Mechanical analogue for cities

Abstract

Motivated from the increasing need to develop a science-based, predictive understanding of the dynamics and response of cities when subjected to natural hazards, in this paper, we apply concepts from statistical mechanics and microrheology to develop mechanical analogues for cities with predictive capabilities. We envision a city to be a matrix where cell-phone users are driven by the city’s economy and other incentives while using the collection of its infrastructure networks in a similar way that thermally driven Brownian particles are moving within a complex viscoelastic material. Mean-square displacements 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 analogues that model satisfactorily the city’s behaviour under normal conditions. Our study concentrates on predicting the response of cities to acute shocks (natural hazards) that are approximated with a rectangular pulse; and we show that the derived solid-like mechanical networks predict that cities revert immediately to their pre-event response suggesting an inherent resilience. Our findings are in remarkable good agreement with the recorded response of the Dallas metroplex following the February 2021 North American winter storm.

The inherent resilience of large cities to natural hazards: records, evidence, and predictions

“…12 The prediction for the response of the Dallas metroplex following the North American winter storm with the amplitude-modulation model given by Eq. ( 6) has been presented in Makris et al 13 The same inherent and immediate resilience to the 2021 North American winter storm manifested by the city of Dallas is also manifested by city of Houston, Texas, and also resumes normal activity upon the expiration of the winter storm with the MSD of its citizens to revert to its normal oscillation pattern as shown in Fig. 6.…”

“…30 In view of the overarching validity of Eq. ( 5) regardless of the complexity of the mechanism that the immersed Brownian particles exchange forces with the surrounding fluid (viscous, inertia, hydrodynamic memory, or viscoelastic forces), Makris et al 13 built upon the profound implications of Eq. ( 5) to conjecture a corresponding relation for cities…”

“…The mathematical model appearing in the right-hand side of Eq. ( 6) was merely constructed by Makris et al 13 by using techniques for manipulating signals in radio communication. 31,32 The function U(t-0) appearing in Eq.…”

“…2 is captured with the amplitude-modulation model appearing on the right of Eq. ( 6) (Makris et al 2023 13 ). Fig.…”

“…In this case, resilience is associated with the magnitude of a disturbance (shock) that needs to be absorbed by the system before it changes its structure and stabilizes at a different equilibrium state. 12 In this work, which builds upon our past study, 13 urban resilience to natural hazards is defined as the ability of a large city, following a natural hazard, to revert to its initial steadystate behavior and resume its normal, preevent activities-a definition that matches Holling's 12 definition of engineering resilience…”