Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2005-04-06
Physical Review E 73 (2006) 016116
Nonlinear Sciences
Adaptation and Self-Organizing Systems
Scientific paper
10.1103/PhysRevE.73.016116
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape of channels in such optimal networks and show that they must be straight with uniform cross-sectional areas. Then, we establish a relation between the cross-sectional areas of adjoining channels at each junction. Indeed, this relation is a generalization of Murray's law, originally established in the context of local optimization. Moreover, we establish a relation between angles and cross-sectional areas of adjoining channels at each junction, which can be represented as a vectorial force balance equation, where the force weight depends on the channel cross-sectional area. A scaling law between the minimal resistance value and the total volume or surface area value is also derived from the analysis. Furthermore, we show that no more than three or four channels meet in one junction of optimal bi-dimensional networks, depending on the flow profile (e.g.: Poiseuille-like or plug-like) and the considered constraint (fixed volume or surface area). In particular, we show that sources are directly connected to wells, without intermediate junctions, for minimal resistance networks preserving the total channel volume in case of plug flow regime. Finally, all these results are illustrated with a simple example, and compared with the structure of natural networks.
No associations
LandOfFree
Architecture of optimal transport networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Architecture of optimal transport networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Architecture of optimal transport networks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-38118