MIT instructor Karol Bacik and his colleagues studied the flow of human crowds and developed a first-of-its-kind way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.

In a paper appearing in the Proceedings of the National Academy of Sciences, the researchers consider a common scenario in which pedestrians navigate a busy crosswalk. The team analyzed the scenario through mathematical analysis and simulations, considering the many angles at which individuals may cross and the dodging maneuvers they may make as they attempt to reach their destinations while avoiding bumping into other pedestrians along the way.

The researchers also carried out controlled crowd experiments and studied how real participants walked through a crowd to reach certain locations. Through their mathematical and experimental work, the team identified a key measure that determines whether pedestrian traffic is ordered, such that clear lanes form in the flow, or disordered, in which there are no discernible paths through the crowd. Called “angular spread,” this parameter describes the number of people walking in different directions.

If a crowd has a relatively small angular spread, this means that most pedestrians walk in opposite directions and meet the oncoming traffic head-on, such as in a crosswalk. In this case, more orderly, lane-like traffic is likely. If, however, a crowd has a larger angular spread, such as in a concourse, it means there are many more directions that pedestrians can take to cross, with more chance for disorder.

In fact, the researchers calculated the point at which a moving crowd can transition from order to disorder. That point, they found, was an angular spread of around 13 degrees, meaning that if pedestrians don’t walk straight across, but instead an average pedestrian veers off at an angle larger than 13 degrees, this can tip a crowd into disordered flow.

“This all is very commonsense,” says Bacik, who is a instructor of applied mathematics at MIT. “The question is whether we can tackle it precisely and mathematically, and where the transition is. Now we have a way to quantify when to expect lanes — this spontaneous, organized, safe flow — versus disordered, less efficient, potentially more dangerous flow.”

The study’s co-authors include Grzegorz Sobota and Bogdan Bacik of the Academy of Physical Education in Katowice, Poland, and Tim Rogers at the University of Bath in the United Kingdom.

Right, left, center

Bacik, who is trained in fluid dynamics and granular flow, came to study pedestrian flow during 2021, when he and his collaborators looked into the impacts of social distancing, and ways in which people might walk among each other while maintaining safe distances. That work inspired them to look more generally into the dynamics of crowd flow.

In 2023, he and his collaborators explored “lane formation,” a phenomenon by which particles, grains, and, yes, people have been observed to spontaneously form lanes, moving in single-file when forced to cross a region from two opposite directions. In that work, the team identified the mechanism by which such lanes form, which Bacik sums up as “an imbalance of turning left versus right.” Essentially, they found that as soon as something in a crowd starts to look like a lane, individuals around that fledgling lane either join up, or are forced to either side of it, walking parallel to the original lane, which others can follow. In this way, a crowd can spontaneously organize into regular, structured lanes.

“Now we’re asking, how robust is this mechanism?” Bacik says. “Does it only work in this very idealized situation, or can lane formation tolerate some imperfections, such as some people not going perfectly straight, as they might do in a crowd?”

Lane change

For their new study, the team looked to identify a key transition in crowd flow: When do pedestrians switch from orderly, lane-like traffic, to less organized, messy flow? The researchers first probed the question mathematically, with an equation that is typically used to describe fluid flow, in terms of the average motion of many individual molecules.

“If you think about the whole crowd flowing, rather than individuals, you can use fluid-like descriptions,” Bacik explains. “It’s this art of averaging, where, even if some people may cross more assertively than others, these effects are likely to average out in a sufficiently large crowd. If you only care about the global characteristics like, are there lanes or not, then you can make predictions without detailed knowledge of everyone in the crowd.”

Bacik and his colleagues used equations of fluid flow, and applied them to the scenario of pedestrians flowing across a crosswalk. The team tweaked certain parameters in the equation, such as the width of the fluid channel (in this case, the crosswalk), and the angle at which molecules (or people) flowed across, along with various directions that people can “dodge,” or move around each other to avoid colliding.

Based on these calculations, the researchers found that pedestrians in a crosswalk are more likely to form lanes, when they walk relatively straight across, from opposite directions. This order largely holds until people start veering across at more extreme angles. Then, the equation predicts that the pedestrian flow is likely to be disordered, with few to no lanes forming.

The researchers were curious to see whether the math bears out in reality. For this, they carried out experiments in a gymnasium, where they recorded the movements of pedestrians using an overhead camera. Each volunteer wore a paper hat, depicting a unique barcode that the overhead camera could track.

In their experiments, the team assigned volunteers various start and end positions along opposite sides of a simulated crosswalk, and tasked them with simultaneously walking across the crosswalk to their target location without bumping into anyone. They repeated the experiment many times, each time having volunteers assume different start and end positions. In the end, the researchers were able to gather visual data of multiple crowd flows, with pedestrians taking many different crossing angles.

When they analyzed the data and noted when lanes spontaneously formed, and when they did not, the team found that, much like the equation predicted, the angular spread mattered. Their experiments confirmed that the transition from ordered to disordered flow occurred somewhere around the theoretically predicted 13 degrees. That is, if an average person veered more than 13 degrees away from straight ahead, the pedestrian flow could tip into disorder, with little lane formation. What’s more, they found that the more disorder there is in a crowd, the less efficiently it moves.

The team plans to test their predictions on real-world crowds and pedestrian thoroughfares.

“We would like to analyze footage and compare that with our theory,” Bacik says. “And we can imagine that, for anyone designing a public space, if they want to have a safe and efficient pedestrian flow, our work could provide a simpler guideline, or some rules of thumb.”

This work is supported, in part, by the Engineering and Physical Sciences Research Council of UK Research and Innovation.

The peer-reviewed study found that electricity serving primary needs, such as heating or lighting, ultimately costs three times more than electricity for tertiary needs such as long-distance mobility — mostly due to taxation policies.

Further highlighting the ongoing social inequalities of fuel and related policies, the findings also demonstrate within the European Union (EU), the wealthiest 1% of all its population is responsible for 66% of the distance currently travelled by air. In fact, air travel is almost non-existent for 50%, and even quite limited for 90% of EU citizens the paper shows.

This 90% of people, therefore, emit less than 0.1 ton of CO₂ equivalent emissions per person, per year. Meanwhile the top 1% emit more than 22 tons per person/year.

Dr Jean-Baptiste Jarin, from the TREE laboratory (Energy and Environment Transitions) at the University of Pau and Pays de l’Adour, who carried out the research, used France as an example of current and future electricity use as a basis for similar countries worldwide — especially across Europe. And although based on EU regulations applied to France, the methodology and conclusions of this study can be transposed to other countries, and to other energy carriers based on electricity, such as hydrogen.

To evaluate the impacts of these electricity tax schemes and final prices, he collected data on electricity consumption for primary (household), secondary (electric vehicle local mobility) and tertiary (e-fuel long distance mobility) needs, and then compared electricity prices, before and after taxation.

Results demonstrate:

• Electricity serving household and local mobility needs cost 194 €/Mwh (euros per megawatt-hour). This was three times more than e-fuel (synthetic sustainable aviation fuels, that are renewable jet fuels produced from fossil-free electricity and recycled carbon dioxide) for aviation — 65.5 €/Mwh.
• Tax policies accounted for 120 €/Mwh of this cost in the case of household and local mobility fuel needs but only 11.2 €/Mwh in the case of aviation.
• Electro-intensive facilities that produce aviation e-fuel benefit from little or no taxation, and jet fuel is also untaxed.
• A round trip by air between Paris and New York for one person, when using this low carbon (which is designed to be more eco-friendly) e-fuel, still requires 7,300 kWh — exceeding the total annual primary and secondary needs (5,000 kWh) of an individual.

The European Union recently introduced the obligation to incorporate e-fuels for aviation as soon as 2030. In the UK, this obligation is as soon as 2028; in-line with its Renewable Transport Fuel Obligations Order 2024.

Dr Jarin has 25 years of experience in the aviation industry, prior to his career in academia. He recommends to key policymakers that ahead of any transformational policies and strategies, aimed at achieving low emissions in aviation, provisions should be made to “not interfere with energy justice.”

Additionally, he indicates that future taxation rates should become proportional to the final purpose of the energy, and this principle should be a “pillar of energy justice.”

Commenting, Dr Jarin says: “As e-fuel, along with other energy carriers based on electricity, is still within its infancy, it’s time for policy-makers to address the potential social injustices which may arise when formulating e-fuel policies.

“Electricity for basic needs such as heating or cooking benefits everyone but using it for air mobility mostly benefits the upper classes. Taxation rates should be proportional to the final purpose of the energy, and policies should drive not only production but also consumption, within a distributive justice perspective.”

Dr Jarin adds: “And that is what I find most worrying about the findings from within my paper, that, essentially, low carbon policies could foster energy injustice to people across society.

“Sadly, a massive production of e-fuel — especially when dedicated to aviation — could mean that tax inequalities, along with volume inequalities, spread the gap between the very wealthiest and the rest. That is why policy makers need to pay close attention.

“I feel that most people perhaps do not yet understand that energy, and therefore electricity, especially when low carbon, is not gifted!

“In the Global South, but also within the EU, during winters of 2022 and 2023, electricity bills were so high in most EU countries that people had to — and even were asked to by some — reduce heating and other appliances consumptions.”

Limitations of the paper include that while all EU countries follow the same tax directive on energies, the focus is limited to France and since electricity prices in Europe vary for each country, the results, when expressed in €/MWh, could be slightly different.

Also, carbon tax and redistribution mechanisms are not addressed in this study, and “where to tax within the value chain remains an important issue,” Dr Jarin adds.

“This,” Dr Jarin says, “is a particularly important issue as low carbon electricity with high load factor is a must to produce e-fuel.

“As such, the EU has significant assets to become a potential producer, rather than a potential importer.”

Researchers at Indiana University and Wuhan University in China have unveiled a groundbreaking chemical process that could streamline the development of pharmaceutical compounds, chemical building blocks that influence how drugs interact with the body. Their study, published in Chem, describes a novel light-driven reaction that efficiently produces tetrahydroisoquinolines, a group of chemicals that play a crucial role in medicinal chemistry.

Tetrahydroisoquinolines serve as the foundation for treatments targeting Parkinson’s disease, cancer, and cardiovascular disorders. These compounds are commonly found in medications such as painkillers and drugs for high blood pressure, as well as in natural sources like certain plants and marine organisms.

Traditionally, chemists have relied on well-established but limiting methods to synthesize these molecules. The new research, co-authored by Kevin Brown, the James F. Jackson Professor of Chemistry in the College of Arts and Sciences at Indiana University Bloomington, and Professors Xiaotian Qi, Wang Wang, and Bodi Zhao of Wuhan University, presents a fundamentally different approach.

How It Works: Light as a Chemical Tool

Instead of using traditional chemical reactions, scientists harness light to trigger a process called photoinduced energy transfer, wherein light initiates a controlled reaction between sulfonylimines (a type of chemical compound) and alkenes (another type of compound), leading to the creation of tetrahydroisoquinolines — a type of complex molecule. This method allows for the development of new structural patterns in the molecules, which were previously difficult or impossible to create using other methods, offering a more efficient way to make complex molecules.

“The key innovation in this study is the use of a light-activated catalyst, a special molecule that speeds up the reaction without being used up itself,” said Professor Brown. “Traditional methods require high temperatures or strong acids — like trying to cook food with a blowtorch instead of a stove. These harsh conditions can sometimes create unwanted side reactions, or make the process less useful for certain chemicals. The new process, however, uses molecules that respond to light, and can bypass heating by access new energy states. This makes the reaction cleaner, more efficient, and less likely to create unwanted byproducts.”

Brown and colleagues also found that tiny changes in the location of electrons within the starting materials had a huge impact on how the reaction played out — akin to if these electrons were puzzle pieces that needed to fit together just right. By tweaking the shapes of these pieces, the scientists made sure that only the desired product was formed, making the process highly selective. This is crucial for making medicines, where even a small mistake in a molecule’s structure can turn a helpful drug into something useless or even harmful.

Implications for Medicine and Other Industries

“The ability to create a wider range of tetrahydroisoquinoline-based molecules means that medicinal chemists can now explore new drug candidates for treating diseases like Parkinson’s, certain types of cancer, and heart conditions,” noted Professor Qi. “Right now, some diseases have very few effective treatment options, and this method could help scientists discover new and better drugs more quickly.”

Beyond pharmaceuticals, this research could also impact other industries that rely on fine chemicals. In agriculture, for example, similar chemical reactions could be used to develop more effective pesticides or fertilizers. In materials science, it could help create new synthetic materials with specific properties, such as better durability and longevity and greater resistance to heat for the aerospace, automotive, electronics, and medical industries.

The researchers plan to fine-tune the reaction conditions, meaning, they will experiment with different ingredients and settings to make the improve the process further. They also aim to find out if this method can work on even more types of molecules, expanding its usefulness. In addition, they hope to partner with pharmaceutical companies to test whether this technique can be used to produce medicines, potentially leading to new drug discoveries that could make a difference in people’s lives.

“This approach gives chemists a powerful new tool,” said Professor Brown. “We hope especially it will open the door to the development of new and improved therapies for patients around the world.”

As the field of photochemistry continues to expand, innovations like this may redefine how medicines and essential chemicals are made, paving the way for faster, cleaner, and more efficient production methods.