Abstract
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.
Original language | English |
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Article number | 39 |
Journal | European Physical Journal B : Condensed MAtter and Complex Systems |
Volume | 90 |
Issue number | 3 |
DOIs | |
Publication status | Published - 8 Mar 2017 |
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Profiles
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Chris Bowen
- Department of Mechanical Engineering - Professor
- Materials and Structures Centre (MAST)
- Centre for Sustainable and Circular Technologies (CSCT)
- Centre for Nanoscience and Nanotechnology
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Institute for Mathematical Innovation (IMI)
- Centre for Biosensors, Bioelectronics and Biodevices (C3Bio)
- Centre for Autonomous Robotics (CENTAUR)
Person: Research & Teaching
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Nick McCullen
- Department of Architecture & Civil Engineering - Lecturer
- Centre for Networks and Collective Behaviour
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Water Innovation and Research Centre (WIRC)
- Centre for Doctoral Training in Decarbonisation of the Built Environment (dCarb)
- Centre for Energy and the Design of Environments (EDEn)
Person: Research & Teaching
Equipment
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High Performance Computing (HPC) Facility
Steven Chapman (Manager)
University of BathFacility/equipment: Facility