Universal roughness and the dynamics of urban expansion

2025/06/12 by Ulysse Marquis, Marquis, Ulysse, Oriol Artime +5 · 1 voice · 2 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Land Use and Ecosystem Services #Physics and Society (physics.soc-ph) #Point processes and geometric inequalities #Regional Economics and Spatial Analysis #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2506.10656

openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Urban sprawl reshapes cities, yet its quantitative laws remain elusive. Analyzing built-up expansion in 19 cities (1985-2015) with tools from surface growth physics in radial geometry, we reveal anisotropic, branch-like growth and a piecewise linear scaling between area and population. We uncover a robust local roughness exponent α_loc≈ 0.54, coexisting with variable β and z. This unusual coexistence of universal and variable exponents offers a rare empirical testbed for nonequilibrium growth and an empirical basis for modeling urban sprawl.

Cited by

• Modeling the spatial growth of cities
• Dynamic roughening of cities driven by multiplicative noise

Discussions

• How do cities expand? Using surface growth physics, we found a unique exponent governing their local geometry. Instead, their dynamics range from smooth diffusion to abrupt coalescence, with demograph [bsky, 10 points, 1 comments]

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