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On the perturbation of a uniform tiling with resistors

Department of Physics, Al-Hussein Bin Talal University, P. O. Box 20, Ma’an 71111, Jordan

Corresponding author.

Department of Physics, Faculty of Arts and Sciences, P. O. Box 7, Palestine Technical University, Kadoorie, Tulkarm, Palestine

E-mail Address: drjasad@yahoo.com

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, and

Zhi-Zhong Tan

Department of Physics, Nantong University, Nantong 226019, P. R. China

E-mail Address: tanzzh@163.com

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https://doi.org/10.1142/S0217979216501666Cited by:16 (Source: Crossref)

Abstract

The perturbation of a uniformly tiled resistor network by adding an edge (a resistor) to the network is considered. The two-point resistance on the perturbed tiling in terms of that on the perfect tiling is obtained using Green’s function. Some theoretical results are presented for an infinite modified square lattice. These results are confirmed experimentally by constructing an actual resistor lattice of size 13 × 13.

Keywords:

PACS: 01.55.+b, 02.30.Vv, 41.20.Cv, 61.50.Ah, 84.37.+q, 05.50.+q

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