Wedge Diffraction Research Articles

An Analytical Seismic Response for Rigid Underground Rectangular Tunnel Subjected to Incident P Waves

A diffraction model based on the diffraction theory of elastic waves for the dynamic response of underground rectangular tunnel subjected to incident P waves is established. The rectangular structure is assumed to be a movable rigid body embedded in a homogenous, isotropic, and linear elastic medium. One particular advantage of the model is that the effects of vital factors such as the rigid scattering, radiation scattering, as well as the two‐dimensional scattering effect, and the wedge diffraction during movement are fully considered. The numerical method is verified by comparing with experimental data and other solutions in the literature. In addition, a parametric analysis of the effects of the incident angle, surrounding rock medium, and aspect ratio on the tunnel is also presented. The results show that with the increase of the incident angle, different parts of the tunnel exhibit obvious nonuniform distribution characteristics, and the bending moment of the sidewall is greater than that of the top slab. When the impedance ratio exceeds 0.26, the influence of surrounding rock characteristics on the dynamics of structure is more obvious; with the increase of the aspect ratio, the peak values of axial force at the top slab increases, whereas it decreases at the sidewall.

Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions

Summary We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener–Hopf approach. Specifically, the analyticity properties of the unknown (spectral) functions of the two-complex-variable Wiener–Hopf equation are studied. We show that these spectral functions can be analytically continued onto a two-complex dimensional manifold, and unveil their singularities in C2. To do so, integral representation formulae for the spectral functions are given and thoroughly used. It is shown that the novel concept of additive crossing holds for the penetrable wedge diffraction problem, and that we can reformulate the physical diffraction problem as a functional problem using this concept.

Approximate time domain solution for studying infinite wedge diffraction, its parameters, and characteristics.

An approximate time domain solution is derived for spherically spreading signals incident on an infinitely long rigid wedge. The solution is a short time approximation of the corresponding exact solution. The presented solution improves the accuracy of an approximate solution derived previously by the authors. The solution is extended to cylindrically spreading and plane wave incident signals. The solutions for all three types of incidence are recast in a unified form. The main advantage of this approximate solution is that it provides insight into the mechanism of diffraction. Specifically, it is shown that the time evolution of diffraction depends on a single time parameter-the diffraction delay time. Furthermore, a generator curve is presented that generates all diffraction impulse responses for all source and receiver locations, all wedge angles, and for all types of incident radiation. Finally, it is shown that any signal (irrespective of its time waveform or its type of spreading) incident on any wedge can be analyzed as an equivalent plane wave incident on a half plane. Thus, the diffraction field of a plane wave incident on a half plane (the simplest diffraction case) encompasses all wedge problems and can be considered a prototype diffraction problem.

Analysis of the Relationship of Video Text and Urban Image Communication Based on the Calculation Method of Wedge Diffraction in Geometrical Optics

City image reflects a city’s comprehensive competitiveness and is also an important indicator of a city’s spiritual civilization and urbanization process. A good city image is an intangible asset of a city, which can contribute to the political, economic, cultural, and social construction of a city and create more value for the city. This paper mainly discusses the research status and research methods of urban image at home and abroad. Based on the calculation method of wedge diffraction in geometrical optics, various heuristic uniform diffraction formulas of lossy wedge are compared and analyzed, and a better heuristic formula of uniform diffraction of lossy wedge is given. Finally, the selection of important channel parameters in the propagation channel is discussed, and a method for predicting the statistical parameters of the propagation channel of urban images based on the results of ray tracing is proposed. Then, the channel parameters are analyzed by using statistical parameters, and the channel parameters of the city image propagation model are analyzed.

Scattering and Diffraction by Wedges [Book Review

This book offers a valuable reference for anyone who is already working on or would like to learn more about the analytical and semianalytical methods for wedge diffraction. The authors aim to illustrate the usefulness and elegance of the Wiener–Hopf technique and, in particular, its generalization to the Fredholm method. The text is written in an accessible manner, with few prerequisites other than undergraduate courses. (Most importantly, a solid understanding of complex analysis and electromagnetism is assumed.) This makes it ideal for Ph.D. students and beyond, but a diligent master’s degree student could also make progress if there is sufficient motivation.

Application of heuristic UTD formulation for describing scattering by a thin and multilayer anisotropic slab

The previously developed heuristic uniform theory of diffraction (UTD) corner and wedge diffraction coefficients for a thin lossless anisotropic slab are generalized and applied for predicting electromagnetic scattering by a thin and multilayer anisotropic slab with complex permittivity and permeability tensors. The effective reflection and transmission coefficients of a thin and multilayer slab are used in the heuristic formulation to determine the scattered fields. Numerical results are provided for various scattering problems that demonstrate the application of the heuristic formulations for a thin and multilayer structure.

A High-Frequency Solution for Scattering by a Multilayer Anisotropic Slab

The previously developed heuristic uniform theory of diffraction corner and wedge diffraction coefficients for a thin lossless anisotropic slab are generalized and applied for predicting electromagnetic scattering by a lossy/lossless multilayer anisotropic slab. The effective reflection and transmission coefficients of a multilayer slab are used in the heuristic formulation to determine the scattered fields. The heuristic coefficients derived for a thin slab are applied to a multilayer slab with a finite thickness. Numerical results are provided for various scattering problems that demonstrate the validity of the heuristic formulations for a multilayer structure.

New Features in Feko and WinProp 2019

This paper describes some of the latest features in the commercial electromagnetic software Feko (including WinProp). These include the modeling of non-ideal cable shield connections, the parallel direct adaptive cross approximation (ACA) solver, edge and wedge diffraction for the ray launching geometrical optics (RL-GO) solver, and several new features related to automotive radar.

Using the reflections method in the wedge diffraction theory

Using the reflections method in the wedge diffraction theory

A Heuristic UTD Solution for Scattering by a Thin Lossless Anisotropic Slab

A heuristic uniform theory of diffraction (UTD) corner and wedge diffraction coefficient for predicting electromagnetic scattering by a thin lossless anisotropic slab is presented. An approach based on modifying UTD corner and wedge diffraction formulations for a half-plane with the reflection and transmission coefficients of an anisotropic medium is proposed. The formulation works for both uniaxial and biaxial media and the final expressions are in closed form and easy to implement in ray-tracing software. Numerical results for various scattering problems showing excellent agreement with reference solutions are provided.

High-contrast approximation for penetrable wedge diffraction

Abstract The important open canonical problem of wave diffraction by a penetrable wedge is considered in the high-contrast limit. Mathematically, this means that the contrast parameter, the ratio of a specific material property of the host and the wedge scatterer, is assumed small. The relevant material property depends on the physical context and is different for acoustic and electromagnetic waves for example. Based on this assumption, a new asymptotic iterative scheme is constructed. The solution to the penetrable wedge is written in terms of infinitely many solutions to (possibly inhomogeneous) impenetrable wedge problems. Each impenetrable problem is solved using a combination of the Sommerfeld–Malyuzhinets and Wiener–Hopf techniques. The resulting approximated solution to the penetrable wedge involves a large number of nested complex integrals and is hence difficult to evaluate numerically. In order to address this issue, a subtle method (combining asymptotics, interpolation and complex analysis) is developed and implemented, leading to a fast and efficient numerical evaluation. This asymptotic scheme is shown to have excellent convergent properties and leads to a clear improvement on extant approaches.

Analytical methods for perfect wedge diffraction: A review

The subject of diffraction of waves by sharp boundaries has been studied intensively for well over a century, initiated by groundbreaking mathematicians and physicists including Sommerfeld, Macdonald and Poincaré. The significance of such canonical diffraction models, and their analytical solutions, was recognised much more broadly thanks to Keller, who introduced a geometrical theory of diffraction (GTD) in the middle of the last century, and other important mathematicians such as Fock and Babich. This has led to a very wide variety of approaches to be developed in order to tackle such two and three dimensional diffraction problems, with the purpose of obtaining elegant and compact analytic solutions capable of easy numerical evaluation.The purpose of this review article is to showcase the disparate mathematical techniques that have been proposed. For ease of exposition, mathematical brevity, and for the broadest interest to the reader, all approaches are aimed at one canonical model, namely diffraction of a monochromatic scalar plane wave by a two-dimensional wedge with perfect Dirichlet or Neumann boundaries. The first three approaches offered are those most commonly used today in diffraction theory, although not necessarily in the context of wedge diffraction. These are the Sommerfeld–Malyuzhinets method, the Wiener–Hopf technique, and the Kontorovich–Lebedev transform approach. Then follows three less well-known and somewhat novel methods, which would be of interest even to specialists in the field, namely the embedding method, a random walk approach, and the technique of functionally-invariant solutions.Having offered the exact solution of this problem in a variety of forms, a numerical comparison between the exact solution and several powerful approximations such as GTD is performed and critically assessed.

Analysis of ITU‐R VHF/UHF propagation prediction methods performance on irregular terrains covered by forest

In the scope of very high-frequency (VHF) and ultra high-frequency (UHF) terrestrial communication or broadcasting systems planning, the use of point-to-area propagation prediction methods is expected. The benchmarking of such models on different scenarios is very helpful to assist the system planner in choosing those most suited to the site in hands. In this sense, this study provides a comparative performance analysis of the International Telecommunication Union radio communication sector (ITU-R) recommendations P.526, P.1546, and P.1812 and a few other models on a site marked by the presence of irregular terrain covered by forest. A set of measurements at 563 MHz at different spots in Rio de Janeiro city with such features was taken as reference. The best prediction performance was achieved by the P.526 and P.1812 methods, in addition to a wedge diffraction model, with path loss mean errors between -5 and 3 dB, and standard deviations between 8.7 and 9.2 dB. Such results were observed when the presence of the forest layer was incorporated adding a representative clutter height.

WEDGE DIFFRACTION AS AN INSTANCE OF RADIATIVE SHIELDING

The celebrated Sommerfeld wedge diffraction solution is reexamined from a null interior field perspective. Exact surface currents provided by that solution, when considered as disembodied half-plane laminae radiating into an ambient, uniform space both inside and outside the wedge proper, do succeed in reconstituting both a specular, mirror field above the exposed face, and a shielding plane-wave field of a sign opposite to that of the incoming excitation which, under superposition, creates both the classical, geometric-optics shadow, and a strictly null interior field at the dominant, plane-wave level. Both mirror and shadow radiated fields are controlled by the residue at just one simple pole encountered during a spectral radiative field assembly, fixed in place by incidence direction $\phi_{0}$ as measured from the exposed face. The radiated fields further provide diffractive contributions drawn from two saddle points that track observation angle $\phi.$ Even these, more or less asymptotic contributions, are found to cancel exactly within the wedge interior, while, on the outside, they recover in its every detail the canonical structure lying at the base of GTD (geometric theory of diffraction). It is earnestly hoped that this revised scattering viewpoint, while leaving intact all details of the existing solution, will impart to it a fresh, physically robust meaning. Moreover, since this viewpoint confirms, admittedly in an extreme limit, the concept of field self-consistency (Ewald-Oseen extinction in more picturesque language), perhaps such explicit vindication may yet encourage efforts to seek exact solutions to scattering/diffraction by electromagnetically permeable (dielectric) wedges, efforts that harness integral equations with polarization/ohmic currents distributed throughout wedge volumes as sources radiating into an ambient, uniform reference medium.

Wedge diffraction model in gravitational lensing by cosmic strings

A cosmic string forms a conical topology, which enables a diffraction phenomenon by a wedge with an inner angle, equals to the double of the deficit angle. A wedge, on the edge of which the string is located, is defined in the flat space-time. The radiated wave from a star is represented by two plane waves, propagating on the two surfaces of the wedge for grazing incidence. The uniform expressions of the diffracted waves are obtained and investigated numerically.

Orthogonal Basis Functions in Discrete-Time Electromagnetics and Their Implementation to Compute the Matrix-Type UTD Transition Function for PEC Wedge Diffractions

A set of orthogonal global time-domain (TD) basis functions of numerical robust is presented and examined for the applications of discrete time electromagnetics (DT-EM). The matrix equations or integrals arising from the expansion of TD field signals by this basis set can be effectively computed since they can be diagonalized by eigenvalue and vector decomposition method. This characteristic is particularly useful in the computation of TD solutions transformed from the corresponding frequency domain formulations such as in the computation of transition functions for the implementation of DT uniform geometrical theory of diffraction (DT-UTD). It may not only avoid the TD field signal divergence along propagation, but also simplify the computational complexity by avoiding the numerical integration of matrix integral. In this paper, the characteristics are examined via the implementation of plane wave propagation and DT-UTD for the diffraction from curved wedges. Numerical examples are presented to demonstrate their validity in DT-EM applications.

A uniform function for the diffraction of spherical waves

A function which occurs in the scattering problem of the spherical waves by a perfectly conducting half-plane is introduced for constructing the transition functions of the uniform theory of diffraction and uniform asymptotic theory of diffraction. The important properties of the function, related with the geometrical optics and diffracted field components, are derived mathematically. A uniform asymptotic theory of wedge diffraction is introduced based on the new function. The resultant field expressions are investigated numerically.

Exact solution and high frequency asymptotic methods in the wedge diffraction problem

AbstractThe Sommerfeld exact solution for canonical 2D wedge diffraction problem with perfectly conducting surfaces is presented. From the integral formulation of the problem, the Malyuzhinets solution is obtained and this result is extended to obtain the general impedance solution of canonical 2D wedge problem. Keller’s asymptotic solution is developed and the general formulation of exact solution it’s used to obtain general asymptotic methods for approximate solutions useful from the computational point of view. A simulation tool is used to compare numerical calculations of exact and asymptotic solutions. The numerical simulation of exact solution is compared to numerical simulation of an asymptoticmethod, and a satisfactory agreement found. Accuracy dependence with frequency is verified.

Effects of impedance wedge diffraction on backscattering from breaking waves

Electromagnetic scattering characteristics change significantly from breaking waves, which is considered to be one reason for sea spike phenomenon（HH polarization scattering intensity close to or even greater than VV polarization scattering intensity). Spiky sea clutter is often treated falsely as targets, which affects radar performance in target detection in the sea surface background. Thus the investigation on the physical mechanism of the sea spike phenomenon can help mitigate false alarms. In this paper, the authors investigate the microwave backscattering from the wedge-shaped breaking waves, which is simulated with the dihedral impedance wedge of finite length. The physical optical field of the breaking waves is calculated with the Kirchhoff approximation. Based on the Maliuzhinets method with using the precise impedance boundary condition, the impedance wedge scattering solution in spectral integral representation is presented. The spectral function is derived by the perturbation method with respect to the oblique incident angle based on the incidence normal to or grazing to the edge. After obtaining the spectral function, the asymptotic theory is used to determine the diffraction field of impedance wedge at an arbitrary skew incidence. The equivalent edge currents are derived from the uniform diffraction of impedance wedge by combining the physical optical coefficients and diffracted coefficients. Backscattering radar cross-sections（RCSs) of the diffracted field from 120 impedance wedge are calculated in both HH and VV polarizations, and the effects of frequency and permittivity on the wedge diffraction are discussed as well. The physical optical field backscattering from 135 impedance wedge is compared with the total field with considering the diffraction effects. Further calculations and analyses for backscattering from the three-dimensional extension breaking waves are presented by using the contribution of edge diffraction field to correct the physical optics field. Numerical results show that the backscattering RCS of impedance diffracted field in HH polarization is greater than that in VV polarization in the Keller cone. Therefore, the diffraction effects will make the backscattering RCS of the total field in HH polarization greater than that in VV polarization when the breaking wave grows to near-collapse stage at a small grazing angle with upwind observation. This indicates that the wedge diffraction is one of the causes of sea spike phenomenon.

Diffraction of waves by a boundary between two half-planes with different resistivities.

The solution of the diffraction problem of waves by a junction between two resistive half-screens is obtained by using the wedge diffraction field expression, introduced by Maliuzhinets [Ann. Phys.461, 107 (1960)]. The two half-planes, located at the same coordinate plane, have different surface resistivities. The new field expression is compared with the solution of Senior ["Diffraction by a material junction," http://deepblue.lib.umich.edu/handle/2027.42/21043] for the scattered waves. The important aspects of the approach are discussed in the light of the numerical results.