A mathematical model reveals that flocks of birds and schools of fish move like a soft crystal, with individuals acting as atoms bound by spring-like forces.
A team of mathematicians at New York University's Courant Institute of Mathematical Sciences has demonstrated that the coordinated movement of flocking birds and schooling fish follows the structural mechanics of soft crystalline materials. In this model, individual animals act like atoms bound by flexible, spring-like interactions, allowing formations to warp without breaking rank when avoiding predators or obstacles.
The research provides a new mathematical framework for interpreting collective biological coordination. Beyond biology, this framework has potential applications in low-drag automotive fleets, robotic swarms, and aerospace systems.
Methodology
The team modeled a flock or school as an elastic solid, akin to a soft crystal where the atomic arrangement is fragile and easily deformed. In single-file formations, each animal generates a fluid wake that regulates its distance from neighbors, functioning like a mechanical spring.
To validate the model, the researchers used a "mock flock" apparatus with 3D-printed wing foils in a water tank. The foils self-organized into evenly spaced formations, precisely as predicted by the theory.
Publication
The study was published in the journal Physical Review Fluids.