% IMPORTANT: The following is UTF-8 encoded. This means that in the presence % of non-ASCII characters, it will not work with BibTeX 0.99 or older. % Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or % “biber”. @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}, }