Scaling in Small-World Resistor Networks

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We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point resistance in the large system-size limit. We find that the small-world structure suppresses large network resistances: both the average resistance and its standard deviation approaches a finite value in the large system-size limit for any non-zero density of random links. We also consider a scenario where the link conductance decays as a power of the length of the random links, $l^{-α}$. In this case we find that the average effective system resistance diverges for any non-zero value of $α$.
15 pages, 6 figures

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Statistical Mechanics, Disordered Systems and Neural Networks

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http://salesiana.dossiersoluciones.com/handle/123456789/96917

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0508056
 http://arxiv.org/abs/cond-mat/0508056
 Physics Letters A 350, 324 (2006)
 doi:10.1016/j.physleta.2005.09.081

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arXiv