M Durand and D Weaire, Optimizing transport in a homogeneous network, Physical Review, 70, 2004, 046125
Physical Review; 70;
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 it. When the flow through each channel is
conserved and derives from a potential function, we show that there exists 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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