Damage and fluctuations induce loops in optimal transport networks.
By E. Katifori, G. Szöllősi, M. Magnasco. Physical Review Letters, 2009
316 citations recorded by the source corpus.
Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e., loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state.
Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/35bf8e0a760ffc1c5c0a19beb010bbdb90f96e35
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
In Statistical and Nonlinear Physics
- Marc Barthelemy
- Santo Fortunato
- Olaf Sporns
- Alessandro Vespignani
- Mark Newman
- Geoff Boeing
- Alex Arenas
- Renaud Lambiotte
Citations in the corpus
- A methodology for the generation of biomimetic design concepts (2015, background): “…beetle (Hamilton and Seely 1976; Nørgaard and Dacke 2010; Parker and Lawrence 2001) represent mechanisms for water gain and transportation, venation (Katifori, Szollosi, and Magnasco 2010) represents mechanisms for transportation, human skin (Randall 1946, 1947) and stoma (Atwell, Kriedemann, and…”
- Sap flow and sugar transport in plants (2016, background): “…i.e., have no loops (Durand, 2006), it was recently pointed out that the loops, which are abundant in leaf venation networks, will be advantageous by inducing multiple connections, if damage occurs to the leaf (Sack et al., 2008; Katifori, Szollosi, and Magnasco, 2010; Katifori and Magnasco, 2012).”
- Spatial Networks (2010, methodology): “Very recently, two studies which appeared simultaneously [98, 187] proposed possible reasons for the existence of a high density of loops in many real optimal networks.”