Optimizing transport in a homogeneous network

Marc Durand (1) , Denis Weaire (2)

1 SEAS - Harvard John A. Paulson School of Engineering and Applied Sciences
2 FOAM PHYSICS - Computational Physics Physics Department

Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the average conductivity associated with. When the flow through each channel is conserved and derives from a potential function, we show that there exist an upper bound of the average conductivity, and explicitly give the expression for this upper bound as a function of the channel permeability and channel length distributions. Moreover, we express the necessary and sufficient conditions on the network structure to maximize the average conductivity. These conditions are found to be independent of the connectivity of the vertices.

Mots clés: networks; conductivity; optimization; structure; transport

Domaines: Adaptation et Systèmes auto-organisés [nlin.AO]; Mécanique statistique [cond-mat.stat-mech]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Matière Molle [cond-mat.soft]; Autre

Marc Durand, Denis Weaire. Optimizing transport in a homogeneous network. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2004, 70, pp.046125. ⟨10.1103/PhysRevE.70.046125⟩. ⟨hal-00004636⟩