Mechanisms for high-density collective motion


Mass gatherings are usually safe, but sometimes things go wrong.

For the most part, concerts, protests, rallies, inaugurations, black Friday sales events, pilgrimages, festivals, and sporting events come and go with little or no injuries.  From time-to-time, however, the event takes a turn for the worse, and we hear stories of medical emergencies and tragic outcomes.  For example, “crowd crush,” an increase in pressure that reaches levels so high that people are asphyxiated, is particularly worrisome because it happens suddenly and without warning.  But how do these disasters happen?  Aren’t people generally good natured?  Why would anyone want to hurt someone else?

Well, the truth is, many of these mass gathering disasters aren’t driven by malicious intent.  Instead, the aggregate behavior of the crowd leads to large-scale collective motion that is itself the source of the trouble.  In other words, no one person is setting out to cause harm.  Instead, the physics underlying how people move when they’re packed-shoulder-to-shoulder is the real driver of the disaster.

In our recent work, we set out to understand the emergent collective properties of densely-packed people.  With an eye towards crowd safety, we focused our efforts on understanding where potentially dangerous collective motions come from, and in the process, stumbled on to a number of surprising results.  For example, simulations of mass gatherings showed us that simply having people randomly packed together is sufficient for a crowd crush.  Essentially, it’s like how waves travel on water – except in this case, it’s waves traveling on people.  This particular type of wave, whose technical name is a “Goldstone mode,” is able to span the entire crowd, but moves in a way that depends on the specifics of where people are standing.

While thinking about incidents where people trip and get hurt by trampling, we started asking ourselves: is there a way to predict who’s most likely to fall?  Is there a way to identify areas in the crowd that are most at risk?  To address this, we turned to material science and the study of “jammed granular media.”  It turns out our problem is related to the way grains flow in a silo, pills move through assembly lines, and coffee beans pack into a bag.   The key similarity in each case is that each of these “grains” (be they people, wheat, pills, or coffee beans) experience frictional forces with their neighbors.  As a result, densely packed grains create a network of contacts where some areas experience more forces and others experience less.  In these low-force regions, grains (again, we’re interested in people, but the physics applies just as well to beans!) have a bit more area to move around.  Thus, when things get jostled, these so-called “soft spots” are the places where things move the most.  In the specific context of people, our analogy means a sudden disruption to the crowd causes people in the soft spots get forcefully displaced the most.  These people, we believe, are the ones most at risk of tripping, and being trampled.

We also looked into what happens as crowds become agitated, and with the help of a stochastic resonance interpretation, found why the risks get worse.  Essentially, extra disorder in the way people move makes it easier for more long-range waves to travel through the crowd.  In turn, this means it becomes easier for a crowd crush to initiate.

Technical details aside, our big take-away from this study is a strategy to stay safe.  Specifically, to minimize risk, be aware of your surroundings and how tightly packed the crowd has become.  Even with the best intentions, people packed should-to-shoulder don’t have full control of how they move.  Random, unexpected collisions between neighbors add up to serious collective effects.  If you find yourself in a crowd that’s noticeably too dense, you can protect yourself and others by spreading out and moving to an area with more physical space.

The paper appeared in Physical Review Letters 117, 228301 (2016).
The paper is also available on the arXiv here.

High-density crowd
Dense crowds with shoulder-to-shoulder contact act like a semi-solid material, with potentially disastrous outcomes. Credit: Photograph by Ulrike Biets, used with permission

2016's Black Friday reported a handful of incidents.  Some articles summarizing the events:

Related reading and links: