When the Department of Defense offers researchers the chance to think big and take risks, and provides the funding to back it up, scientists tend to get really excited.

“That’s music to the ears of anyone doing basic research, the freedom to be able to go deep,” said Robert Ghrist, a Penn Integrates Knowledge professor with appointments in the University of Pennsylvania’s School of Arts & Sciences’ Department of Mathematics and the School of Engineering and Applied Science’s Department of Electrical and Systems Engineering.

He and Nader Engheta, the H. Nedwill Ramsey Professor in Penn Engineering, recently earned the chance to push their research further through a DOD award called the National Security Science and Engineering Faculty Fellowship, an honor only seven scientists across the country received in 2015.

For Ghrist, the Andrea Mitchell University Professor at Penn, that means $2.2 million dollars over five years to continue work on a field of math called algebraic topology. To explain it, he describes a cocktail party.

In the room full of people some are close to you and others are quite remote. What’s the exact distance to the nearest person? How far apart are conversations actually happening? In most cases, the precise numbers don’t matter as much as the proximity of one person to the next. Topology aims to understand the spaces between the people, the holes in the room, what types and how many there are.

The project Ghrist proposed extracts data at the local level to understand its global structure. On its own, the concept sounds abstract, but think for a minute about how cell phones work, for example.

“They communicate with each other wirelessly. If they don’t have a GPS or if they’re indoors or underground, they don’t have exact latitude and longitude coordinates,” he explained. “Nevertheless a collection of cell phones can determine how everyone is arranged: what the hallways look like, how many classrooms there are, how many floors in the building there are. These are all qualitative properties.”

In other words, topology can bring a level of order to a group of seemingly distinct items.

For his part, Engheta’s grant of $3 million over five years will further his decades of foundational work on the science of metamaterials. These compound materials are engineered with nanoscale patterns that give rise to properties not found in naturally occurring substances.  

“This award will provide me with an exciting opportunity to explore some of the fundamental aspects of science and engineering of extreme manipulation of light, sound and heat,” Engheta said.

Naturally occurring materials have electromagnetic properties that are determined by the internal arrangement of their atoms. By making structures out of multiple materials, arranged in patterns smaller than the wavelengths they are designed to operate on, otherwise impossible properties and behaviors can be achieved.

Engheta’s previous work has entailed building flat lenses, waveguides that can channel light around objects, effectively forming an “invisibility cloak,” and metamaterials that manipulate incoming light waves in a way analogous to how circuit elements manipulate the flow of electrons. The DOD award will extend Engheta’s work on using metamaterials as a kind of analog computer, among other applications.      

“This will provide new paradigms for novel applications in photonic information processing, phononic signals and thermal management,” Engheta said.