Commuter flows in cities are regular and predictable. This should come as no surprise to anyone who has witnessed crowds jostle for space on a city-bound train platform in the morning. A widespread approach to capture these regularities mathematically considers flows in gravitational terms, where people behave as masses. However, its somewhat ad-hoc nature has made researchers look for alternatives.
Mattia Mazzoli and co-workers have now revealed that the gravitational picture is more rigorous than it may seem. From Twitter and census data, they divided several cities into 1 × 1 km2 cells and constructed an empirical vector field pointing in the average direction of commuter flow for each cell. Such a vector field was shown to satisfy the divergence theorem and have vanishing curl. This made it possible to rigorously define a potential field, reducing the dimensionality of the problem and highlighting basins of attraction, offering help for urban planning.
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Levi, F. People’s potential. Nat. Phys. 15, 986 (2019). https://doi.org/10.1038/s41567-019-0689-z
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DOI: https://doi.org/10.1038/s41567-019-0689-z
