Optimising Transport in a Homogeneous Network - WEAIRE, DENIS LAWRENCE (American Physical Society, 2004)
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.
PUBLISHED
Keywords: Condensed Matter Physics; channel length distributions