ON VOLTERRA'S DISLOCATIONS IN A SEMI-INFINITE ELASTIC MEDIUM

1958 ◽  
Vol 36 (2) ◽  
pp. 192-205 ◽  
Author(s):  
J. A. Steketee
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Displacement Field ◽  
General Problem ◽  
Function Method ◽  
Green’S Functions ◽  
Boundary Surface ◽  
Green’S Function Method ◽  
Plane Parallel

In this paper a Green's function method is developed to deal with the problem of a Volterra dislocation in a semi-infinite elastic medium in such a way that the boundary surface of the medium remains free from stresses. (A Volterra dislocation is here defined as a surface across which the displacement components show a discontinuity of the type Δu = U + Ω ×r, where U and Ω are constant vectors.) It is found that the general problem requires the construction of six sets of Green's functions. The method for the construction is outlined and applied to one of the six sets, which is of the type of two double forces with moments in a plane parallel with the boundary. The displacement field thus generated is computed. Several of the results obtained are believed to be of geophysical interest, but a more detailed discussion of these applications is postponed to a further communication which is being prepared.

scholarly journals Pedagogical introduction to equilibrium Green's functions: condensed-matter examples with numerical implementations

2016 ◽  
Vol 39 (1) ◽  
Author(s):  
Mariana M. Odashima ◽  
Beatriz G. Prado ◽  
E. Vernek
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Relaxation Times ◽  
Scientific Language ◽  
Green’S Function Method ◽  
Discrete Lattices ◽  
Interacting Electrons

The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible to extract information from the system under study, such as the density of states, relaxation times and response functions. Despite its power and versatility, it is known as a laborious and sometimes cumbersome method. Here we introduce the equilibrium Green's functions and the equation-of-motion technique, exemplifying the method in discrete lattices of non-interacting electrons. We start with simple models, such as the two-site molecule, the infinite and semi-infinite one-dimensional chains, and the two-dimensional ladder. Numerical implementations are developed via the recursive Green's function, implemented in Julia, an open-source, efficient and easy-to-learn scientific language. We also present a new variation of the surface recursive Green's function method, which can be of interest when simulating simultaneously the properties of surface and bulk.

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
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