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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. [ABSTRACT FROM AUTHOR]

An expression for the Green function of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states, phase shift and scattering cross-section are expressed in terms of complete elliptic integrals of the first kind. [ABSTRACT FROM AUTHOR]

The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's 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. [ABSTRACT FROM AUTHOR]

The effective capacitance between the origin and any other lattice site, in an infinite 3D simple cubic network consisting of identical capacitors, is evaluated in terms of the lattice Green function of the network. The perfect case is reviewed shortly, while the perturbed case (a capacitor is removed) is studied in two cases. Numerical values of the effective capacitance are presented and the asymptotic behavior is studied for the both cases. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities. [ABSTRACT FROM AUTHOR]

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 Green's 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An expression for the Green's Function for triangular lattice is evaluated analytically and numerically for single impurity lattices of zero range potential. Also the S-phase shift, and scattering cross section are expressed in terms of complete elliptic integrals. [ABSTRACT FROM AUTHOR]

In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement. [ABSTRACT FROM AUTHOR]

We investigate the fractional harmonic oscillator on a moving platform. We obtained the fractional Euler-Lagrange equation from the derived fractional Lagrangian of the system which contains left Caputo fractional derivative. We transform the obtained differential equation of motion into a corresponding integral one and then we solve it numerically. Finally, we present many numerical simulations. [ABSTRACT FROM AUTHOR]

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 Green's 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 Dyson's equation exactly. Numerical results are presented for the infinite perturbed square network. Finally, the asymptotic behavior of the effective capacitance has been studied. [ABSTRACT FROM AUTHOR]