Comparison of descriptor analysis with effective medium approximations for evaluating the admittance of large-scale three-dimensional RLC networks

We discuss the modelling of networks composed of a mixture of capacitors, inductors and resistors, and investigate the relation between their composition and admittance response. Such networks can be employed as lumped-parameter models for composite materials containing conductive, resonant and insulating grains. The proposed models are also of further relevance to the modelling of electromechanical and electrochemical systems governed by integro-differential equations as well as other flow processes in randomly connected physical systems. The dynamics of the excited networks are studied using a model in descriptor form derived from a randomized incidence matrix. The computational modelling further benefits from sparse matrix representations which enable the frequency-domain simulation of large networks. We show that the descriptor model formulation is in good agreement with the effective medium approximation (EMA) as extended for three elements of differing conductivity and provides an alternative to existing percolation, spectral density approaches, as well as Archie’s law of dispersion and Kohlrausch-Williams-Watts (KWW) models. An emergent behaviour for different connectivity realizations is observed. Changes in the network composition can be used to tune the emergent responses. Applications in nano-science, biosciences, and complex systems research are discussed.