Atomistic study of fracture of nanoscale materials by molecular dynamics and lattice Green's function methods

2001 ◽  
Vol 11 (PR5) ◽  
pp. Pr5-11-Pr5-18 ◽  
Author(s):  
K. Masuda-Jindo ◽  
M. Menon ◽  
V. Van Hung
Keyword(s):  
Molecular Dynamics ◽  
Green’S Function ◽  
Green's Function ◽  
Nanoscale Materials ◽  
Atomistic Study ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

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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