Think of it as mathematics with a bite: Researchers at CU Boulder have uncovered the statistical rules that govern how gigantic colonies of fire ants (Solenopsis invicta) form bridges, ladders and floating rafts.

In a new study, a team led by CU Boulder's Franck Vernerey set out to understand the engineering principles that underlie self-assembled structures of fire ants - each one containing hundreds to thousands of insects or more. Specifically, the researchers wanted to lay out how those structures become so flexible, changing their shapes and consistencies in seconds.

To do that, they used statistical mechanics to calculate the way that ant colonies respond to stresses from outside, shifting how they hang onto their neighbors based on key thresholds.

The findings may help researchers understand other "dynamic networks" in nature, including cells in the human body, said Vernerey, an associate professor in the Department of Mechanical Engineering.

Such networks "are why human bodies can self-heal," Vernerey said. "They are why we can grow. All of this is because we are made from materials that are interacting and can change their shape over time."

The study, published last week in the Journal of the Royal Society Interface, could also help engineers to craft new smart polymers and swarming robots that work together seamlessly.

Fire ants are "a bio-inspiration," said Shankar Lalitha Sridhar, a graduate student in mechanical engineering at CU Boulder and a coauthor of the new study. The goal is "to mimic what they do by figuring out the rules."

The team first drew on experimental results from Georgia Tech University that demonstrated how ant colonies maintain their flexibility through a fast-paced dance. Those experiments showed that individual ants hang onto the insects next to them using the sticky pads on their feet. But they also don't stay still: In a typical colony, those ants may shift the position of their feet, grabbing onto a different neighbor every 0.7 seconds.

The researchers from CU Boulder then turned to mathematic simulations to calculate how ant colonies manage that internal cha-cha.

They discovered that as the forces, or shear, on ant colonies increase, the insects pick up their speed. If the force on an individual ant's leg hits more than eight times its body weight, the insect will compensate by switching between its neighbors twice as fast.

"If you start increase your rate of shear, then you will start stretching their legs a little bit," Vernerey said. "Their reaction will be, 'oh, we are being stretched here, so let's exchange our turnover rate.'"

But if you keep increasing the forces on the ants, they can no longer keep up. When that happens, the ants will stop letting go of their neighbors, and instead hold on for dear life.

"Now, they will be so stressed that they will behave like a solid," Vernerey said. "Then at some point you just break them."

The researchers explained that they've only just scratched the surface of the mathematics of fire ant colonies. But their calculations are general enough that researchers can already begin using them to explore designs for new dynamic networks, including molecular machines that deliver drugs directly to cells.

Research paper

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