Green's tensors and lattice sums for electrostatics and elastodynamics

1997 ◽  
Vol 453 (1958) ◽  
pp. 643-662 ◽  
Author(s):  
A. B. Movchan ◽  
N. A. Nicorovici ◽  
R. C. McPhedran
Keyword(s):  
Lattice Sums

scholarly journals On the calculation of lattice sums

Physica ◽  
1957 ◽  
Vol 23 (1-5) ◽  
pp. 309-321 ◽  
Author(s):  
B.R.A. Nijboer ◽  
F.W. De Wette
Keyword(s):  
Lattice Sums

Some simple theorems concerning crystal lattice sums of electric potential, electric field, and electric field gradient in crystals

1967 ◽  
Vol 20 (12) ◽  
pp. 2551 ◽  
Author(s):  
CK Coogan
Keyword(s):  
Electric Field ◽  
Field Gradient ◽  
Electric Potential ◽  
Higher Symmetry ◽  
Lattice Sums ◽  
Symmetry Properties ◽  
Lattice Sum ◽  
Direct Lattice ◽  
Electric Potential Field ◽  
Conver Gence

The conditions under which direct lattice sums of electric potential, field, and field gradient converge are discussed. The analogous conditions under which differences in these lattice sums, for two points in the crystal, converge are also outlined. These conditions are applied to direct lattice sum calculations in crystals in which the ideal lattice is distorted close to a defect of some kind. The conver- gence conditions are then applied to the case of determining the direct lattice sums in crystals in which higher symmetry properties can be invoked, which leads to a knowledge by inspection of the lattice sum at one point in the unit cell.

Linear Dependence of Lattice Sums

1958 ◽  
Vol 110 (1-6) ◽  
pp. 112-126 ◽  
Author(s):  
Pinhas Naor
Keyword(s):  
Linear Dependence ◽  
Lattice Sums

Lattice sums arising from the Poisson equation

2013 ◽  
Vol 46 (11) ◽  
pp. 115201 ◽  
Author(s):  
D H Bailey ◽  
J M Borwein ◽  
R E Crandall ◽  
I J Zucker
Keyword(s):  
Poisson Equation ◽  
Lattice Sums ◽  
The Poisson Equation

On the convergence problem for lattice sums

1990 ◽  
Vol 23 (12) ◽  
pp. 2523-2528 ◽  
Author(s):  
J P Buhler ◽  
R E Crandall
Keyword(s):  
Convergence Problem ◽  
Lattice Sums

scholarly journals Banach lattice sums with hereditary Fatou properties

2014 ◽  
Vol 50 (2) ◽  
pp. 271-282
Author(s):  
Mieczysław Mastyło ◽  
Enrique A. Sánchez-Pérez
Keyword(s):  
Banach Lattice ◽  
Lattice Sums
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