Matched Asymptotic Expansions of the Green’s Function for the Electric Potential in an Infinite Cylindrical Cell

1976 ◽  
Vol 30 (2) ◽  
pp. 222-239 ◽  
Author(s):  
A. Peskoff ◽  
R. S. Eisenberg ◽  
J. D. Cole
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Asymptotic Expansions ◽  
Electric Potential ◽  
Matched Asymptotic Expansions ◽  
Cylindrical Cell

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

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120579 ◽  
Author(s):  
D. J. Colquitt ◽  
M. J. Nieves ◽  
I. S. Jones ◽  
A. B. Movchan ◽  
N. V. Movchan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Asymptotic Expansions ◽  
Square Lattice ◽  
Line Defect ◽  
Linear Superposition ◽  
Asymptotic Expressions ◽  
Yield Information ◽  
Finite Line ◽  
Single Mass

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.

scholarly journals ASYMPTOTIC EXPANSIONS FOR APPROXIMATE SOLUTIONS OF HAMMERSTEIN INTEGRAL EQUATIONS WITH GREEN'S FUNCTION TYPE KERNELS

2014 ◽  
Vol 19 (1) ◽  
pp. 127-143 ◽  
Author(s):  
Rekha P. Kulkarni ◽  
Akshay S. Rane
Keyword(s):  
Approximate Solution ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Asymptotic Expansions ◽  
Approximate Solutions ◽  
Richardson Extrapolation ◽  
Function Type ◽  
Hammerstein Equation ◽  
Hammerstein Integral Equations

We consider approximation of a nonlinear Hammerstein equation with a kernel of the type of Green's function using the Nyström method based on the composite midpoint and the composite modified Simpson rules associated with a uniform partition. We obtain asymptotic expansions for the approximate solution unat the node points as well as at the partition points and use Richardson extrapolation to obtain approximate solutions with higher orders of convergence. Numerical results are presented which confirm the theoretical orders of convergence.

Green’s function of the electric potential equation

2020 ◽  
Author(s):  
Resti Julia Susanti ◽  
Evi Noviani ◽  
Fransiskus Fran
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Electric Potential ◽  
Potential Equation

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method
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