The origin of power-law emergent scaling in large binary networks

D. P. Almond; C. J. Budd; M. A. Freitag; G. W. Hunt; N. J. McCullen; N. D. Smith

doi:10.1016/j.physa.2012.10.035

The origin of power-law emergent scaling in large binary networks

D. P. Almond, C. J. Budd, M. A. Freitag, G. W. Hunt, N. J. McCullen, N. D. Smith

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Abstract

We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.

Original language	English
Pages (from-to)	1004-1027
Journal	Physica A: Statistical Mechanics and its Applications
Volume	392
Issue number	4
Early online date	2 Nov 2012
DOIs	https://doi.org/10.1016/j.physa.2012.10.035
Publication status	Published - 15 Feb 2013

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10.1016/j.physa.2012.10.035

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title = "The origin of power-law emergent scaling in large binary networks",

abstract = "We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.",

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AU - Almond, D. P.

AU - Budd, C. J.

AU - Freitag, M. A.

AU - Hunt, G. W.

AU - McCullen, N. J.

AU - Smith, N. D.

PY - 2013/2/15

Y1 - 2013/2/15

N2 - We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.

AB - We study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction in terms of the component proportions p and the total number of components N. These formulae correctly identify both the percolation limits and also the emergent power-law behaviour between the percolation limits and show the interplay between the size of the network and the deviation of the proportion from the critical value of p=1/2. The results compare excellently with a large number of numerical simulations.

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

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The origin of power-law emergent scaling in large binary networks

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The origin of power-law emergent scaling in large binary networks

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