Volume 84, Number 2, October 2008
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||14 October 2008|
Transport in networks with multiple sources and sinks
Minerva Center and Department of Physics, Bar-Ilan University - Ramat Gan 52900, Israel
2 Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA
Corresponding author: firstname.lastname@example.org
Accepted: 9 September 2008
We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for small n, increasing n improves the total transport in the network, while for large n bottlenecks begin to form. For the case of flow, this leads to an optimal n* above which the transport is less efficient. For current, the typical decrease in the length of the connecting paths for large n compensates for the effect of the bottlenecks. We also derive an expression for the average flow as a function of n under the common limitation that transport takes place between specific pairs of sources and sinks.
PACS: 89.75.Hc – Networks and genealogical trees / 05.60.Cd – Classical transport / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2008
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