A review of the theoretical approach for calculating the resistance between two arbitrary lattice points in an infinite square lattice (perfect and perturbed cases) is carried out using the lattice Green's function. We show how to calculate the resistance between the origin and any other site using the lattice Green's function at the origin, Go (0, 0), and its derivatives. Experimental results are obtained for a finite square network consisting of 30 ×30 identical resistors, and a comparison with those obtained theoretically is presented.

A. J. Sakaji

Unit of Basic Medical Sciences

College of Dentistry

J.H. Asad

R.S. Hijjawi

J.M. Khalifeh

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

61.50.Ah Theory of crystal structure, crystal symmetry

calculations and modeling Crystal growth

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Ajman University

European Physical Journal B

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors each of capacitance C is calculated. The method is generalized to infinite Simple Cubic (SC) lattice of identical capacitors each of capacitance C. We make use of the superposition principle and the symmetry of the infinite grid. © 2010 World Scientific Publishing Company.

Modern Physics Letters B

Infinite networks of identical capacitors

An infinite regular three-dimensional network is composed of identical resistors each of resistance joining adjacent nodes. What is the equivalent resistance between the lattice site and the lattice site, when two bonds are removed from the perfect network? Three cases are considered here, and some numerical values are calculated. Finally, the asymptotic behavior of the equivalent resistance is studied for large distances between the two sites. © 2008 EDP Sciences.

EPJ Applied Physics

Infinite simple 3D cubic lattice of identical resistors (two missing bonds)

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. © 2007 EDP Sciences.

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

The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l, m) for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the Lattice Green's Function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for infinite separation between the origin and the site (l, m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight- binding Hamiltonian. This method can be applied directly to other lattice structures. © World Scientific Publishing Company.

International Journal of Modern Physics B

Infinite network of identical capacitors by Green's Function

The resistance between arbitrary sites of infinite square network of identical resistors is studied when the network is perturbed by removing two bonds from the perfect lattice. A connection is made between the resistance and the lattice Green's function of the perturbed network. By solving Dyson's equation the Green's function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Some numerical results are presented for an infinite square lattice. © 2005 Springer Science + Business Media, Inc.

International Journal of Theoretical Physics

Remarks on perturbation of infinite networks of identical resistors

An expression for the Green's function (GF) of face centered cubic (FCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind. © 2005 Springer Science + Business Media, Inc.

Journal	Data powered by TypesetEuropean Physical Journal B
Publisher	Data powered by TypesetSpringer
ISSN	14346028
Open Access	No