# What the Physics of Phase Transitions Can Teach us About Deadly Stampedes and Crushing Crowds

After the polar vortex that recently plunged much of North America into subzero temperatures, examples of stunning phase transitions abound. Videos of boiling water condensing into snow and supercooled water instantly crystalizing swept the internet alongside my personal favorite: bubbles freezing before your eyes.

Ajinkya Kulkarni, Sumesh Thampi, and Mahesh Panchagnula of the Indian Institute of Technology Madras (IITM) also have freezing on the mind, but for a very different reason. They study crowd control using a social force based model, which assigns fictitious forces to simulated “people” in order to use the same mathematics as in physics. “You kind of use the same nomenclature, use the same terminology, and you make analogies,” Panchagnula says, referring to the similarities between social forces and Newtonian forces.

Although this method can be applied to wide swaths of social sciences—market dynamics, for example—the IITM team’s research focuses on preventing fatal stampedes in evacuating crowds. Like other researchers before them, they distinguish between “ordered” crowd, where individuals are coordinated in moving towards a common exit or exits, and “disordered” crowds, where individuals are panicked and moving in random directions, resulting in gridlock. By assigning social forces such as an individual’s desire for personal space (which, it turns out, can be modeled as a spring force), the group was able to construct a mathematical framework for each scenario. They then used this framework to simulate both an ordered and a disordered crowd, and, crucially, the transition between the two in the hopes of identifying warning signs of an uncontrolled stampede.

These two videos show ordered (top) and disordered (bottom) crowd states. In the disordered state, individuals are locked into place, while in the ordered state the high level of coordination allows the individuals to arrange themselves into a vortex. (The vortex arises because there is no exit in this simulation.) Credit: Kulkarni et al.

Interestingly, they found that it was possible to have regions of asphyxia-inducing crowd pressure—known as a “crush”—in both scenarios, but the disordered state is much more dangerous since the gridlock drastically lowers people’s chance of escape. However, the biggest surprise came when they looked at the details of the order-to-disorder transition and realized it looked very familiar: it’s simply a first-order phase transition, exactly like bubbles freezing! “That’s a nice thing to know because all the physics we know associated with melting and solidification would apply here as well,” Panchagnula says with a grin.

This slow-motion video of a bubble freezing is very similar to the transition that takes place as communication breaks down in a moving crowd. At first, the liquid making up the surface of the bubble swirls around relatively smoothly, although some regions move faster than others. Soon, however, small crystals begin to form as the constituent molecules slow down and lock in place. These nuclei quickly spread across the entire surface of the bubble until all motion ceases—just like a panicked crowd is unable to make it to the exits. Credit: Adrian Ybarra

While the visuals are great, the most exciting implication of this finding is the fact that a first-order phase transition is reversible—after all, a little heat will warm that bubble up (or what’s left of it) in no time. By extending the analogy, the IITM group hoped they could find a way to push a dangerously slow-moving crowd back into an effective evacuation. To encourage such a transition, they introduced a small group of coordinated individuals termed “Game Changers” or GC into the model. In real life, these GC might be law enforcement or docents who are trained in evacuation plans, anyone who is able to nudge individuals in the right direction.

Running the simulation with GC in different locations, they were able to determine their optimal placement: precisely where the crowd would be moving fastest if it were moving at all. This depends on the geometry of a given enclosure, but for their simple model of a circular arena the GC are best placed around an imaginary ring 70% of the way between the center and the perimeter. Although they focused on a scenario where GC make up 10% of the overall crowd, they also managed to show that even when GC make up just 1% of the crowd the phase transition could be effectively reversed!

Of course, it’s difficult to say exactly how well this model approximates actual crowd behavior without performing experiments on an actual crowd—and that simply isn’t possible. “We’re looking at dense crowds,” Panchagnula explains. “We can never get ethical clearance to do a dense crowd controlled experiment here. It simply won’t happen!” Instead the group is restricted to analyzing video footage of real-life tragedies to see if the crowd behavior in those critical moments matches his expectations. Even that isn’t incredibly helpful though, since it’s not a controlled experiment. “It’s hard to get good data to simulate. Even in those situations, the geometry may not be very well defined for us to run a simulation post facto,” Panchagnula says.

Nevertheless, he hopes that emergency planners will look to the IITM model when deciding how to manage large crowds. “Let’s say you have a football stadium with eight outlets and individuals evacuating. You can use the model to predict the optimal placement of the exits, first, and the optimal placement of the police people, next.” he says. Since the model is already developed, all that’s needed is a little time to run the simulation given the specific geometry of the stadium.

So next time you’re caught up in a moving crowd, think of a shimmery bubble and be glad it’s well above freezing.

—Eleanor Hook