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001     1005791
005     20240226075342.0
024 7 _ |a 10.1103/PhysRevResearch.4.043208
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100 1 _ |a Dahlmanns, Matthias
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245 _ _ |a Branching in flow networks with linear congestion
260 _ _ |a College Park, MD
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520 _ _ |a In our modern world, we rely on the proper functioning of a variety of networks with complex dynamics. Many of them are prone to congestion due to high loads, which determines their operation and resilience to failures. In this article, we propose a fundamental model of congestion where travel times increase linearly with the load. We show that this model interpolates between shortest path and Ohmic flow dynamics, which both have a broad range of applications. We formulate the model as a quadratic programme and derive a generalization of Ohm's law, where the flow of every link is determined by a potential gradient in a nonlinear way. We provide analytic solutions for fundamental network topologies that elucidate the transition from localized flow to a branched flow. Furthermore, we discuss how to solve the model efficiently for large networks and investigate the resilience to structural damages.
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700 1 _ |a Kaiser, Franz
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700 1 _ |a Witthaut, Dirk
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|e Corresponding author
773 _ _ |a 10.1103/PhysRevResearch.4.043208
|g Vol. 4, no. 4, p. 043208
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|t Physical review research
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|y 2022
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856 4 _ |u https://juser.fz-juelich.de/record/1005791/files/INV_22_DEC_009915.pdf
856 4 _ |u https://juser.fz-juelich.de/record/1005791/files/PhysRevResearch.4.043208.pdf
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