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Universal Roughness and the Dynamics of Urban Expansion.

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Urban sprawl exhibits anisotropic, branchlike growth, challenging previous models. This study reveals universal and variable exponents, providing a new framework for understanding city expansion dynamics.

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Area of Science:

  • Urban studies
  • Geospatial analysis
  • Complexity science

Background:

  • Urban sprawl's quantitative laws are not well understood.
  • City growth patterns are complex and require advanced analytical tools.

Purpose of the Study:

  • To quantitatively analyze urban sprawl using principles from surface growth physics.
  • To identify universal and variable scaling laws governing built-up area expansion.

Main Methods:

  • Analysis of built-up expansion data from 19 cities between 1985 and 2015.
  • Application of surface growth physics models in a radial geometry framework.

Main Results:

  • Observed anisotropic, branchlike growth patterns in urban expansion.
  • Identified a piecewise linear scaling relationship between urban area and population.
  • Uncovered a robust local roughness exponent (αloc ≈ 0.54) coexisting with variable exponents (β and z).

Conclusions:

  • The findings provide a novel empirical basis for modeling urban sprawl.
  • The coexistence of universal and variable exponents offers a unique test bed for nonequilibrium growth theories.
  • This research advances the quantitative understanding of urban form and dynamics.