New research from New York University mathematicians indicates that schools of fish and flocks of birds move through environments by mimicking the behavior of soft crystalline materials. According to the study published in Physical Review Fluids, individual animals act as “atoms” in a lattice, maintaining orderly, repeating patterns that allow for rapid, collective responses to external stimuli like water currents or predators.
How do animal collectives maintain formation?
Birds and fish maintain their complex, columnar formations by utilizing flexible, spring-like bonds between individuals. Christiana Mavroyiakoumou, a researcher formerly at NYU’s Courant Institute and now a fellow at Oxford University’s Mathematical Institute, explains that this structure allows for a high degree of responsiveness. Because the formation behaves like a soft crystal, the group is inherently fragile, yet this fragility is precisely what enables the collective to adjust its shape instantly when faced with obstacles or shifts in the environment.
The “soft crystal” model suggests that the distance between birds or fish in a flock is not random, but follows a mathematical lattice similar to how atoms arrange themselves in solid matter.
What are the engineering applications for this discovery?
The findings provide a framework for advancements in aerospace engineering, robotics, and energy harvesting. Leif Ristroph, director of NYU’s Applied Mathematics Laboratory, notes that by understanding how these biological components interact, engineers may be better equipped to manipulate or design artificial systems that mirror these efficient, coordinated movements. The research builds on previous laboratory work which established that these creatures avoid collisions through specific aerodynamic and hydrodynamic interactions.
How was the mathematical model verified?
To test the crystalline theory, the research team—which included NYU undergraduate Jiajie Wu—utilized data from experiments involving “mock flocks.” These experiments employed 3D-printed plastic wings driven by motors to simulate the flapping of birds in water. By tracking how these mechanical flappers organized themselves into queues while moving through the water at varying speeds, the team confirmed that the physical behavior of the machines matched the predictions of their mathematical model.
When studying biomimicry in robotics, look for systems that prioritize “responsive fragility”—the ability to trade structural rigidity for the agility required to navigate changing environments.
Frequently Asked Questions
- Why do flocks and schools appear to be “fragile”?
According to Mavroyiakoumou, their organization is susceptible to deformations, which allows the group to quickly sense and react to external forces like air currents or predators. - What role does the “lattice” play in movement?
The lattice represents the orderly, repeating spacing between individuals, which acts as a framework for the entire group to move as a single, coordinated unit. - Who funded this research?
The study was supported by a grant from the National Science Foundation.
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