Resistance computation of generalized decorated square and simple cubic network lattices

Abstract

In the present work, the lattice Green’s function technique has been used to investigate the equivalent two-site resistance between arbitrary pairs of lattice sites in infinite, generalized decorated square and simple cubic lattices with identical resistors. Some results for the resistance are presented. The results for the generalized decorated square lattice are numerically confirmed by commercial software (National Instruments software Multisim). The asymptotic values of the resistance for the generalized decorated simple cubic lattice are calculated numerically when the separation of the two lattice points goes to infinity. Keywords: Generalized decorated square lattice, Two-site resistance, Green’s function