Conference: Emergent Phenomena in Nonlinear Dispersive Waves

英国剑桥艾萨克·牛顿研究所将于2024年7月22日至8月16日在英国诺森布里亚大学和位于泰恩河畔纽卡斯尔的纽卡斯尔大学举行为期一个月的卫星研究密集项目，名为“非线性频散波中的紧急现象”(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式描述的动态和随机的多尺度频散波现象的背景下进行探索。该计划将在任何给定的时间接待大约35名长期居民访客，并在为期一周的研讨会上接待60名或更多的参与者。学员名单多样化，包括应用数学科学领域的顶尖研究人员。这项国家科学基金奖为来自美国的早期职业应用数学家参加研讨会和项目提供旅行支持。传统上在应用数学领域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互动。这种互动和接触对于初级研究人员来说是非常宝贵的，既可以激励研究，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。这些研究人员将是下一代应用数学家，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发挥着基础作用。在一个由非常多的基本成分组成的系统中，例如经典或量子粒子，可以观察到的宏观行为可以是非常不平凡的。这种从短尺度到大尺度的转变是非均匀动态多体状态流体力学理论的核心。当微观成分是波时，就会产生一种非常不同的流体动力学。弥散流体动力学的主题--非线性弥散波中的多尺度现象理论--最近引起了人们的极大关注，并成为在英国剑桥艾萨克·牛顿研究所举行的2022年“弥散流体动力学”(HYD2)计划的焦点。卫星PDW计划旨在利用成功的HYD2计划，探索与非线性波中涌现现象这一主要主题有关的弥散流体力学的新前沿。特别是，PDW将专注于三个高度协同的主题：(I)可积和不可积系统中的紧急流体动力学；(Ii)非线性频散波的稳定性和不稳定波系统中的紧急现象；(Iii)孤子气体、广义流体动力学和可积系统的统计力学。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，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.