Infinite 3D Cubic Lattices of Identical Resistors

2013 ◽  
Vol 313-314 ◽  
pp. 324-328
Author(s):  
J.H. Asad
Keyword(s):  
Asymptotic Behavior ◽  
Green's Function ◽  
Lattice Point ◽  
Numerical Results ◽  
The Other ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Other Hand ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

We expressed the resistance between the origin and any lattice point in an infinite perfect Simple Cubic (i.e., SC) network rationally in terms of the known value of the Lattice Green's Function at the origin (i.e., ), and . On the other hand, we investigated the asymptotic behavior of the resistance. Finally, some numerical results has been calculated.

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.

ELECTRICAL NETWORKS WITH INTERSTITIAL SINGLE CAPACITOR

2013 ◽  
Vol 27 (16) ◽  
pp. 1350123 ◽  
Author(s):  
M. Q. OWAIDAT ◽  
R. S. HIJJAWI ◽  
J. H. ASAD ◽  
J. M. KHALIFEH
Keyword(s):  
Asymptotic Behavior ◽  
Explicit Formula ◽  
Green's Function ◽  
Numerical Results ◽  
Function Approach ◽  
Electrical Networks ◽  
Perfect Lattice ◽  
Effective Capacitance ◽  
Equivalent Capacitance ◽  
Lattice Green's Function

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.

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

2014 ◽  
Vol 28 (32) ◽  
pp. 1450252 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
J. M. Khalifeh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Three Dimensional ◽  
Numerical Results ◽  
Effective Resistance ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Simple Cubic Lattice

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.

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