Structure of Optimal Transport Networks Subject to a Global Constraint

Marc Durand (1)

1 MSC - Matière et Systèmes Complexes

The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which minimizes 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 the efficient computation of optimal pipe networks are also discussed.

Mots clés: networks; optimization; resistance; dissipative energy; Steiner tree; spanning tree; optimal mass transport; weighted networks; transport; irrigation; pipe networks; channel networks

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Optimisation et contrôle [math.OC]; Adaptation et Systèmes auto-organisés [nlin.AO]; Mécanique statistique [cond-mat.stat-mech]

Marc Durand. Structure of Optimal Transport Networks Subject to a Global Constraint. Physical Review Letters, 2007, 98 (8), pp.088701. ⟨10.1103/PhysRevLett.98.088701⟩. ⟨hal-00089022v3⟩