Conference: Emergent Phenomena in Nonlinear Dispersive Waves

英国剑桥艾萨克·牛顿研究所为期一个月的研究密集型卫星计划，题为“非线性色散波中的涌现现象”（PDW），将于2024年7月22日至8月16日在英国泰恩河畔纽卡斯尔的诺森比亚大学和纽卡斯尔大学举行（见计划网站https：//www.newton.ac.uk/event/pdw/）。出现的概念将在动态和随机，多尺度色散波现象的非线性偏微分方程描述的背景下进行探索。 该计划将在任何时间接待约35名长期居住的游客，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的主要研究人员。这个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旅行支持，以参加研讨会和计划。传统上在应用数学代表性不足的群体将被鼓励申请。这种支持使持续的机会与来自世界各地的领先研究人员进行互动。这种互动和接触对于刚开始的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，在理论物理和数学物理的许多领域都起着重要作用。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、动态多体状态的流体力学理论的核心。当微观成分是波时，就产生了一种非常不同的流体动力学。色散流体动力学的主题--非线性色散波中多尺度现象的理论--最近备受关注，也是英国剑桥艾萨克·牛顿研究所举办的2022年“色散流体动力学”（HYD 2）计划的重点。卫星PDW计划旨在利用成功的HYD 2计划，探索与非线性波中涌现现象的总体主题有关的色散流体动力学的新前沿。特别是，PDW将集中在三个高度协同的主题：（一）在可积和不可积系统的涌现流体动力学;（二）非线性色散波的稳定性和不稳定波系统中的涌现现象;（iii）孤立子气体，该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的知识产权评估的支持。优点和更广泛的影响审查标准。

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.