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Radiation Fields
Published in Guillermo Gonzalez, Advanced Electromagnetic Wave Propagation Methods, 2021
The theory of Green functions and its applications are discussed in Chapter 5 where it is shown that a most important property of the Green function is that once the Green function is known, the solution to the associated inhomogeneous wave equation is readily obtained. Basically, the Green function is the impulse response (i.e., a unit delta function excitation) solution to an inhomogeneous linear differential equation. Since using superposition a source (i.e., Je,z) can be represented as a sum of delta functions, the response involves a sum of Green function solutions. Hence, the solution to [∇2+β2]A=−μJe
Computational Modeling of Nanoparticles
Published in Sarhan M. Musa, ®, 2018
The electron density and the current for an open scattering system can be modeled in different ways. The wave functions obey the open boundary conditions that depend on electron energy, so that there exist an infinite number of wave functions. This is because for an infinite system the energy spectrum of electrons is continuous. Because the central quantity is the total electron density, calculations include integrations over the electron energy so that only a finite number of wave functions are actually calculated. Typically, energy integration paths include rapid variations, for example, sharp resonance peaks, so that a large amount of wave functions are needed making the calculations heavy. The scattering problem can also be formulated using the Green’s function approach. In the continuum limit this gives the same results as the scattering wave function method. We use the single-particle Green’s functions as the auxiliary functions in the Kohn–Sham equations [34–37] This is done in order to implement open boundary conditions, to add the finite bias-voltage between the leads, and to calculate the current.
Sound Radiation and Propagation Fundamentals
Published in Colin H. Hansen, Foundations of Vibroacoustics, 2018
The Green’s function technique is a convenient approach to analysing sound radiation and propagation problems, whether sound radiation by a structure into free space is considered or whether sound transmission through a structure into an enclosed space is of interest. Physically, a Green’s function is simply a transfer function that relates the response at one point in an acoustic medium or a structure to an excitation by a unit point source at another point. The value of the Green’s function for a particular physical system is dependent on the location of the source and observation points and the frequency of excitation. Note that here, neither the type of excitation source nor the type of response has been defined. This will be done when specific examples are considered.
Coupling vibration of composite pipe-in-pipe structure subjected to gas-liquid mixed transport by means of green’s functions
Published in Mechanics of Advanced Materials and Structures, 2023
X.P. Chang, J.M. Fan, C.J. Qu, Y.H. Li
In this paper, Green’s functions of the system are obtained by Laplace transform and inverse Laplace transform. Laplace transform is performed on Eq. (24), and the dynamic equations of the PIP system in the Laplace transform domain are obtained as follows where is the complex variable in the transform domain, and are image functions. The expressions of functions and are as follows where
Wave field in a layer with a linear background profile and multiscale random irregularities
Published in Waves in Random and Complex Media, 2022
We analyzed the previously obtained integral representation (4) for the field of a point source in a layer with a linear profile and in the presence of random irregularities of different scales. The stationary phase method was considered taking into account the large contribution of the vicinity of the turning point to the statistical characteristics of the reflected wave. This made it possible to integrate some integrals and obtain integral representations (21), (23) of a lower-order. The resulting integral representations are convenient for studying the statistical moments, and, in particular for studying the effect of various (but greater than the wavelength) irregularities on wave reflection from the layer. In addition, since the solution obtained is a Green’s function, it can be used to calculate the scattering of waves by various objects in an inhomogeneous plasma. This makes it possible to study scattering on small-scale (less than or on the order of the wavelength) irregularities (33). The solutions obtained are quite simple and can be used in the interpretation of experimental data and their processing in the study of ionospheric plasma [29–30] and thermonuclear fusion plasma [26].
Nonequilibrium Green’s functions (NEGF) in vibrational energy transport: a topical review
Published in Nanoscale and Microscale Thermophysical Engineering, 2021
The transport equations (Eqs. 3 to 8) depend on the retarded Green’s function , the self-energies of the contacts , and the broadening matrices. These matrices carry all the physics of the problem. The main ingredient, the Green’s function, is the impulse response of a linear differential operator. For our case, the differential operator is the set of equations of motion of all the atoms in the system, which in the frequency domain is given by [36, 42, 64, 99]