### Abstract

Original language | English |
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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 | |

Publication status | Published - 15 Feb 2013 |

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*Physica A: Statistical Mechanics and its Applications*,

*392*(4), 1004-1027. https://doi.org/10.1016/j.physa.2012.10.035

**The origin of power-law emergent scaling in large binary networks.** / Almond, D. P.; Budd, C. J.; Freitag, M. A.; Hunt, G. W.; McCullen, N. J.; Smith, N. D.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 392, no. 4, pp. 1004-1027. https://doi.org/10.1016/j.physa.2012.10.035

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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

VL - 392

SP - 1004

EP - 1027

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 4

ER -