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@ARTICLE{Dahlmanns:1005791,
      author       = {Dahlmanns, Matthias and Kaiser, Franz and Witthaut, Dirk},
      title        = {{B}ranching in flow networks with linear congestion},
      journal      = {Physical review research},
      volume       = {4},
      number       = {4},
      issn         = {2643-1564},
      address      = {College Park, MD},
      publisher    = {APS},
      reportid     = {FZJ-2023-01636},
      pages        = {043208},
      year         = {2022},
      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.},
      cin          = {IEK-STE},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IEK-STE-20101013},
      pnm          = {1112 - Societally Feasible Transformation Pathways
                      (POF4-111)},
      pid          = {G:(DE-HGF)POF4-1112},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000906793000001},
      doi          = {10.1103/PhysRevResearch.4.043208},
      url          = {https://juser.fz-juelich.de/record/1005791},
}