Optimizing transport in a homogeneous network

Details Optimizing transport in a homogeneous network Optimizing transport in a homogeneous network

2005-04-06

arxiv.org/abs/nlin/0504017v1

Physical Review E 70 (2004) 046125

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1103/PhysRevE.70.046125

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.

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