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

2010 ◽  
Vol 24 (19) ◽  
pp. 2057-2068 ◽  
Author(s):  
M. Q. OWAIDAT ◽  
R. S. HIJJAWI ◽  
J. M. KHALIFEH
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Experimental Results ◽  
Square Lattice ◽  
Perfect Lattice ◽  
Arbitrary Lattice ◽  
Lattice Green's Function ◽  
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 Green's function. The relation between the resistance and the lattice Green's function for the perturbed lattice is derived. 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. Numerical and experimental results are presented.

PERTURBATION OF AN INFINITE NETWORK OF IDENTICAL CAPACITORS

2007 ◽  
Vol 21 (02) ◽  
pp. 199-209 ◽  
Author(s):  
R. S. HIJJAWI ◽  
J. H. ASAD ◽  
A. J. SAKAJI ◽  
J. M. KHALIFEH
Keyword(s):  
Asymptotic Behavior ◽  
Green’S Function ◽  
Green's Function ◽  
Numerical Results ◽  
Square Lattice ◽  
Infinite Network ◽  
Arbitrary Lattice ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

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.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

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.

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