Green’s function representation of laser induced thermal dynamics and determination of thermal criteria for optically induced neural activation

2013 ◽  
Author(s):  
Bryan Norton ◽  
Meghan Bowler
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Neural Activation ◽  
Thermal Dynamics ◽  
Function Representation ◽  
Optically Induced

scholarly journals On the Marchenko equation for multicomponent single-sided reflection data

2014 ◽  
Vol 199 (3) ◽  
pp. 1367-1371 ◽  
Author(s):  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Green’S Function ◽  
Recent Work ◽  
Green's Function ◽  
Scattered Field ◽  
Iterative Solution ◽  
Virtual Source ◽  
Function Representation ◽  
Reflection Data ◽  
Marchenko Equation ◽  
Multicomponent Data

Abstract Recent work on the Marchenko equation has shown that the scalar 3-D Green's function for a virtual source in the subsurface can be retrieved from the single-sided reflection response at the surface and an estimate of the direct arrival. Here, we discuss the first steps towards extending this result to multicomponent data. After introducing a unified multicomponent 3-D Green's function representation, we analyse its 1-D version for elastodynamic waves in more detail. It follows that the main additional requirement is that the multicomponent direct arrival, needed to initiate the iterative solution of the Marchenko equation, includes the forward-scattered field. Under this and other conditions, the multicomponent Green's function can be retrieved from single-sided reflection data, and this is demonstrated with a 1-D numerical example.

The Green's Function and its Oscillatory Properties for a Single Branch Structure of a Pinned Beam-Rod System

2011 ◽  
Vol 291-294 ◽  
pp. 2014-2020
Author(s):  
Min He ◽  
Qi Shen Wang
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Qualitative Properties ◽  
Direct Integral ◽  
Rod System ◽  
Support Conditions ◽  
Oscillation Properties ◽  
Single Branch ◽  
Oscillatory Properties

This paper concerns the determination of qualitative properties of linear vibrational systems, in particular for a single branch structure consisting of a pinned beam-rod system. First, we establish the characteristic equations satisfied by the Green’s function for this structure. The Green’s functions corresponding to support conditions where the left end of the beam was pinned-end are deduced by adopting the direct integral method. Using the theory of oscillation kernels established by Gantmakher and Krein, oscillatory properties of the Green's function for the beam-rod system are proved. Furthermore, four oscillation properties associated with frequencies and mode functions for the system are given.

scholarly journals Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Sami Boudieb ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Abelian Field ◽  
The Green Function

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

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