TY  - JOUR
AU  - Dahlmanns, Matthias
AU  - Kaiser, Franz
AU  - Witthaut, Dirk
TI  - Branching in flow networks with linear congestion
JO  - Physical review research
VL  - 4
IS  - 4
SN  - 2643-1564
CY  - College Park, MD
PB  - APS
M1  - FZJ-2023-01636
SP  - 043208
PY  - 2022
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000906793000001
DO  - DOI:10.1103/PhysRevResearch.4.043208
UR  - https://juser.fz-juelich.de/record/1005791
ER  -