Finally, we know some of the math behind how birds flock

The infinite beauty and mystery of nature can’t help but make you think: math. In a new study, for example, an international team of researchers has discovered the previously unknown formula behind flocking, or at least a small part of the phenomenon, allowing us to finally harness nature’s ingenuity to achieve our own mechanical purpose.

This area of ​​research is important because animals are known to use movements such as air or water left behind by other members of the group to save energy needed to move or reduce drag, or drag, explains Leif Ristroff, NYU Library Lang Institute of Mathematical Sciences associate professor and senior author of the paper said in a statement.

The team limited their study to birds that move in columns, where groups of fliers line up directly behind each other, rather than attempt the more adventurous murmurings achieved by some birds. This should not be seen as a disadvantage, by the way, these motions can be very complex, similar to the quantum dynamics of superfluid helium, and even collecting enough data to model the equations can be very difficult.

In fact, previous studies of the mathematics behind aggregation have considered even fewer birds: only two were considered in a paper by the same team about five years ago. But the new paper shows how important broadening the scope of research is to understanding the movement of groups of these animals, as it turns out that the effects of the dynamics involved actually depend on the size of the group.

Sophie Ramananarivo, an assistant professor at Ecole Polytechnique and one of the paper’s authors, explained that aerodynamic interactions in a flock of small birds help each member maintain a certain position relative to its leading neighbor. kind of special location. But larger groups are disturbed by an effect that displaces members from these positions and can lead to conflict.

This observation was confirmed by the mechanical replica wings the team created to simulate a flock of birds, which were driven through water to simulate the airflow around real birds in flight.

Listrov explained that they found that the cutoff point is about four: with fewer people flying than this, aerodynamic interactions help everyone relative to everyone else. If a flyer strays from its position, he said, the vortex or vortex left by the leading neighbor helps push the follower back into position and hold it there. This means that leaflets can be automatically assembled into regularly spaced, ordered queues without any additional effort because physics does all the work.

More importantly, however, it becomes difficult to maintain formation. [The] Ristrov said water flow interactions can cause later members to be pushed around and lose position, often causing the flock to collapse due to collisions between members. This means that the very long colonies seen in some birds do not form easily at all.

The team found that, in essence, each bird was influenced by the bird before it but was unable to have any reciprocal influence on the bird before it. These waves, which the researchers call “frons,” accumulate through the column, so by the time we get to the end of the line, the birds may be oscillating violently: They may have to constantly try to maintain their position and avoid bumping into their neighbors, Riestero said. Husband explained.

While this is all great fun, is it particularly helpful to those of us without feathers? Well, actually, yes.What we found [] Joel Newbolt, a graduate student in physics at New York University, points out that this has some interesting connections to materials physics. [The] Birds in an ordered flock resemble atoms in a regular crystal.

Listrov added that the research could also have some more direct real-world implications.

He suggested that our work may also have applications in transportation, such as efficient propulsion through air or water, and energy, such as more efficiently harvesting energy from wind, currents or waves.

The research was published in the journal Nature Communications.