The Mathematical Institute, University of Oxford, Eprints Archive

Advection, diffusion, and delivery over a network

Heaton, L L M and Lopez, E and Maini, P. K. and Fricker, M D and Jones, N S (2012) Advection, diffusion, and delivery over a network. Physical Review E, 86 (2). 021905-1-021905-10.

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Abstract

Many biological, geophysical, and technological systems involve the transport of a resource over a network. In this paper, we present an efficient method for calculating the exact quantity of the resource in each part of an arbitrary network, where the resource is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. The key conceptual step is to partition the resource into material that does or does not reach a node over a given time step. As an example application, we consider resource allocation within fungal networks, and analyze the spatial distribution of the resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, and such growth necessarily involves the movement of fluid. We develop a model of delivery in growing fungal networks, and find good empirical agreement between our model and experimental data gathered using radio-labeled tracers. Our results lead us to suggest that in foraging fungi, growth-induced mass flow is sufficient to account for long-distance transport, if the system is well insulated. We conclude that active transport mechanisms may only be required at the very end of the transport pathway, near the growing tips.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1596
Deposited By:Philip Maini
Deposited On:06 Sep 2012 08:39
Last Modified:06 Sep 2012 08:39

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