力学”（HYD2）项目的重点。卫星PDW计划旨在利用成功的HYD2计划，探索与非线性波中出现现象的总体主题相关的色散流体动力学的新领域。PDW将特别关注三个高度协同的主题：(i)可积和不可积系统中的涌现流体动力学；（ii）非线性色散波的稳定性和不稳定波系中的涌现现象；(3)可积系统的孤子气体、广义流体力学和统计力学。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.