Urban Percolation

• Applicant: Dr. Diego Rybski
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; City Planning, Spatial Planning, Transportation and Infrastructure Planning, Landscape Planning ; Theoretical Condensed Matter Physics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 451083179

There is a competition for land and a shift from natural to artificial land covers. These global changes represent a reaction to the increasing need to provide food, shelter, and timber for more people than ever. One of the consequences of the ongoing land-cover transition is the fragmentation of landscapes. While some landscapes naturally exhibit patchiness, urban growth and agricultural expansion cause a fragmentation of natural landscapes – and habitat fragmentation has a lasting impact on the ecosystems. The opposite, i.e. connectivity, is essential to percolation theory. Previous work has studied percolation properties of urban land cover but it remains unclear, what determines the critical threshold. Consequently, the UPon project aims for a deeper understanding of the percolation properties of cities and the urban fabric. The goal is to find out how the spatial organization of cities and settlements determines the percolation threshold and based on which factors the critical value can be 'predicted'. Why do some countries have particularly small or large critical values? One may argue that the population density may play a role, but even for the same fraction of urban pixels (analogous to the occupation probability in percolation theory), these pixels can be distributed in arbitrary clusters so that a wide range of percolation thresholds are possible. From percolation theory it is known that cluster sizes follow power-law distributions. In the case of cities, this corresponds to Zipf’s law. In contrast to random percolation, cities also exhibit power-law size distributions further away from criticality. The project work aims at understanding why and how the exponent of the city size distribution depends on the aggregational scale. In summary, the project consists of three work packages with seven tasks in total, addressing the prediction of the percolation threshold, poles of inaccessibility (complementary to cluster formation), travel time percolation, and spatial correlations of urban clusters (are there correlations in the size of neighboring clusters and beyond?). To address this work, a set of more technical tasks will also be conducted, including a variant of the Leath algorithm, parameter free clustering, and a clustering comparison exercise. Overall, the project represents a systematic, data-driven assessment of urban percolation properties.

• DFG Programme: Research Grants