Herds of wildebeest, swarms of bees, and schools of fish all provide mesmerizing displays of coordinated motion. Fish, birds, and other animals numbering even in the millions can act as one not through centralized control, but through local actions and decisions, as each individual assesses the speed and orientation of its neighbors. This self-organization is reminiscent of other natural phenomena — the precise angles of repose of sandpiles, the magnetization of magnets, and the atomic order of crystalline solids, for example — so it seems an appropriate topic for biophysical investigation, and therefore #13 in the series of “What is biophysics?” posts. (Here are #1 and #12).
It turns out, however, that physics physics has a deeper relevance: physical principles suggest that the ability of animals to flock together is even more remarkable than one might think.
The struggle between order and disorder is ubiquitous. Often, some parameter like temperature decides the winner: crystalline ice at low temperature, for example, and liquid water with its molecules haphazardly arranged at high temperature, with a clearly delineated “phase transition” separating the two regimes. The wildebeest migrating on the savannah might prefer an ordered state, all facing the same direction, rather than chaos. We might imagine that the inaccuracy of a wildebeest’s evaluation of its neighbors’ directions plays a role analogous to temperature: too high and organized motion is impossible; low enough, and coherence emerges. How accurate does the wildebeest need to be?
The answer, surprisingly, is “perfectly accurate,” at least according to classic models of phase transitions. A wildebeest, I’m sure, is not infallible in its measurements, and yet the herd manages to organize itself, blissfully unaware of theory. How?
This scenario of wildebeest pointing together, or not, maps onto others that physicists have studied, such as whether the arrow-like “spins” of atoms align with their neighbors to make a material magnetic or not. There’s a particular temperature below which large-scale alignment occurs; for a three-dimensional chunk of iron, for example, it’s 770 degrees Celsius (1420 F). It turns out that for a two dimensional material (like atoms of one type occupying the surface of another substance) this critical temperature is zero. At any non-zero temperature, disorder will win. The wildebeest on the plain are constrained to two dimensions, thus the prediction of disorder for any but absolutely perfect wildebeest.
As mentioned, the wildebeest are, in fact, able to organize. The solution to the paradox is motion. One of my colleagues here at the University of Oregon, John Toner, along with another physicist, Yuhai Tu, figured out how motion leads to new possibilities for ordered phases about 25 years ago. For more about the hydrodynamics and phases of flocks, see “Hydrodynamics and phases of flocks” by Toner, Tu, and Ramaswamy, Annals of Physics 318 (2005) 170-244 Link. Prior to this analytic model, fascinating simulations suggested the link between motion and self-organization — see T. Vicsek, et al. “Novel Type of Phase Transition in a System of Self-Driven Particles.” Phys. Rev. Lett. 75, 1226-1229 (1995) Link. These simulations are easy and fun to write; perhaps I’ll revisit that in another post.
In three dimensions self-organization is less surprising, but nonetheless the movement of birds, bees, and fish makes their task easier than if they were still. More importantly, the connections between motion and animal collectives lead to forms of “matter” that are intriguingly different from passive forms. The influx of energy in the form of motion is key. Toner and co.’s extremely influential work launched a whole field of “active matter” that occupies many physicists today. Current work by physicists spans theory (as above) and also experiments and observations; see for example work by Andrea Cavagna and Irene Giardina.
Flocking and active matter, as fascinating as they are, didn’t make the cut for my pop-science biophysics book, though they fall under the umbrella of self-assembly that forms one of the book’s major themes. (Maybe if I write a sequel…) Nonetheless, here are the usual book links: My description, Publisher, Amazon.)
Today’s illustration: An egret. No, they don’t flock, but that’s what I felt like painting.
— Raghuveer Parthasarathy; January 5, 2023
The Eighteenth Elephant 