GPS data from cellphones for Mechanical Analog

Motivated by 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 city’s economy 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 city’s behavior 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 remarkably 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.