Infinite 2D square network of identical capacitors with two missing bonds

¹ Tabuk University, Teachers' College, Department of Sciences (Physics), PO Box 1144, Tabuk, Saudi Arabia
² Department of Physics, Mutah University, Jordan
³ Department of Physics, Ajman University, UAE
⁴ Department of Physics, University of Jordan, 11942 Amman, Jordan

Corresponding author: jhasad1@yahoo.com

Received: 22 April 2007
Revised: 17 July 2007
Accepted: 7 September 2007
Published online: 13 December 2007

Abstract

The capacitance between any two arbitrary lattice sites of an infinite square network consisting of identical capacitors is studied analytically and numerically for a perturbed network. The perturbation is as a result of removing the bonds and from the perfect network. The equivalent capacitance is expressed in terms of the Lattice Green's Function (LGF) of the perturbed network. Solving Dyson's equation we express the LGF and the capacitance of the perturbed network in terms of those of the infinite perfect network. The asymptotic behavior of the perturbed capacitance is also studied. Finally, some numerical results are presented for the perturbed infinite square lattice, and a comparison is carried out for those of the perturbed and perfect infinite square network.