Eur. Phys. J. Plus (2014) 129: 29
https://doi.org/10.1140/epjp/i2014-14029-y

Regular Article

Perturbation theory of uniform tiling of space with resistors

¹ Department of Physics, Al-Hussein Bin Talal University, 71111, Ma’an, Jordan
² Department of Physics, Mutah University, Karak, Jordan
³ Department of Physics, The University of Jordan, 11942, Amman, Jordan

^* e-mail: owaidat@ahu.edu.jo

Received: 22 October 2013
Revised: 29 December 2013
Accepted: 14 January 2014
Published online: 17 February 2014

Abstract

Using the general Green method, the resistance between two arbitrary nodes of any resistor network structure, which is a periodic (uniform) tiling of d -dimensional space with electrical resistors, is studied when the network is perturbed by replacing one edge (resistor) by another one. The analytical expression of the resistance for perturbed lattice in terms of that for the perfect one is derived. Theoretical results are presented for the infinite perturbed centered square lattice. In addition, these results are verified experimentally and numerically.