2023-05-06 17:00:09
The beautiful photograph, published in the April 28 issue of the prestigious Science, reveals a tangled mass made up of regarding 200 black worms, Lumbriculus variegatus. It illustrates an American study mixing mathematics, physics and biology. Vishal P. Patil, a mathematician from Stanford, California, and Harry Tuazon, a biologist at Georgia Tech in Atlanta, Georgia, have been trying to model how these worms manage to get tangled up in minutes and, more importantly, untangled in hundredths of a second.
Using an ordinary ultrasound machine, the researchers examined the interior of this living ball, recorded the helical movement of each animal – like endless screws – and put all this information into equations. This branch of mathematics – topology – is concerned with geometric objects that deform continuously without breaking, like elastic materials. According to the authors, this work will be useful for developing fibers that self-assemble in a reversible manner.
“The problem posed is interesting, because there are many types of materials in which fibers are intermingled. It might be polymers, DNA, or even wood,” observed mathematician Etienne Ghys, permanent secretary of the Academy of Sciences and regular columnist at The world. This subject harnesses the notion of nematics in physics, describing an intermediate state of matter between crystalline and liquid phases.
Spectacular videos
The species of aquatic earthworm chosen for the study lives near the water surface. These worms have the distinguishing feature of entangling themselves in a bundle to ensure biological functions such as maintaining a constant temperature to protect themselves from heat or cold, retain moisture, or to move in groups. They also have the ability to escape from this tangle very quickly, to flee a predator by spreading out or to protect themselves from environmental threats. Videos made by the researchers for their study show this in a spectacular way.
To translate the observation of this natural phenomenon into mathematical equations, they first modeled the movements of each Lumbriculus in two dimensions, and found that the helical movements sometimes shifted in one direction and sometimes in the other. They then built their dynamic 3D model. “The model reveals that alternating helical waves in resonance allow for both entanglement formation and ultrafast untangling,” they wrote. Each worm forms an entanglement with at least two others, and what looks like a bag of knots actually includes none.
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