Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops

Details Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops

2006-05-18

arxiv.org/abs/cond-mat/0605452v1

Physica A: Statistical Mechanics and its Applications Volume 372, Issue 2, 15 December 2006, Pages 354-361

Physics

Condensed Matter

Statistical Mechanics

14 pages, 5 figures

Scientific paper

10.1016/j.physa.2006.08.035

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 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 for each process type.

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