In view that cities will continue to house the majority of the world’s population at an increasing rate in the face of climate change, in this report we develop a science-based analysis framework for the quantification of urban and community resilience to natural hazards by applying concepts from statistical mechanics and the quantitative theory of Brownian motion. We envision a city to be a matrix where its citizens are driven by the city’s economy and other incentives, while using its infrastructure networks, in a similar way that thermally driven Brownian particles are moving within a complex viscoelastic material. The premise in this study is that urban and community resilience are understood as an outcome and we adopt the notion of ”engineering resilience” that was introduced in the seminal work of Holling (1973; 1996) who distinguishes engineering resilience (an outcome) from ecological resilience (a process).
This work brings forward the notion that in addition to the robustness of the transportation, utility, electricity and telecommunication networks, perhaps the most robust network that serves urban and community resilience is the living network of the citizens of a city. Accordingly, in this study urban and community resilience is encoded in a single metric—that’s the mean-square displacement (MSD) of its citizens that is computed from large numbers
of cell-phone users (particle tracking) or from traffic-flow data (monitoring the number of vehicles crossing sections of major traffic city arteries).
We first present recorded mean-square displacements distilled from large numbers of cellphones users from the cities of Houston, Miami and Jacksonville when struck by hurricanes Harvey 2017, Irma 2017 and Dorian 2019 together with the recorded mean-square displacements of the citizens of Dallas and Houston when experiencing the 2021 North American winter storm. All these recorded mean-square displacements revert invariably to the pre-event
regime immediately after the natural hazard struck, suggesting that large American cities with average to high population density manifest a great degree of engineering resilience.
Subsequently, we process traffic-flow data (number of vehicles per time) at various locations on major traffic city arteries to compute the probability density for finding a vehicle at some distance x, from the city center at time t; and subsequently we calculate the time history of the mean-square displacement (MSD) of vehicles from the city center. Our study uncovers that the shape of the MSD time-histories computed from traffic-flow data exhibits striking similarities with the MSD time-histories computed by tracking GPS locations from individual cell-phone users (particle tracking). The recorded mean-square displacements presented in this study, also validate a mechanical model for cities that is rooted in Langevin dynamics and predicts that following a natural hazard, large cities and local communities revert immediately to their initial steady-state behavior and resume their normal, pre-event activities. In summary, our work explores both an inductive and a deductive route to quantify urban and community resilience. The inductive route starts with the specific observation that large American cities exhibit an inherent engineering resilience to natural hazards as evidenced from the recorded mean-square displacement by either distilling cell-phone GPS location data or traffic-flow data. Nevertheless, the inductive reasoning builds upon a pattern recognition that can be falsified with a counter example. At the same time, our work also explored a science-based deductive route to quantify urban and community resilience.
Our deductive reasoning starts with the central result from statistical mechanics—that the MSD of a collection of agents ⟨r2(t)⟩, is proportional to the creep compliance, J(t) of a deterministic mechanical network (⟨r2(t)⟩ = WJ(t)); and formulates the hypothesis (conjecture) that the same relation between the stochastic quantity (MSD) and a deterministic time response function (creep compliance = J(t)) holds for large cities. The predictions of our conjectured mechanical model for cities are tested against the post-event recorded MSD of several cities subjected to natural hazards. The ever-growing remarkable predictions of our proposed mathematical model establish an analysis framework with predictive capabilities and confirm an overarching finding that large American cities with average to high population density manifest a great degree of engineering resilience.
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