Disordered lattice networks: general theory and simulations

SUMMARY In this work we develop a theory for describing random networks of resistors of the most general topol- ogy. This approach generalizes and unies several statistical theories available in literature. We consider an n-dimensional anisotropic random lattice where each node of the network is connected to a reference node through a given random resistor. This topology includes many structures of great interest both for theoretical and practical applications. For example, the one-dimensional systems correspond to random ladder networks, two-dimensional structures modellms deposited on substrates and three-dimensional lattices describe random heterogeneous materials. Moreover, the theory is able to take into account the anisotropic percolation problem for two- and three-dimensional structures. The analytical results allow us to obtain the average behaviour of such networks, i.e. the electrical characterization of the corresponding physical systems. This eective medium theory is developed starting from the properties of the lattice Green's function of the network and from an ad hoc meaneld procedure. An accurate analytical study of the related lattice Green's functions has been conducted obtaining many closed form results expressed in terms of elliptic integrals. All the theoretical results have been veried by means of numerical Monte-Carlo simulations obtaining a remarkably good agreement between numerical and theoretical values. Copyright ? 2005 John Wiley & Sons, Ltd.

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