### Abstract

Language | English |
---|---|

Article number | 39 |

Journal | European Physical Journal B : Condensed MAtter and Complex Systems |

Volume | 90 |

Issue number | 3 |

DOIs | |

Status | Published - 8 Mar 2017 |

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### Cite this

*European Physical Journal B : Condensed MAtter and Complex Systems*,

*90*(3), [39]. https://doi.org/10.1140/epjb/e2017-70438-8

**Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks.** / Aouaichia, Mustapha; McCullen, Nicholas; Bowen, Christopher; Almond, Darryl; Budd, Christopher; Bouamrane, R.

Research output: Contribution to journal › Article

*European Physical Journal B : Condensed MAtter and Complex Systems*, vol. 90, no. 3, 39. https://doi.org/10.1140/epjb/e2017-70438-8

}

TY - JOUR

T1 - Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks

AU - Aouaichia, Mustapha

AU - McCullen, Nicholas

AU - Bowen, Christopher

AU - Almond, Darryl

AU - Budd, Christopher

AU - Bouamrane, R

PY - 2017/3/8

Y1 - 2017/3/8

N2 - In this paper large resistor-capacitor (RC) networks that consist of randomly distributed conductive and capacitive elements which are much larger than those previously explored are studied using an efficient algorithm. We investigate the emergent power-law scaling of the conductance and the percolation and saturation limits of the networks at the high and low frequency bounds in order to compare with a modification of the classical Effective Medium Approximation (EMA) that enables its extension to finite network sizes. It is shown that the new formula provides a simple analytical description of the network response that accurately predicts the effects of finite network size and composition and it agrees well with the new numerical calculations on large networks and is a significant improvement on earlier EMA formulae. Avenues for future improvement and explanation of the formula are highlighted. Finally, the statistical variation of network conductivity with network size is observed and explained. This work provides a deeper insight into the response of large resistor-capacitor networks to understand the AC electrical properties, size effects, composition effects and statistical variation of properties of a range of heterogeneous materials and composite systems.

AB - In this paper large resistor-capacitor (RC) networks that consist of randomly distributed conductive and capacitive elements which are much larger than those previously explored are studied using an efficient algorithm. We investigate the emergent power-law scaling of the conductance and the percolation and saturation limits of the networks at the high and low frequency bounds in order to compare with a modification of the classical Effective Medium Approximation (EMA) that enables its extension to finite network sizes. It is shown that the new formula provides a simple analytical description of the network response that accurately predicts the effects of finite network size and composition and it agrees well with the new numerical calculations on large networks and is a significant improvement on earlier EMA formulae. Avenues for future improvement and explanation of the formula are highlighted. Finally, the statistical variation of network conductivity with network size is observed and explained. This work provides a deeper insight into the response of large resistor-capacitor networks to understand the AC electrical properties, size effects, composition effects and statistical variation of properties of a range of heterogeneous materials and composite systems.

U2 - 10.1140/epjb/e2017-70438-8

DO - 10.1140/epjb/e2017-70438-8

M3 - Article

VL - 90

JO - European Physical Journal B : Condensed MAtter and Complex Systems

T2 - European Physical Journal B : Condensed MAtter and Complex Systems

JF - European Physical Journal B : Condensed MAtter and Complex Systems

SN - 1434-6028

IS - 3

M1 - 39

ER -