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

The United States recorded 28 natural disasters causing at least $1 billion in damages each in 2023, the highest number in the nation's history. Now researchers at NYU Tandon are helping develop a robotic system that could significantly reduce disaster recovery times while improving efficiency for contractors working in confined spaces.

Along with colleagues from New Jersey Institute of Technology, who led the project, and a researcher from The University of Scranton, the Tandon team led by Maurizio Porfiri and Semiha Ergan is part of a three-year, $5 million U.S. National Science Foundation (NSF)-funded project to create the Kastor robotic system. The funding comes from the NSF Directorate for Technology, Innovation and Partnerships, which supports research that brings together multiple disciplines and sectors to solve complex societal and operational challenges.

This Phase 2 award follows a previous $650,000 Phase 1 grant that developed a prototype robot and algorithms.

The Kastor robotic system uses swarms of self-assembling robots to transport equipment and clear debris in disaster zones, addressing a persistent challenge in disaster response: much of the workforce effort goes toward moving supplies and removing debris rather than critical tasks like searching for survivors.

The technology takes its design cues from fire ants and slime molds. Fire ants can link their bodies to form bridges over difficult terrain, while slime molds create efficient transport networks across varied surfaces. The Kastor system applies these biological strategies to create networks of flat metal robotic tiles that can autonomously reconfigure themselves as conditions change.

The tiles move themselves into position and use wheels and treads to transport pallets across disaster sites without human intervention. Algorithms developed by the research team guide their assembly and movement patterns.

Porfiri — who directs NYU's Center for Urban Science + Progress (CUSP) and is Institute Professor in the departments of Mechanical and Aerospace Engineering, Biomedical Engineering, and Civil and Urban Engineering (CUE) — brings expertise in urban science and virtual reality to the project. His role focuses on ensuring the technology integrates with existing disaster response workflows in urban environments.

Ergan — an associate professor in CUE, and on the faculty of CUSP, Institute of Design and Construction (IDC) Innovation Hub, and C2SMARTER transportation center — is leading virtual and on-site pilot studies that will test the system in realistic construction and recovery scenarios.

"Each community faces different challenges when disasters strike, and current response methods often require inefficient manual labor for debris removal and supply transport," Porfiri said. The project team has consulted with police officers, emergency responders, contractors and construction companies to understand operational requirements.

"We want to bring the high-tech automation of distribution facilities and smart warehouses to messy, unstructured outdoor environments," said Petras Swissler, an assistant professor of mechanical and industrial engineering at NJIT and the project's principal investigator.

Beyond disaster response, the researchers found the same challenges exist in construction projects, where efficiency improvements have lagged behind other industries.

"This technology will also assist at construction sites where space is tight and the ability to navigate in multiple directions while carrying dirt and construction materials is limited," Ergan said.  

The project will develop a production-ready robotic system, create interfaces for operators to control the robot swarms, and conduct pilot studies in both disaster response and construction settings. Along with Porfiri and Ergan, the other co-principal investigators are Simon Garnier, a biology professor at NJIT, and Jason Graham, a mathematics professor at The University of Scranton.

New York City offers nearly every type of medical specialist but provides fewer specialty healthcare providers per capita than smaller cities, according to a new study that challenges conventional assumptions about urban healthcare advantages and reveals a troubling paradox across America's largest metropolitan areas.

The research, published in Nature Cities, analyzed data from 1.4 million healthcare providers across 75 medical specialties in 898 metropolitan and micropolitan areas. The innovative approach combines urban scaling theory—which examines how city characteristics change with population size—with network science and economic geography to examine healthcare access in unprecedented detail.

Rather than treating healthcare as a single entity, the researchers examined each medical specialty separately, revealing that 88% exhibit what they call "sublinear scaling," meaning larger cities have proportionally fewer specialists per resident than smaller ones.

"We're discovering that the healthcare advantages of living in big cities may be an illusion when it comes to specialized care," explains lead researcher Maurizio Porfiri. "We all assume residents of large metropolitan areas have better access to healthcare than residents of smaller cities, but this is really true only for primary care services. Our findings suggest this assumption breaks down completely for medical specialists. A small city may not offer all the specialties of large cities, but in what it offers it may outperform them.”

Porfiri is an NYU Tandon Institute Professor with appointments in the Departments of Mechanical and Aerospace Engineering (MAE), Biomedical Engineering (BME), Civil and Urban Engineering (CUE), and Technology Management and Innovation (TMI). He also serves as Director of the NYU Center for Urban Science + Progress (CUSP).

The study represents the latest application of Porfiri's urban scaling methodology, which he has previously used to analyze gun violence patterns and the relationship between city living, ADHD and obesity. His research uses Scale-Adjusted Metropolitan Indicators (SAMIs) to control for population differences and reveal how cities deviate from expected patterns.

The study found that while cities like New York and Chicago offer nearly all examined specialties (NYC has 74 — missing only anesthesiology assistants — and Chicago has all 75), residents may face longer wait times and specialists higher patient loading.

In contrast, smaller cities may lack certain specialties entirely—73 of the 75 specialties showed significant associations between availability and population size—but those that exist serve fewer patients per provider. For example, Marshfield, Wisconsin provides 16.8 specialists per 1,000 residents compared to New York's 4.7 per 1,000.

Among the most underrepresented specialties in large cities per capita are addiction medicine, preventive medicine, osteopathic manipulative medicine, and micrographic dermatologic surgery.

Addiction medicine shows the starkest disparity, with large cities providing dramatically fewer specialists per resident than smaller areas. These fields showed the strongest sublinear scaling, meaning residents of major metropolitan areas have significantly fewer of these specialists available relative to their population size compared to smaller cities.

The research identifies two mechanisms driving this paradox: higher patient loads overwhelming specialists in large cities, and economic clustering that concentrates medical expertise in dense hospital networks, creating geographic inequalities.

“The findings have serious implications as the U.S. population ages. The study found sublinear scaling in geriatric specialties like urology and gerontology, suggesting major metropolitan areas may be unprepared for growing elderly populations,” said Tian Gan, a NYU Tandon mechanical engineering PhD student in the urban science track, and the paper’s lead author.

Geographic patterns reveal stark regional disparities. The highest specialist concentrations cluster in the Midwest—Minnesota alone claims two of the top five cities—while all five cities with the lowest access are in the South.

Not all specialties follow this pattern. Several key specialties—including anesthesiology, internal medicine, and clinical psychology—actually have more providers per capita in large cities, reflecting higher urban demand for these services.

The research provides a framework for understanding healthcare distribution that moves beyond the traditional urban-rural dichotomy. Rather than viewing cities as uniformly advantaged, policymakers must consider the complex interplay between diversity and provision of medical services.

Along with Porfiri and Gan, the paper's additional author is Tanisha Dighe, NYU Tandon MS student in applied urban science and information. The study was supported by National Science Foundation grants.

APPENDIX: Medical Specialist Availability by City

CITIES WITH THE MOST MEDICAL SPECIALISTS (Cities offering all specialty types)

1. Chicago-Naperville-Elgin, IL-IN: 75 specialties
2. Houstone-Pasadena-The Woodlands, TX: 75 specialties
3. Atlanta-Sandy Springs-Roswell, GA: 75 specialties
4. Washington-Arlington-Alexandria, DC-VA-MD-WV: 75 specialties
5. Miami-Fort Lauderdale-West Palm Beach, FL: 75 specialties

CITIES WITH THE FEWEST MEDICAL SPECIALISTS (Fewest specialty types available)

1. Monroe, LA: 5 specialties
2. Zapata, TX: 6 specialties
3. Raymondville, TX: 6 specialties
4. Synder, TX: 11 specialties
5. Andrews, TX: 11 specialties

CITIES WITH THE HIGHEST CONCENTRATION OF SPECIALISTS OVERALL (All non-primary-care specialists combined per 1,000 residents)

1. Rochester, Minnesota: 21.1 specialists (home to Mayo Clinic)
2. Marshfield, Wisconsin: 16.8 specialists
3. Sunbury, Pennsylvania: 16.3 specialists
4. Easton, Maryland: 15.7 specialists
5. Albert Lea, Minnesota: 15.4 specialists

CITIES WITH THE LOWEST CONCENTRATION OF SPECIALISTS OVERALL (Fewest specialists per 1,000 residents)

1. Monroe, Louisiana: 0.1 specialists
2. Virginia Beach-Norfolk, Virginia: 0.4 specialists
3. Danville, Virginia: 0.8 specialists
4. Rio Grande City-Roma, Texas: 1.0 specialists
5. Bonham, Texas: 1.0 specialists

SPECIALTIES MOST UNDERREPRESENTED IN MAJOR METROS, 1M+ POPULATION

(Scaling exponents - how fast they grow with population growth )

1. Addiction Medicine (0.305) - Most underrepresented
2. Preventive Medicine (0.331)
3. Osteopathic Manipulative Medicine (0.351)
4. Micrographic Dermatologic Surgery (0.379)
5. Maxillofacial Surgery (0.398)
6. Marriage and Family Therapist (0.400)
7. Nuclear Medicine (0.408)
8. Advanced Heart Failure and Transplant Cardiology (0.446)
9. Certified Clinical Nurse Specialist (0.457)
10. Sleep Medicine (0.457)

SPECIALTIES MOST OVERREPRESENTED IN MAJOR METROS

(Scaling exponents - - how fast they grow with population growth)

1. Anesthesiology (1.154) - Most overrepresented
2. Internal Medicine (1.100)
3. Physical Therapy (1.089)
4. Clinical Psychology (1.069)
5. Physician Assistant (1.057)
6. Obstetrics/Gynecology (1.050)
7. Neurology (1.039)
8. Psychiatry (1.031)
9. Gastroenterology (1.022)

NYC SPECIALIST COUNTS (74 out of 75 research specialties)

Missing only: Anesthesiology Assistant

Top 10:

1. Nurse Practitioner: 8,977
2. Internal Medicine: 8,194
3. Physical Therapy: 7,515
4. Physician Assistant: 6,224
5. Clinical Social Worker: 4,842
6. Anesthesiology: 3,637
7. Family Practice: 3,259
8. Diagnostic Radiology: 2,843
9. Emergency Medicine: 2,545
10. Psychiatry: 2,465

Notable underrepresented specialties (bottom 5):

70. Maxillofacial Surgery: 40
71. Micrographic Dermatologic Surgery: 25
72. Preventive Medicine: 21
73. Marriage and Family Therapist: 18
74. Addiction Medicine: 16

Gan, T., Dighe, T. & Porfiri, M. Trade-off between diversity and provision of specialized healthcare in US cities. Nat Cities (2025).