New research from mathematicians at New York University offers a detailed account of how large groups—bird flocks and fish schools—coordinate their motion. The study, published in Physical Review Fluids and building on earlier work from NYU’s Applied Mathematics Laboratory, proposes a mathematical model that likens these groups to a soft crystalline material.
In the model, individual animals act like atoms in a regular lattice, keeping roughly even spacing and interacting through flexible, spring-like bonds. This analogy explains why formations can be fragile and easily deformed yet still respond rapidly to changes in air or water flow or to nearby objects and predators. Courant researcher Christiana Mavroyiakoumou described the formations as similar to soft crystals, and Courant Professor Leif Ristroph said the work opens ways to analyse and possibly influence group interactions.
The team tested the model against earlier experiments, including trials with mechanized flappers that mimicked columnar formations. The flappers had 3D-printed plastic wings and were driven by motors to flap in water; the mock flock moved at different speeds and was free to rearrange itself in a line. The observed group behaviour matched the model’s predictions. The authors connect their findings to hydrodynamic and aerodynamic interactions and suggest relevance for aerospace and automotive engineering, robotics and energy harvesting. The study included NYU undergraduate Jiajie Wu and was supported by a grant from the National Science Foundation.
- Paper: Physical Review Fluids
- Model: soft crystalline analogy
- Tests: mechanized flappers in water
Difficult words
- lattice — regular network of points or connected elements
- analogy — comparison that shows similarity between two things
- fragile — easily broken, damaged, or disturbed
- deform — change shape or form under forcedeformed
- hydrodynamic — relating to forces and motion in fluids
- aerodynamic — relating to motion of air and forces
- mechanize — equip or operate using machinesmechanized
- rearrange — change the order or positions of parts
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Discussion questions
- How could treating flocks and schools like a soft crystal help engineers design better robots or vehicles? Give one or two possible examples.
- The article says formations can be fragile yet respond rapidly. What are possible benefits and risks of this fragile-but-responsive behaviour for animals in nature or for engineered systems?
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