CAREER: Mathematical Modeling, Physical Experiments, and Biological Data for Understanding Flow Interactions in Collective Locomotion

这个项目旨在了解在一起活动的动物，如鱼群和鸟群，如何利用游泳或飞行过程中产生的水或空气的流动，实现作为一个群体的利益，这是个人无法实现的。这些好处是通过每个人与其他人产生的流动相互作用而产生的，可以采取节省能源或提高速度的形式。还将探讨流动互动的更微妙的方面，如维持或保持群体，防止碰撞，建立个人的自然队形或模式，以及通过在群体中传播的运动进行交流。这项研究工作将结合对个人和周围流体(水或空气)运动的数学描述，对机动化游泳者或飞行者的“机器人群”进行的实验室实验，以及对鸟类编队飞行的视频片段的分析。不同的方法将允许完全理解一个群体中的流体动力相互作用，以及对动物如何利用或修改这种机制的洞察。因此，这项工作将澄清流动在动物群体中的作用，并在这样做的同时也表明如何在流动、能量收集和有效推进等应用中利用这种影响。此外，教育和外展计划将培训高中生、大学本科生和研究生进行STEM研究，特别是数学在自然科学和工程科学中的重要作用。具体地说，关于机械游泳者的物理实验，流动-运动相互作用模型和模拟，以及来自大众来源的生物数据将互动地结合在一起，并应用于理解编队游泳和飞行。研究将从对少体系统的详细询问开始，以便交叉验证所有方法并了解基本机制。实验和模拟将为基于涡旋-物体相互作用的模型提供信息，而与生物测量的比较将为鸟类编队飞行的行为模型提供信息。然后将研究串联阵列的多体系统，使用所有方法来理解原理，例如通过类比传统的物质状态，其中将探索诸如群凝聚、结晶或其他图案化、动态不稳定性和信息传输等方面。还将研究与生物相关的问题，包括自组织和集体优势，并将建立和测试结构和动态度量。教育工作将包括一门关于数学建模实验建设性互动的研究生课程，以及一个让纽约市贫困高中生参与STEM研究的暑期研究夏令营。所有级别的学生将从课程中招募，直接参与研究，更广泛的公众将通过众包活动作为公民科学家参与进来。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，被认为值得支持。

This project aims to understand how animals moving together, such as fish schools and bird flocks, make use of the flows of water or air generated during swimming or flying to achieve benefits as a group that are not possible as individuals. These benefits occur through interactions of each individual with the flows produced by others and may take the form of energy savings or speed enhancement. Also to be explored are more subtle aspects of flow interactions such as maintaining or holding together a group, preventing collisions, establishing natural formations or patterns of individuals, and communication through motions that spread across the group. The research work will combine mathematical descriptions of the motions of individuals and the surrounding fluid (water or air), laboratory experiments on "robotic flocks" of motorized swimmers or flyers, and the analysis of video footage of birds flying in formations. The different approaches will allow for a complete understanding of the fluid-dynamical interactions in a group as well as insights into how animals exploit or modify such mechanisms. The work thus stands to clarify the role of flows in animal groups and in so doing also suggest how such effects can be exploited in applications such as flow energy harvesting and efficient propulsion. Additionally, education and outreach programs will train high school students, university undergraduate and graduate students in STEM research and especially the important role of mathematics in the natural and engineering sciences.Specifically, physical experiments on mechanical swimmers, flow-locomotor interaction models and simulations, and crowd-sourced biological data will be combined interactively and applied towards understanding formation swimming and flying. Research will start with the detailed interrogation of few-body systems in order to cross-validate all approaches and to understand fundamental mechanisms. Experiments and simulations will inform models based on vortex-body interactions, and comparison against biological measurements will inform behavioral models in the context of formation flight of birds. Many-body systems of in-line arrays will then be studied, with all methods used to understand principles, for example through analogies to conventional states of matter, in which aspects such as group cohesion, crystallization or other patterning, dynamical instabilities, and information transfer will be explored. Biologically-relevant issues including self-organization and collective advantages will also be studied, and structural and dynamical metrics will be established and tested. The educational effort will include a graduate course on the constructive interaction of experiment with math modeling and a summer research camp that will engage underprivileged NYC high school students in STEM research. Students at all levels will be recruited from courses to become directly involved in research, and the wider public will be engaged as citizen-scientists through crowd-sourcing campaigns.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.