Download Advection, Diffusion and Delivery over a Network by Luke L. M. Heaton, at al, Many biological, geophysical and technological systems involve the transport of resource over a network. in this paper we present an algorithm for calculating the precise concentration of resource at any point in space or time, given that the resource in the network is lost or delivered out of the network at a given rate, whereas being subject to advection and diffusion. we take into account the implications of advection, diffusion and delivery for simple models of glucose delivery through a vascular network, and conclude that in certain circumstances, increasing the amount of blood and the variety of glucose transporters can actually decrease the overall rate of glucose delivery. we also consider the case of empirically determined fungal networks, and analyze the distribution of resource that emerges as such networks grow over time. fungal growth involves the enlargement of fluid filled vessels, which necessarily involves the movement of fluid. In three empirically determined fungal networks we found that the minimum currents consistent with the observed growth would effectively transport resource throughout the network over the time-scale of growth. this means that in foraging fungi, the active transport mechanisms observed in the growing tips may not be needed for long range transport.