Premium
Disordered lattice networks: general theory and simulations
Author(s) -
Giordano Stefano
Publication year - 2005
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.335
Subject(s) - lattice (music) , monte carlo method , resistor , statistical physics , percolation theory , topology (electrical circuits) , anisotropy , continuum percolation theory , node (physics) , computer science , random graph , mathematics , discrete mathematics , physics , percolation critical exponents , scaling , combinatorics , quantum mechanics , critical exponent , geometry , graph , statistics , voltage , acoustics
In this work we develop a theory for describing random networks of resistors of the most general topology. This approach generalizes and unifies 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 model films 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 effective medium theory is developed starting from the properties of the lattice Green's function of the network and from an ad hoc mean field 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 verified by means of numerical Monte‐Carlo simulations obtaining a remarkably good agreement between numerical and theoretical values. Copyright © 2005 John Wiley & Sons, Ltd.