A model for describing the hydrodynamics of crowds

January 4, 2019, CNRS
Image A: Image of the starting area for the 2016 Bank of America Chicago Marathon. Image B: Zoom on the area framed by A, showing the movement sequence of the race organizers (yellow vests) as they guide runners toward the starting area, thereby inducing speed and density disruptions that spread at a constant speed through the crowd. Image C: Speed and density waves in the same crowd, spreading in the opposite direction as the crowd's movement. Credit: Nicolas Bain/Science

Precise simulations of the movement and behavior of crowds can be vital to the production of digital sequences or the creation of large structures for crowd management. However, the ability to quantitatively predict the collective dynamic of a group responding to external stimulation remains a largely open issue, based primarily on models in which each individual's actions are simulated according to empirical behavioral rules. Until now, there was no experimentally tested physical model that describes the hydrodynamics of a crowd without assuming behavioral rules.

Researchers from a laboratory affiliated with the CNRS, l'ENS de Lyon, and l'Université Claude Bernard Lyon 1 have provided a first equation of this type, deduced from a measurement campaign conducted on crowds numbering tens of thousands of individuals. The physicists focused on cohorts of runners at the beginning of a marathon, as they are guided to the starting line by a row of organizers in successive sequences of walking and halting. This protocol creates a periodic and controlled disturbance similar to the stimulations that are typically used to probe the mechanical response of fluids.

Remarkably, varies very little from one assembly of runners to another, one race to another, and one country to another, with speed propagating constantly at a little over one meter per second. The researchers established a generic description that can precisely predict flows, as flows observed in a road-race in Chicago in 2016 helped predict those of thousands of runners at the start of the Paris marathon in 2017.

Start of the 2016, 2017 and 2018 Bank of America Chicago Marathons, sped up eight times. Credit: Nicolas Bain and Denis Bartolo

By using technical standards from to analyze images from the starting corrals of five races, successfully measured crowd speed at each instant, subsequently describing it as a liquid flow. Their results show that information regarding the speed to adopt spreads to the back of the group in the form of waves measuring hundreds of meters, with no loss of intensity. In contrast, any change to the crowd's movement trajectory dissipates quickly, spreading just a few meters through the crowd. In short, speed information spreads easily through this fluid, while orientational information does not.

The physicists now want to study the response of groups to extreme disturbances in order to test the limits of their hydrodynamic description of crowds.

Start of the 2016 Bank of America Chicago Marathon. Left panel: images after correction from perspective distortion effects. Right panel: Walking speed of the crowd, measured from a PIV analysis. Credit: Nicolas Bain and Denis Bartolo

Explore further: Running a marathon can increase cardiac strain in amateur runners

More information: Nicolas Bain et al. Dynamic response and hydrodynamics of polarized crowds, Science (2019). DOI: 10.1126/science.aat9891

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