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

Research output: Contribution to journal › Article › peer-review

13 Citations (SciVal)

205 Downloads (Pure)

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

Access to Document

10.1016/j.physa.2012.10.035

Almond2012 originFinal published version, 1.4 MB

Cite this

@article{dce9d7c46d274820b5465bb1444dbce7,

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.",

author = "Almond, {D. P.} and Budd, {C. J.} and Freitag, {M. A.} and Hunt, {G. W.} and McCullen, {N. J.} and Smith, {N. D.}",

year = "2013",

month = feb,

day = "15",

doi = "10.1016/j.physa.2012.10.035",

language = "English",

volume = "392",

pages = "1004--1027",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier",

number = "4",

}

TY - JOUR

T1 - The origin of power-law emergent scaling in large binary networks

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.

UR - http://www.scopus.com/inward/record.url?scp=84871719696&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.physa.2012.10.035

U2 - 10.1016/j.physa.2012.10.035

DO - 10.1016/j.physa.2012.10.035

M3 - Article

SN - 0378-4371

VL - 392

SP - 1004

EP - 1027

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 4

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

New Fibres for New Lasers

Microstructural Silica Fibres for Surgical Applications

ESTABLISHMENT OF THE UNIVERSITY OF BATH CENTRE FOR COMPLEX S YSTEMS - O/HEAD SPLIT SM75% EN25%

Cite this

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

Abstract

Access to Document

Other files and links

Fingerprint

Projects

New Fibres for New Lasers

Microstructural Silica Fibres for Surgical Applications

ESTABLISHMENT OF THE UNIVERSITY OF BATH CENTRE FOR COMPLEX S YSTEMS - O/HEAD SPLIT SM75% EN25%

Cite this