title: Modeling walker synchronization on the Millennium Bridge.
abstract: On its opening day the London Millennium footbridge experienced unexpected large amplitude wobbling subsequent to the migration of pedestrians onto the bridge. Modeling the stepping of the pedestrians on the bridge as phase oscillators, we obtain a model for the combined dynamics of people and the bridge that is analytically tractable. It provides predictions for the phase dynamics of individual walkers and for the critical number of people for the onset of oscillations. Numerical simulations and analytical estimates reproduce the linear relation between pedestrian force and bridge velocity as observed in experiments. They allow prediction of the amplitude of bridge motion, the rate of relaxation to the synchronized state and the magnitude of the fluctuations due to a finite number of people.
authors.affiliation: Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany.
authors.forename: Bruno
authors.initials: B
authors.lastname: Eckhardt
authors.forename: Edward
authors.initials: E
authors.lastname: Ott
authors.forename: Steven H
authors.initials: SH
authors.lastname: Strogatz
authors.forename: Daniel M
authors.initials: DM
authors.lastname: Abrams
authors.forename: Allan
authors.initials: A
authors.lastname: McRobie
mesh_terms: D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics; D013314:Stress, Mechanical; D016138:Walking / Q000502:physiology*; D016474:Weight-Bearing / Q000502:physiology*