1. Scaling in small-world resistor networks
- Author
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Gyorgy Korniss, Kevin E. Bassler, Balazs Kozma, Derek Abbott, M. B. Hastings, Matthew J. Berryman, Korniss, G, Hastings, M, Bassler, M, Kozma, B, Berryman, Matthew John, and Abbott, Derek
- Subjects
Physics ,Statistical Mechanics (cond-mat.stat-mech) ,Process (computing) ,FOS: Physical sciences ,General Physics and Astronomy ,Conductance ,Propagator ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Condensed Matter Physics ,01 natural sciences ,Standard deviation ,010305 fluids & plasmas ,law.invention ,Power (physics) ,law ,0103 physical sciences ,Small-world model ,Resistor networks ,Scaling ,Limit (mathematics) ,Statistical physics ,Resistor ,010306 general physics ,Condensed Matter - Statistical Mechanics - Abstract
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, $l^{-\alpha}$. In this case we find that the average effective system resistance diverges for any non-zero value of $\alpha$., Comment: 15 pages, 6 figures
- Published
- 2006
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