Percolation-based effective conductivity calculations for bimodal distributions of local conductances

Abstract

Several percolation-based schemes for calculating the effective conductivity of complex, correlated media with bimodal distributions of the local conductivity are compared with numerical simulations. A means of calculating the correlation length is employed to distinguish regions of validity of the calculations. In most cases, a rather simple scaling formulation closely related with universal scaling is found to perform best. This scaling formulation employs geometric mean values of the modes of the conductivity distribution as scale factors.

Keywords:

• disordered media
• effective conductivity
• upscaling
• percolation theory
• effective medium approaches
• bi-modal distributions

Acknowledgments

Jim Smith is an important member of the physics community for at least three reasons: his research, his principles and his ability to notice the unnoticed. We hope this manuscript is good enough to contribute to an issue of Philosophical Magazine in his honour.