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Stanford researchers design a frugal way to study complex systems and materials

Illustration of droplet lattices that can be rapidly prototyped to study the role of geometry in macroscopic analogs of complex materials.

Illustration of droplet lattices that can be rapidly prototyped to study the role of geometry in macroscopic analogs of complex materials. (Image credit: Rebecca Konte, Resident Artist, Prakash Lab)

Nov 15 2021

By Taylor Kubota

To celebrate the 60th birthday of King Oscar II of Sweden and Norway in 1889, the journal Acta Mathematica offered a prize for manuscripts that could help solve the following question, generally referred to as the 3-body problem: Can we predict the orbits of planets, moons and other celestial bodies over time? Although mathematician Henri Poincaré was awarded the gold medal and 2,500 Swedish kronor prize for his submission (later found to have an error), the general analytical solution to the “n-body” problem has remained difficult to track. Beyond celestial mechanics, “n-body” problems occur in everything from how proteins fold to understanding complex materials.

While no single analytical insight has cracked these complex problems, various macroscopic analogies that replicate multi-body interaction and specific geometry of the problem are tremendously insightful. Among those, now, a simple table-top experimental method developed by Stanford University engineers in the lab of Manu Prakash, associate professor of bioengineering and Wu Tsai Neuro faculty affiliate. All that’s needed to begin is a slippery surface (say a glass slide), a permanent marker and a mixture of water and propylene glycol, a common ingredient in food coloring.

With these supplies, the researchers invented a new way to rapidly prototype complex geometries mirroring symmetries present in problems of interest. Instead of planets strewn about the solar system, many tiny droplets interact with each other at a distance and the observer can directly watch and manipulate how the system evolves over time. The researchers detailed their new method in a paper published Aug. 24 in Proceedings of the National Academy of Sciences.

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