Urban sprawl reshapes cities worldwide, yet its spatial dynamics are still largely described in qualitative or descriptive terms. In this seminar, Marc Barthelemy will present a quantitative framework for urban expansion inspired by nonequilibrium surface growth physics.

Using high-resolution built-up area data and historical population records for 19 cities across multiple continents, they studied urban growth in a radial geometry, treating population as a natural dynamical variable. They uncovered strongly anisotropic, branch-like expansion patterns and identified two competing growth mechanisms: smooth local accretion at the urban fringe and abrupt coalescence with surrounding clusters. Remarkably, despite large variability in urban histories and growth rates, all cities share a universal local roughness exponent close to 1/2, while global growth exponents (beta and z) vary widely.

This anomalous scaling behavior places urban expansion outside standard universality classes and highlights the role of anisotropy, coalescence, and quenched heterogeneity in shaping cities. These findings provide quantitative constraints for future models of urban form and evolution.

References:
[1] Marquis, Artime, Gallotti, MB, “Universal roughness and the dynamics of urban expansion”, Phys. Rev. Lett. 135:187403 (2025).
[2] MB, Marquis, “Mathematical modelling of urban sprawl”, Spatial Economic Analysis 1-21 (2026).