Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 372, Issue 2, Pages 354-361Publisher
ELSEVIER
DOI: 10.1016/j.physa.2006.08.035
Keywords
transport processes; planar graphs; noise fluctuations; maximum-flow trees
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We consider the role of network geometry in two types of diffusion processes: transport of constant-density information packets with queuing on nodes, and constant voltage-driven tunneling of electrons. The underlying network is a homogeneous graph with scale-free distribution of loops, which is constrained to a planar geometry and fixed node connectivity k = 3. We determine properties of noise, flow and return-times statistics for both the processes on this graph and relate the observed differences to the microscopic process details. Our main findings are: (i) through the local interaction between packets queuing at the same node, long-range correlations build up in traffic streams, which are practically absent in the case of electron transport; (ii) noise fluctuations in the number of packets and in the number of tunnelings recorded at each node appear to obey the scaling laws in two distinct universality classes; (iii) the topological inhomogeneity of betweenness plays the key role in the occurrence of broad distributions of return times and in the dynamic flow. The maximum-flow spanning trees are characteristic of each process type. (c) 2006 Elsevier B.V. All rights reserved.
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