Nikhil Bajaj received an NSF CAREER Award

Nikhil Bajaj, assistant professor in the Swanson School of Engineering’s Department of Mechanical Engineering and Materials Science, has spent much of his career on nonlinear systems — the kind whose behavior shifts sharply once a threshold is crossed.

Many of those systems depend on devices that exhibit bifurcation behavior, reading inputs and turning them into outputs in ways that can sharpen sensitivity or ease of use. And those similarities turn up across disciplines.

Bajaj has been awarded a $649,684 National Science Foundation Faculty Early Career Development (CAREER) Award to help him flip the usual design process on its head. Rather than building a system and asking what it will do, his goal is to start with a desired behavior and work backward to engineer the system that produces it, an approach he calls behavior-first design. The framework targets nonlinear systems such as micro-electro-mechanical systems (MEMS), including ultrasensitive gas-leak detectors capable of sensing hazardous compounds at parts-per-billion levels as well as energy harvesters and aerospace structures.

In a system with bifurcations, a quantitative change results in a qualitative change — that is, a change in the value of the input results in a change of the type of outcome. Once a certain threshold is met, the system doesn’t do more of what it was doing; it instead does something different. For example, a somewhat flexible column loaded with heavier and heavier weights will compress more and more, but once a specific load is placed on it, it will move in a different way, bulging out to one side or buckling.

Today, researchers can characterize these kinds of systems using a lot of trial and error and analogies to previous systems. “Say I’m building a car, and I want it to have 400 horsepower,” Bajaj said. If he didn’t know how to hit that number, he might take any engine and keep tweaking it — tightening something here, disconnecting a part there — until it worked. And horsepower is an easy case, a smooth dial you can turn up or down. The challenge multiplies when the goal is a threshold behavior: getting a system to switch into a new kind of motion at exactly the right input, and not a moment before.

“Designing in bifurcation behavior can feel a bit like working in the dark,” Bajaj said. Even so, the field has made remarkable progress. Across nonlinear systems, libraries of relationships have accumulated for many decades as researchers test inputs and observe outputs via theory and experiment. They’ve found that systems with bifurcations of all kinds — a wing vibrating erratically at speed, a material buckling under pressure, a neuron firing in the brain —seem to be governed by similar principles. The equations aren’t identical, but when systems engineers compare notes, they find meaningful similarities behind the different variables and outputs.

“We play the same mathematical games, just on different fields,” Bajaj said. At a nonlinear dynamics conference, he might have a specific engineering question on his mind. “But then I could run into someone doing the same thing on a biological system and I think, ‘I can use their method to apply to my problem.’”

Bajaj will use his CAREER Award to develop a unified computational framework for designing nonlinear systems from a desired behavior, rather than discovering their behavior through trial and error. “I want to pick all my parameters, all the knobs I can turn, so that it does the things I want it to do and not necessarily the things that are undesirable.” The framework is intentionally general; he will demonstrate the approaches on small and large scales — from MEMS gas sensors on the micrometer-scale to flutter in aircraft wings.