Dahlmanns, Matthias, Kaiser, Franz and Witthaut, Dirk (2022). Branching in flow networks with linear congestion. Phys. Rev. Res., 4 (4). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2643-1564
Full text not available from this repository.Abstract
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.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-669067 | ||||||||||||||||
DOI: | 10.1103/PhysRevResearch.4.043208 | ||||||||||||||||
Journal or Publication Title: | Phys. Rev. Res. | ||||||||||||||||
Volume: | 4 | ||||||||||||||||
Number: | 4 | ||||||||||||||||
Date: | 2022 | ||||||||||||||||
Publisher: | AMER PHYSICAL SOC | ||||||||||||||||
Place of Publication: | COLLEGE PK | ||||||||||||||||
ISSN: | 2643-1564 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/66906 |
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