Maurizio Porfiri

A new discovery in physics could help engineers stabilize robots and structures without relying on complex sensors and control systems, and design metamaterials and network systems that are presently beyond reach.

The finding, published in Nature Communications by researchers at NYU Tandon School of Engineering and Stony Brook University, shows that a mechanical system can be kept stable simply by switching between two behaviors at the right rhythm, even when neither behavior is stable on its own. No sensors watching the motion. No software constantly correcting it.

Once the timing is set, the physics does the rest.

Many machines must constantly stabilize their motion — keeping a walking robot from tipping over or preventing an aircraft wing from vibrating uncontrollably. Robots and other actively controlled systems typically do this by monitoring their environment and correcting their motion in real time, which requires sensors, processing power and software.

To test an alternative, the researchers built what they informally call the Frankenstein oscillator: a thin plastic strip fixed at one end with a small weight at the tip, subject to multiple loading conditions.

They then created two different kinds of instability. A magnetic coil pushed the beam away from its resting position in a way similar to a ball balanced on a horse’s saddle: if it moves slightly off center, it slides away in certain directions. A small fan blew air across the strip, feeding energy into the motion so that its swings grew larger rather than fading away, similar to how a playground swing rises higher when someone pushes at the right moment.

Both forces were switched on and off in carefully timed pulses.

The result was striking. Stability appeared only within a narrow band of switching speeds, with periods between roughly 218 and 238 milliseconds. Inside that window the beam stayed nearly still. Outside it, the motion quickly grew and the beam swung away.

Why should switching between two unstable behaviors make anything stable?

The idea builds on Kapitza's pendulum, named after Russian Nobel laureate Pyotr Kapitza. Vibrate the base of an inverted pendulum at exactly the right frequency and it stays upright, with no one watching or adjusting. Unlike a person balancing a stick on one hand, constantly shifting to stop it from falling, Kapitza's pendulum requires no such attention. Physics takes over.

In the classic case, the vibration provides a stabilizing effect, making the system virtually alternate between one stable and one unstable state. The new research asked a different question: what would happen if there were no stable states at all, if the physics were always pushing the system away from its resting position?

The answer depends on the type of instability involved. The “sliding” type — like the ball on the saddle — has one special direction in which motion actually shrinks instead of growing. The “swinging” type continually rotates the motion through different directions.

If the switching is timed correctly, that rotation can steer the motion into the shrinking direction before it has time to run away. The two instabilities, surprisingly, end up stabilizing each other.

 “I have been thinking about the problem of stabilization of unstable systems through switching for over two decades,” said the paper’s senior author Maurizio Porfiri, an NYU Tandon Institute Professor and Director of both the NYU Urban Institute and the Center for Urban Science + Progress (CUSP). “In between ups and downs on the research, I was almost convinced that stabilization of two unstable systems would require some form of nonlinearity or even chaotic dynamics, but that is not the case: a simple, linear mechanical system can do the trick. The solution was in front of me for years, an extension of the marvelous ideas presented by Landau and Lifshitz in their Mechanics textbook that my uncle gave to me as a gift when I took my undergraduate dynamics class."

The researchers developed the theory first and then confirmed it experimentally with the beam. The narrow stability window they observed in the lab closely matched what the mathematical model predicted.

"Honestly, I had no belief that we would be able to demonstrate this phenomenon experimentally, as this involved working with a system that not only is unstable, but also features multiple sources of instability,” said Paolo Celli, Assistant Professor in Civil Engineering at Stony Brook University and co-corresponding author of the study. “The joy we felt when our carefully-designed experiment showed that narrow stability window is hard to explain. I am now super excited to see how this dynamic stabilization idea can be applied to other structural and robotic systems on the verge of instability"

The broader implication is a new design philosophy. Instead of always trying to eliminate instability, engineers may sometimes be able to build stable systems out of unstable pieces, harnessing the laws of physics rather than fighting them

The research was supported by the National Science Foundation through grants to both institutions. Along with Porfiri — who wrote about this research in a Behind the Paper post — and Celli, David Xiedeng — a Ph.D. student in Celli’s lab — is a co-author on the paper.

For as long as there have been humans, there have been migrations — some driven by the promise of a better life, others by the desperate need to survive. But while the world has changed dramatically, the mathematical models used to explain how people move have often lagged behind reality. A new study in PNAS Nexus from a team led by Institute Professor Maurizio Porfiri argues that the patterns of human movement can’t be fully understood without reckoning with inequality.

For decades, researchers have relied on models that treat all cities and regions as if they were equal. The “radiation” and “gravity” models, the workhorses of mobility science, describe migration as a function of population size and distance: how many people live in one place, and how far they have to go to reach another. These equations have been useful for predicting broad commuting and migration trends, but they share a blind spot: they assume that opportunities and living conditions are evenly distributed. In a world where climate change, war, and widening economic divides are shaping the way people move, that assumption no longer makes sense.

Porfiri and his colleagues built a new model that explicitly incorporates inequality. It assigns each location a different “opportunity distribution,” a measure of how attractive it is based on social, economic, or environmental conditions. Cities or towns suffering from war, poverty, or environmental disasters are penalized in the model; their residents are more likely to leave, and outsiders are less likely to move in. The result is a mathematical system that behaves more like the real world.

The team tested their model in two settings: South Sudan and the United States—places that could hardly be more different, yet both marked by deep disparities. In South Sudan, years of civil conflict and catastrophic flooding have displaced millions. The researchers assembled a new dataset that tracked these internal movements across the country’s counties between 2020 and 2021. When they compared their inequality-aware model to the traditional one, the difference was stark. The new approach captured how people fled not just from areas of violence but also from those hit hardest by floods, revealing the powerful influence of environmental stress on migration. In fact, flooding alone explained more of the observed migration patterns than conflict did.

In the United States, the researchers turned their attention to a more familiar form of movement: the daily commute. Using data from the American Community Survey, they explored how factors like income inequality, poverty, and housing costs shape commuting flows between counties. Once again, inequality mattered. The model showed that places where rent consumed a larger share of income, or where poverty was more widespread, had distinctive commuting patterns — ones that standard models could not explain.

What the study suggests is that mobility is as much a story of inequality as it is of geography. People do not simply move because of distance or population pressure; they move because some places have become unlivable, unaffordable, or unsafe. “Mobility reflects human aspiration, but also human constraint,” said Porfiri, who serves as Director of the Director of Center for Urban Science + Progress, Interim Chair of the Department of Civil and Urban Engineering, as well as Director of NYU’s Urban Institute. “Understanding both sides of that equation is crucial if we want to plan for the future.”

The implications are far-reaching. As climate change intensifies floods, droughts, and heat waves, and as economic gaps widen within and between nations, migration pressures are likely to grow. Models like this one could help policymakers anticipate where displaced people will go, and what stresses those movements might place on cities and infrastructure. They could also inform strategies to reduce inequality itself — by identifying which regions are most vulnerable to losing their populations, and which are absorbing more than they can sustain.

Alongside Porfiri, contributing authors include Alain Boldini of the New York Institute of Technology, Manuel Heitor of Instituto Superior Técnico, Lisbon, Salvatore Imperatore and Pietro De Lellis of the University of Naples, Rishita Das of the Indian Institute of Science, and Luis Ceferino of the University of California Berkeley. This study was funded in part by the National Science Foundation.

Alain Boldini, Pietro De Lellis, Salvatore Imperatore, Rishita Das, Luis Ceferino, Manuel Heitor, Maurizio Porfiri, Predicting the role of inequalities on human mobility patterns, PNAS Nexus, Volume 5, Issue 1, January 2026, pgaf407, https://doi.org/10.1093/pnasnexus/pgaf407