Mathematics illuminates wee sensor assembly

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Understanding how molecules’ shape determines the patterns into which they aggregate gives nanoscientists a valuable tool as they design their experiments.

For example, circularly symmetric molecules in a plane will aggregate into patches, like Cheerios floating in milk.  Star-shaped molecules will aggregate into branched structures that nanoprocessing techniques can force into linear patterns.

Holm is extending the mathematics behind nanosensor construction in new directions.  Traditionally, mathematicians want to avoid singularities, he notes, because in many systems, they can indicate a problem in the original definition of a system or that the solution has broken down.

In this system, however, the mathematical singularity describes how the molecules are self-assembling, and the researchers are forced to examine these solutions further to tease out the mechanisms.

“We need this kind of solution in order to describe these nanoprocesses,” Holm says.  “And moreover we need to find the dynamics of these solutions, how they form, where they form, what their time dependence is and what happens after they form, because you may want to still move them and find out how they interact with each other.”

Holm’s work is extending applied mathematics by challenging conventional wisdom, an attitude he traces to his childhood.

“Sputnik happened the day I turned 10,” he says, and he and other gifted students in Minneapolis were launched into an accelerated and enriched math and science program.

When Holm was 13, an after-class discussion with his higher algebra teacher led him to stay up late, finding his own approaches to problems.

“What I discovered sometime in the middle of the night was that mathematics is a power that allows you to make your own rules,” Holm says.  “As long as your rules are consistent and you can explain them, no one can arbitrarily say they aren’t right.  As a kid, I was thrilled about creating new rules and seeing where they led.  And that’s the path I’ve always followed.”

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