J. H. Asad

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.

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.

Fractional Bateman-Feshbach Tikochinsky Oscillator

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grunwald—Letnikov approach, which is power series expansion of the generating function.

Exact Evaluation of the Resistance in an Infinite Face-Centered Cubic Network

The equivalent resistance between the origin and the lattice site (2n,0,0), in an infinite Face Centered Cubic (FCC) network consisting from identical resistors each of resistance R, has been evaluated analytically and numerically. The asymptotic behavior of the equivalent resistance has been also investigated. Finally, some numerical values for the equivalent resistance 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.

Resistance calculation of the decorated centered cubic networks: Applications of the Green's function

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Greens function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

INFINITE NETWORKS OF IDENTICAL CAPACITORS

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.

INFINITE SIMPLE 3D CUBIC NETWORK OF IDENTICAL CAPACITORS

In this paper, the effective capacitance between the origin (0, 0, 0) and any other lattice site (l1, l2, l3), in an infinite simple cubic (SC) network consisting of identical capacitors each of capacitance C, has been expressed rationally in terms of the known value go and π. The asymptotic behavior is also investigated, and some numerical values for the effective capacitance are presented.