Mechanical Analog for Cities

Motivated from the increasing need to develop a quantitative, science-based, predictive understanding of the dynamics and response of cities when subjected to hazards, in this paper we apply concepts from statistical mechanics and microrheology to develop mechanical analogs for cities with predictive capabilities. We envision a city to be a matrix where people (cell-phone users) are driven by the economy of the city and other associated incentives while using the collection of its infrastructure networks in a similar way that thermally driven Brownian probe particles are moving within a complex viscoelastic material. Mean-square displacements (ensemble averages) of thousands of cell-phone users are computed from GPS location data to establish the creep compliance and the resulting impulse response function of a city. The derivation of these time-response functions allows the synthesis of simple mechanical analogs that model satisfactorily the behavior of the city under normal conditions. Our study concentrates on predicting the response of cities to acute shocks (natural hazards that stress the entire urban area) that are approximated with a rectangular pulse with finite duration; and we show that the solid-like mechanical analogs for cities that we derived predict that cities revert immediately to their pre-event response suggesting that they are inherently resilient. Our findings are in remarkable good agreement with the recorded response of the Dallas metroplex following the February 2021 North American winter storm which happened at a time for which we have dependable GPS location data.