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

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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.