Patterns on a tropical fish might not seem like a chemistry problem, but Ankur Gupta has a knack for seeing—and describing—how the rules of physical chemistry explain the world around us.

By accounting for the way particles move in a chemical gradient—a phenomenon known as diffusiophoresis—the University of Colorado Boulder chemical engineer and his colleague Ben Alessio improved a model that mathematician Alan Turing developed to explain patterns in nature, such as the shape of a zebra’s stripes or the spacing of a jellyfish’s tentacles.

Gupta’s work on diffusiophoresis was part of his postdoctoral research with chemical engineer Howard Stone of Princeton University. Stone’s group has been exploring diffusiophoresis as a way to make clean water. In animal patterns, diffusiophoresis better accounts for sharp lines than Turing’s model did. Gupta is still thinking about where he might go with it.

The Turing patterns prompted Gupta to look for diffusiophoresis everywhere there are concentration gradients—and concentration gradients are everywhere in biology. Having considered diffusiophoresis across groups of cells in the Turing pattern work, Gupta is now thinking about gradients around individual cells. It’s possible that diffusiophoresis could help get drug molecules where they need to go, for instance.

The work on Turing patterns is not the main focus of Gupta’s lab, although it does look pretty. (Gupta has been thinking more about the way he presents his work, whose mathematical foundations can make for dry descriptions.) Broadly, his team uses mathematical equations to study how chemicals move. Most recently, the group explained the movement of ions in porous materials. Gupta’s intuition told him to step back from looking at a single pore to look at the whole network of pores.

That reminded him of the electronic circuits he learned about in high school. A set of equations called Kirchhoff’s laws describe the behavior of junctions in circuitry—principles Gupta modified to predict the movements of ions. A C&EN article described it as the “rules of the road for ions.”

Similar to the diffusiophoresis work, Gupta is examining fundamental effects that could have practical applications. For example, ions moving in and out of porous electrodes are the foundation of rechargeable batteries, which store energy from renewable sources and power electric vehicles.

Stone says that Gupta has a rare ability to intuit mathematical descriptions of physical processes: “Ankur can see in his mind how math and the physical world connect.”

Gupta is aware of how his relationship to math is maturing. He could tell early on that math came more easily to him than to others, including some of his teachers. A turning point came in his first physical chemistry class, when he discovered that chemistry could be precisely described with math.

That led him to transport phenomena—which deals mathematically with how mass, energy, and momentum are transferred—and chemical engineering. His first class on transport phenomena inspired the rest of his academic path. Gupta says there’s something irresistible about using math to demystify a physical process.

Math was a comforting common language when Gupta first came to the US from India for graduate school in 2012. “I could always think and talk with math,” he says.

More recently, Gupta has observed his sharpening instincts for equations—something he has admired in and learned from his academic role models. “Math has this intuitive quality if you do it enough,” he says. He senses without solving it how the terms in an equation relate to a physical phenomenon.

It’s not a solitary pursuit, either. His office features a wall-sized whiteboard on which he and his group can sketch out and discuss equations to describe the phenomenon they’re studying.

Gupta is quick to credit his students for some of the ideas that his name ends up attached to. He says questions students ask in his classroom lead him to understanding concepts in new ways. Because there’s another kind of movement that inspires him—that of ideas between people.