Disorder Crossover in Urban-Front Growth
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918465864990720 |
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| author | Hendrick, Martin Trique, Maximilian Manoli, Gabriele |
| author_facet | Hendrick, Martin Trique, Maximilian Manoli, Gabriele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Disorder Crossover in Urban-Front Growth Hendrick, Martin Trique, Maximilian Manoli, Gabriele Physics and Society Disordered Systems and Neural Networks 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. |
| title | Disorder Crossover in Urban-Front Growth |
| topic | Physics and Society Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2604.21437 |