R. S. Hijjawi

INFINITE NETWORK OF IDENTICAL CAPACITORS BY GREEN'S FUNCTION

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 Greens 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.

Resistance Calculation for an infinite Simple Cubic Lattice Application of Green's Function

It is shown that the resistance between the origin and any lattice point (l,m,n) in an infinite perfect Simple Cubic (SC) lattice is expressible rationally in terms of the known value of G0 (0,0,0). The resistance between arbitrary sites in an infinite SC lattice is also studied and calculated when one of the resistors is removed from the perfect lattice. The asymptotic behavior of the resistance for both the infinite perfect and perturbed SC lattice is also investigated. Finally, experimental results are obtained for a finite SC network consisting of 8×8×8 identical resistors, and a comparison with those obtained theoretically is presented.

Interstitial single resistor in a network of resistors application of the lattice Green's function

The resistance between two arbitrary nodes of a network of resistors is studied when the network is perturbed by connecting an extra resistor between two arbitrary nodes in the perfect lattice. The lattice Greens function and the resistance of the perturbed network are expressed in terms of those of the perfect lattice by solving Dysons equation. A comparison is carried out between numerical and experimental results for a square lattice.

PERTURBATION OF AN INFINITE NETWORK OF IDENTICAL CAPACITORS

The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the lattice Greens function of the perturbed network, where they are expressed in terms of those of the perfect network. The asymptotic behavior of the perturbed capacitance is investigated as the separation between the two sites goes to infinity. Finally, numerical results are obtained along different directions and a comparison is made with the perfect capacitances.

SUBSTITUTIONAL SINGLE RESISTOR IN AN INFINITE SQUARE LATTICE APPLICATION TO LATTICE GREEN'S FUNCTION

The resistance between two arbitrary lattice sites in an infinite square lattice of identical resistors is studied when the lattice is perturbed by substituting a single resistor using lattice Greens function. The relation between the resistance and the lattice Greens function for the perturbed lattice is derived. Solving Dysons equation, the Greens function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical and experimental results are presented.

Lattice Green's Function for the Face Centered Cubic Lattice

An expression for the Greens 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.

ELECTRICAL NETWORKS WITH INTERSTITIAL SINGLE CAPACITOR

We investigate the equivalent capacitance between two arbitrary nodes in a perturbed network (i.e. an interstitial capacitor is introduced between two arbitrary points in the perfect lattice) based on the lattice Greens function approach. An explicit formula for the capacitance of the perturbed lattice is derived in terms of the capacitances of the perfect lattice by solving Dysons equation exactly. Numerical results are presented for the infinite perturbed square network. Finally, the asymptotic behavior of the effective capacitance has been studied.

Lattice Green's Function for the Body-Centered Cubic Lattice

An expression for the Greens function (GF) of Body-Centered Cubic (BCC) lattice is evaluated analytically and numerically for a single impurity lattice. The density of states (DOS), phase shift, and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.

Remarks on the lattice Green’s function: The Glasser case

We have investigated the lattice Green’s function for the Glasser cubic lattice. Expressions for its density of states, phase shift, and scattering cross section in terms of complete elliptic integrals of the first kind are derived.

Lattice Green's Function in the General Glasser Case

We have investigated the lattice Greens function for the general Glasser cubic lattice. Expressions for its density of states, phase shift, and scattering cross section in terms of complete elliptic integrals of the first kind are derived.