Transport processes on homogeneous planar graphs with scale-free loops

Milovan Šuvakov and Bosiljka Tadić

Physica A: Statistical Mechanics and its Applications, 2006, vol. 372, issue 2, 354-361

Abstract: 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.

Keywords: Transport processes; Planar graphs; Noise fluctuations; Maximum-flow trees (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:372:y:2006:i:2:p:354-361

DOI: 10.1016/j.physa.2006.08.035

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