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001005791 1001_ $$0P:(DE-Juel1)180231$$aDahlmanns, Matthias$$b0
001005791 245__ $$aBranching in flow networks with linear congestion
001005791 260__ $$aCollege Park, MD$$bAPS$$c2022
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001005791 520__ $$aIn 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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001005791 7001_ $$0P:(DE-Juel1)176610$$aKaiser, Franz$$b1
001005791 7001_ $$0P:(DE-Juel1)162277$$aWitthaut, Dirk$$b2$$eCorresponding author
001005791 773__ $$0PERI:(DE-600)3004165-X$$a10.1103/PhysRevResearch.4.043208$$gVol. 4, no. 4, p. 043208$$n4$$p043208$$tPhysical review research$$v4$$x2643-1564$$y2022
001005791 8564_ $$uhttps://juser.fz-juelich.de/record/1005791/files/INV_22_DEC_009915.pdf
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