Structure of optimal channel networks subject to a global constraint
Résumé
Structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the pipe networks possible to build with a given amount of total pipe volume (or pipe lateral surface area), the network minimizing the dissipation rate is shown to be loopless. Furthermore, such an optimal network is shown to contain at most N-2 nodes, in addition to the N sources plus sinks that it connects. These results are valid whether the possible locations for the additional nodes are chosen freely or from a set of nodes (such as points of a grid). Applications of these results to various physical situations and to efficient computation of optimal pipe networks are also discussed.