%0 Journal Article
%A Dahlmanns, Matthias
%A Kaiser, Franz
%A Witthaut, Dirk
%T Branching in flow networks with linear congestion
%J Physical review research
%V 4
%N 4
%@ 2643-1564
%C College Park, MD
%I APS
%M FZJ-2023-01636
%P 043208
%D 2022
%X 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000906793000001
%R 10.1103/PhysRevResearch.4.043208
%U https://juser.fz-juelich.de/record/1005791