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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 12: Urban Systems and Traffic Flow

SOE 12.1: Talk

Wednesday, March 20, 2024, 10:00–10:15, MA 001

Analytical and numerical treatment of the every-pair-interaction problem — Fabiano L. Ribeiro¹, Yunfei Li², Stefan Born³, and •Diego Rybski² — ¹Department of Physics (DFI), Federal University of Lavras (UFLA), Lavras MG, Brazil — ²Potsdam Institute for Climate Impact Research (PIK), P.O. Box 601203, 14412 Potsdam, Germany — ³Technische Universität Berlin, Chair of Bioprocess Engineering and Institute of Mathematics, Strasse des 17. Juni 135, 10623 Berlin, Germany

We systematically treat every-pair interactions (a) that exhibit power-law dependence on the Euclidean distance and (b) act in structures that can be characterized using fractal geometry. We analytically derive the mean interaction field of the cells and find that (i) in a long-range interaction regime, the mean interaction field increases following a power-law with the size of the system, (ii) in a short-range interaction regime, the field saturates, and (iii) in the intermediate range it follows a logarithmic behavior. For long-range interactions, the theoretical calculations align closely with the numerical simulations. For short-range interactions, we observe that discreteness significantly affects the results, which requires an expansion that substantially improves the accuracy of the analytical expression. We conclude with applications. Early version of the respective manuscript: https://arxiv.org/abs/2307.07783

Keywords: fractal dimension; interactions; average distance; cities