“Multiple-scattering” (green's function) model for polyatomic molecules II. Theory

2009 ◽  
Vol 1 (S1) ◽  
pp. 361-367 ◽  
Author(s):  
Keith H. Johnson
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Polyatomic Molecules ◽  
Function Model

scholarly journals Unified double- and single-sided homogeneous Green’s function representations

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160162 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Time Reversal ◽  
Wave Theory ◽  
Boundary Integral ◽  
Open Boundary ◽  
Quantum Mechanical ◽  
Holographic Imaging ◽  
Scattering Time

In wave theory, the homogeneous Green’s function consists of the impulse response to a point source, minus its time-reversal. It can be represented by a closed boundary integral. In many practical situations, the closed boundary integral needs to be approximated by an open boundary integral because the medium of interest is often accessible from one side only. The inherent approximations are acceptable as long as the effects of multiple scattering are negligible. However, in case of strongly inhomogeneous media, the effects of multiple scattering can be severe. We derive double- and single-sided homogeneous Green’s function representations. The single-sided representation applies to situations where the medium can be accessed from one side only. It correctly handles multiple scattering. It employs a focusing function instead of the backward propagating Green’s function in the classical (double-sided) representation. When reflection measurements are available at the accessible boundary of the medium, the focusing function can be retrieved from these measurements. Throughout the paper, we use a unified notation which applies to acoustic, quantum-mechanical, electromagnetic and elastodynamic waves. We foresee many interesting applications of the unified single-sided homogeneous Green’s function representation in holographic imaging and inverse scattering, time-reversed wave field propagation and interferometric Green’s function retrieval.

Mean dyadic Green's function of a randomly rough surface

1994 ◽  
Vol 72 (1-2) ◽  
pp. 20-29 ◽  
Author(s):  
Saba Mudaliar
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Multiple Scattering ◽  
Rough Surface ◽  
Green's Function ◽  
Diagram Method ◽  
Dyadic Green’S Function ◽  
Dyadic Green's Function ◽  
Special Cases ◽  
Randomly Rough Surface

The problem of wave propagation and scattering over a randomly rough surface is considered from a multiple-scattering point of view. Assuming that the magnitude of irregularities are small an approximate boundary condition is specified. This enables us to derive an integral equation for the dyadic Green's function (DGF) in terms of the known unperturbed DGF. Successive iteration of this integral equation yields the Neumann series. On averaging this and using a diagram method the Dyson equation is derived. Bilocal approximation to the mass operator leads to an integral equation whose kernel is of the convolution type. This is then readily solved and the results are presented in a simplified and useful form. It is observed that the coherent reflection coefficients involve infinite series of multiple scattering. Two special cases are considered the results of which are in agreement with our expectations.

scholarly journals Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

2014 ◽  
Vol 90 (20) ◽  
Author(s):  
Aftab Alam ◽  
Suffian N. Khan ◽  
A. V. Smirnov ◽  
D. M. Nicholson ◽  
Duane D. Johnson
Keyword(s):  
Green’S Function ◽  
Multiple Scattering ◽  
Green's Function ◽  
Scattering Theory ◽  
Basis Set ◽  
Multiple Scattering Theory
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