Disorder Crossover in Urban-Front Growth

Abstract

Urban expansion fronts display a robust local roughness exponent together with strongly dispersed growth and nonuniversal dynamic exponents. We show that this coexistence can arise from a disorder-controlled crossover in projected-front growth. Introducing a minimal Eden model, in which geographic constraints act as quenched dilution and coalescence as quenched local acceleration, we demonstrate that the resulting front enters a long disorder-dominated preasymptotic regime, whose scaling near threshold is set by ordinary two-dimensional percolation. In this regime, the local roughness remains close to $1/2$, while the large-scale exponents vary broadly with disorder and acceleration. These results provide a minimal explanation of urban-front roughening and suggest a more general mechanism for stochastic growth in heterogeneous media.