scholarly journals Localization for a line defect in an infinite square lattice

Author(s):  
D. J. Colquitt ◽  
M. J. Nieves ◽  
I. S. Jones ◽  
A. B. Movchan ◽  
N. V. Movchan

Localized defect modes generated by a finite line defect composed of several masses, embedded in an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations of the lattice Green's function are presented and discussed. The problem is reduced to an eigenvalue system and the properties of the corresponding matrix are examined in detail to yield information regarding the number of symmetric and skew-symmetric modes. Asymptotic expansions in the far field, associated with long wavelength homogenization, are presented. Asymptotic expressions for Green's function in the vicinity of the band edge are also discussed. Several examples are presented where eigenfrequencies linked to this system and the corresponding eigenmodes are computed for various defects and compared with the asymptotic expansions. The case of an infinite defect is also considered and an explicit dispersion relation is obtained. For the case when the number of masses within the line defect is large, it is shown that the range of the eigenfrequencies can be predicted using the dispersion diagram for the infinite chain.

2016 ◽  
Vol 30 (24) ◽  
pp. 1650166 ◽  
Author(s):  
M. Q. Owaidat ◽  
J. H. Asad ◽  
Zhi-Zhong Tan

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.


2008 ◽  
Vol 53 (9(6)) ◽  
pp. 3645-3649
Author(s):  
NguyenVan Hieu ◽  
NguyenBich Ha ◽  
V.P. Gerdt ◽  
O. Chuluunbaatar ◽  
A.A. Gusev ◽  
...  

2010 ◽  
Vol 24 (19) ◽  
pp. 2057-2068 ◽  
Author(s):  
M. Q. OWAIDAT ◽  
R. S. HIJJAWI ◽  
J. M. KHALIFEH

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.


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