Green's function for electromagnetic scattering from a random rough surface

In previous work [D. P. Vasholz, J. Acoust. Soc. Am. 60, S33(A) (1976)] a general black-box approach to wave propagation through a randomly fluctuating medium based upon the stochastic Green's function G was presented. Motivated by parallels with quantum field theory the quantities 𝒢 and M, related to the first and second moments of G, were defined. It was then shown how these quantities may be conveniently used to describe such effects as frequency broadening and coherence losses induced by the medium. In the present work it is pointed out that stochastic Green's functions readily lend themselves to interpretations of recent experimental work which have been made in terms of the random walk taken by the time-varying transfer function in the complex plane [W. H. Munk and G. O. Williams, Nature 267, 775 (1977)]. In particular it is shown how these random walks arise in a stochastic Green's function formulation and how their principal parameters may be very simply expressed in terms of 𝒢 and M.

Green's matrix of the plane problem of elasticity theory for an orthotropic strip

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/'s and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.

This paper presents a physics-oriented, hybrid deterministic-stochastic model for analyzing the statistical electromagnetic coupling to complex cavities via apertures. The key ingredient is an aperture-aware, site-specific stochastic Green's function method, which integrates the system-specific, non-chaotic interactions with the universal statistical behavior of the system. Compared to existing work, the in-situ stochastic Green's function is augmented with the short-orbit contribution through a ray-sensing approach. The outcome leads to improved fidelity in the statistical prediction. The results are particularly useful for studying wideband electromagnetic coupling through apertures.

While recent studies have proven an unexpected liquid–vapor phase transition of adsorbed liquid films, a comprehensive description of the mechanisms of different types of phase change regimes over realistic representations of random rough surfaces is absent in the literature. The current comprehensive study investigates the effects of a gold random rough surface, liquid film thickness, and substrate temperature on the liquid–vapor phase change regime of an adsorbed sodium liquid film, considering the evaporator section of a wicked heat pipe (WHP) using a molecular dynamics (MD) simulation. At first, to generate a realistic random rough surface, a new and promising method is proposed that is entirely based on MD simulations. Then, to simulate the evaporator section of a WHP, a unique configuration for eliminating the vapor domain is developed. The simulation results reveal that three distinct regimes, namely, normal evaporation, cluster boiling, and film boiling, could be identified, which are presented on two-dimensional diagrams with the substrate temperature and liquid film thickness as coordinates for the ideally smooth and random rough surfaces. The results also manifest that even though using the random rough surface could lead to different phase transition regimes, the type of regime depends mainly on the substrate temperature and liquid film thickness. Furthermore, this study displays two different modes for normal evaporation. Also, it is shown that the impacts of the liquid film thickness and substrate temperature on the mode of normal evaporation are much more significant than the surface roughness.

Electromagnetic fields created in a homogeneous medium by a known distribution of electric current are determined by integral equations involving free space Green's functions. In actual situations, however, current distributions are not known beforehand and must be determined, in such a way that the total fields satisfy the boundary conditions on the conductors. The integral equation technique was extended to treat also heterogeneous structures, in order to analyze and design multilayer printed circuits and antennas, such as the broadband strip-slot-foam-inverted patch printed antenna. Sommerfeld integrals provide Green's functions for stratified media, which are evaluated by means of specifically developed, efficient computer algorithms. Structures including coaxial or line feeds and coupling through slots can now be easily analyzed with commercially available software packages.

Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles

In the context of the backscattering of waves from a random rough surface, a theoretical model is used to investigate the geometrical self-shadowing of a surface described by Gaussian statistics. Expressions are derived for various shadowing probabilities as functions of the parameter characterizing surface roughness and of the angle of incidence of the illuminating beam. The theoretical shadowing functions compare closely with those obtained experimentally from a recent computer simulation of a Gaussian surface.

A rigorous three-dimensional (3-D) electromagnetic model is developed to analyze the scattering from anti-personnel (AP) nonmetallic mine-like target when it is buried near a clutter object under two-dimensional (2-D) random rough surfaces. The steepest descent fast multipole method (SDFMM) is implemented to solve for the unknown electric and magnetic surface currents on the ground surface, on the target and on the clutter object. A comprehensive numerical investigation of two clutter sources; the ground roughness and the nearby benign object, is presented based on using more than 800 random rough surface realizations which could not be achieved without using fast algorithms such as the SDFMM. The statistics of the scattered near-electric fields are computed using the Monte Carlo simulations for both polarizations. For the parameters used here, the results show that the average and the standard deviation of the target signature represent 5-7% and 3-3.5% of the total scattered signal, respectively, while they represent 16-20% and 7-12% of the signal for the clutter object, respectively. This study indicates the high possibility of a false alarm during the detection process when the target is located nearby a realistic object such as a piece of a tree root.

The physical optics approach and Lorentz transformations are combined to formulate scatter from a random rough surface in uniform motion. The perfectly conducting scatterer is excited by an elliptically polarized plane electromagnetic wave and the analysis ends in the velocity‐dependent expressions for the scattering cross section per unit area, the depolarization factor and the radial tilt. The direction of motion is considered parallel as well as normal to the scatterer's mean plane. The combined effect of roughness and motion on scattering and depolarization is investigated through a numerical example. The calculations reveal that parallel motion modifies scatter through aberration while normal motion results in scatter amplification. The depolarization factor and/or radial tilt might be used for motion estimation.

A statistical model of wave scattering from random rough surfaces

This paper presents a physics-oriented, mathematically tractable statistical wave model for analyzing the naturally occurring chaotic dynamics of high-frequency reverberation within complex cavity environments. The key ingredient is a vector dyadic stochastic Green's function method derived from Wigner's random matrix theory and Berry's random wave hypothesis. The stochastic Green's function statistically replicates the multipath, ray -chaotic interactions between ports of entry and ports of interference without involving the complex details within the target's enclosure. The work achieves a physics-based modeling and simulation capability that predicts the probabilistic behavior of backdoor coupling to complex electronic enclosures.

In this paper, the model developed for predicting the scattering characteristics from statistically rough surfaces is based upon the integral-equation model with multiple scattering. Its objective is to examine the bistatic scattering characteristics from randomly rough surfaces along different azimuth angles. For a better understanding of the scattering behavior from randomly rough surfaces, information about scattering must be known omnidirectionally, not just in the specular or backscatter direction. Comparisons between the model prediction and the experimental measurements are made for both like and cross polarizations. This model prediction demonstrates good agreement with the experimental data. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 25: 271–275, 2000.

The guided normal waves or modes in a waveguide would be perturbed if the boundaries of the waveguide were to become statistically irregular or rough. Due to the accumulation effects of multiple scattering along the entire propagation path, even very slight boundary irregularities can give rise to a considerable influence on the propagation characteristics of the guided modes. In this paper, a way is proposed to treat the scattering problem of guided waves in a waveguide with a slightly rough boundary by applying the stochastic functional approach, which has been used successfully in the scattering problems of a plane scalar or electromagnetic wave in free space from various shaped random rough surfaces and has been shown to be good for treating the multiple scattering effects. As a prototype of the basic theory, only the planar structure of the waveguide and the Dirichlet boundary condition are considered. The waveguide's Green's function is expanded in terms of the Wiener-Hermite stochastic functionals of a homogeneous Gaussian random surface. Expressions for the modified normal waves (modes) of the average or coherent Green's function are given for the Dirichlet boundary condition. A mass operator is derived which contains the information of the multiple scattering ofmore » the modes from the rough boundary and can be evaluated in an iterative way. The second order statistical moment or the correlation function of the Green's function is also considered. Some numerical examples are given for illustration. It has been shown that our approach gives more thorough results than those given by the graphical or Feynman diagram method.« less

ABSTRACTMany‐body Green's function theory in the GW approximation with the Bethe–Salpeter equation (BSE) provides a powerful framework for the first‐principles calculations of single‐particle and electron–hole excitations in perfect crystals and molecules alike. Application to complex molecular systems, for example, solvated dyes, molecular aggregates, thin films, interfaces, or macromolecules, is particularly challenging as they contain a prohibitively large number of atoms. Exploiting the often localized nature of excitation in such disordered systems, several methods have recently been developed in which GW‐BSE is applied to a smaller, tractable region of interest that is embedded into an environment described with a lower‐level method. Here, we review the various strategies proposed for such embedded many‐body Green's functions approaches, including quantum–quantum and quantum–classical embeddings, and focus in particular on how they include environment screening effects either intrinsically in the screened Coulomb interaction in the GW and BSE steps or via extrinsic electrostatic couplings.