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Emergence of the London Millennium Bridge instability without synchronisation

Published version
Peer-reviewed

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Authors

Champneys, Alan R. 
Jeter, Russell 

Abstract

Abstract: The pedestrian-induced instability of the London Millennium Bridge is a widely used example of Kuramoto synchronisation. Yet, reviewing observational, experimental, and modelling evidence, we argue that increased coherence of pedestrians’ foot placement is a consequence of, not a cause of the instability. Instead, uncorrelated pedestrians produce positive feedback, through negative damping on average, that can initiate significant lateral bridge vibration over a wide range of natural frequencies. We present a simple general formula that quantifies this effect, and illustrate it through simulation of three mathematical models, including one with strong propensity for synchronisation. Despite subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger. More broadly, we describe an alternative to Kuramoto theory for emergence of coherent oscillations in nature; collective contributions from incoherent agents need not cancel, but can provide positive feedback on average, leading to global limit-cycle motion.

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Keywords

Article, /639/166/986, /639/705/1041, /639/766/25, article

Journal Title

Nature Communications

Conference Name

Journal ISSN

2041-1723

Volume Title

12

Publisher

Nature Publishing Group UK
Sponsorship
National Science Foundation (NSF) (DMS-1909924)
Ministry of Education and Science of the Russian Federation (Minobrnauka) (0729-2020-0036)