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Convection–diffusion effects in marathon race dynamics

Author

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  • Rodriguez, E.
  • Espinosa-Paredes, G.
  • Alvarez-Ramirez, J.

Abstract

In the face of the recent terrorist attack event on the 2013 Boston Marathon, the increasing participation of recreational runners in large marathon races has imposed important logistical and safety issues for organizers and city authorities. An accurate understanding of the dynamics of the marathon pack along the race course can provide important insights for improving safety and performance of these events. On the other hand, marathon races can be seen as a model of pedestrian movement under confined conditions. This work used data of the 2011 Chicago Marathon event for modeling the dynamics of the marathon pack from the corral zone to the finish line. By considering the marathon pack as a set of particles moving along the race course, the dynamics are modeled as a convection–diffusion partial differential equation with position-dependent mean velocity and diffusion coefficient. A least-squares problem is posed and solved with optimization techniques for fitting field data from the 2011 Chicago Marathon. It was obtained that the mean pack velocity decreases while the diffusion coefficient increases with distance. This means that the dispersion rate of the initially compact marathon pack increases as the marathon race evolves along the race course.

Suggested Citation

  • Rodriguez, E. & Espinosa-Paredes, G. & Alvarez-Ramirez, J., 2014. "Convection–diffusion effects in marathon race dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 498-507.
    • Handle: RePEc:eee:phsmap:v:393:y:2014:i:c:p:498-507
    DOI: 10.1016/j.physa.2013.09.051
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    References listed on IDEAS

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    Cited by:

    1. Kwong, Hok Shing & Nadarajah, Saralees, 2019. "Modelling dynamics of marathons – A mixture model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. Guo, Junke & Mohebbi, Amin & Zhang, Tian C., 2022. "Application of general unit hydrograph model for marathon finish time distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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