Plane wave diffraction by a thin material strip: The case of E polarization

The plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique and approximate boundary conditions. An asymptotic solution is obtained under the condition that the strip width is large compared with the wavelength. Applying the saddle point method, the scattered far field is evaluated asymptotically. Numerical results on the radar cross section are presented.

We construct the exact solution of the problem of diffraction of a plane wave by a strip. The construction leads immediately to high frequency approximations with error estimates. Thus we are able to prove the asymptotic nature of the approximate solution of this problem given by geometrical diffraction theory.

The plane wave diffraction by a slit in a material screen is analyzed using the Wiener-Hopf technique together with generalized boundary conditions (GBC). Exact and high-frequency asymptotic solutions are obtained. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Numerical examples on the far field intensity are presented and the scattering characteristics of the slit are discussed.

The problem of E -polarized plane wave diffraction by a strip with fractional boundary conditions (FBC) is analyzed using the Wiener-Hopf technique. Introducing the Fourier transform for the unknown scattered field and applying FBC, the problem is formulated in terms of the Wiener-Hopf equation. The Wiener-Hopf equation is solved via the factorization and decomposition procedure leading to the exact and asymptotic solution. Our final solution is valid for the case where the strip width is large in comparison to the wavelength. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Numerical examples on the radar cross section (RCS) are presented for various physical parameters and the scattering characteristics of the strip are discussed in detail.

Previous article Addendum to: Diffraction of Plane Waves by a Strip; Exact and Asymptotic Solutions—the Solution in the General CasePeter WolfePeter Wolfehttps://doi.org/10.1137/0124063PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[B1] D. S. Ahluwalia, , R. M. Lewis and , J. Boersma, Uniform asymptotic theory of diffraction by a plane screen, SIAM J. Appl. Math., 16 (1968), 783–807 10.1137/0116065 MR0241047 0189.40801 LinkISIGoogle Scholar[B2] R. M. Lewis and , J. B. Keller, Asymptotic methods for partial differential equations: The reduced wave equation and Maxwell's equation, Res. Rep., EM 194, New York University, New York, 1964 Google Scholar[B3] P. Wolfe, Diffraction by a strip; The solution in the general case, Tech. Rep., TR 71-56, Dept. of Mathematics, University of Maryland, College Park, 1971 Google Scholar Previous article FiguresRelatedReferencesCited ByDetails Diffraction of a plane wave by a circular diskJournal of Mathematical Analysis and Applications, Vol. 67, No. 1 | 1 Jan 1979 Cross Ref The decay of solutions of the two dimensional wave equation in the exterior of a straight stripTransactions of the American Mathematical Society, Vol. 231, No. 2 | 1 January 1977 Cross Ref Diffraction of a pulse by a stripJournal of Mathematical Analysis and Applications, Vol. 48, No. 1 | 1 Oct 1974 Cross Ref Volume 24, Issue 4| 1973SIAM Journal on Applied Mathematics425-618 History Submitted:21 December 1971Published online:17 February 2012 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0124063Article page range:pp. 613-618ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail.

Diffraction coefficients are derived for a thin dielectric half plane and strip having arbitrary permittivity and permeability. This is accomplished by modeling the thin material layer by a pair of modified resistive and conductive sheets. By means of this model the dielectric half plane is first treated via the dual integral equation approach. By employing the half plane solution, up to third‐order multiply diffracted fields are then derived for the case of a strip. These are obtained via the extended spectral ray method and include the surface wave diffraction effects in a uniform manner. Numerical results are also presented which validate the accuracy of the model and that of the derived diffraction coefficients.

The plane wave diffraction by a terminated semi infinite parallel-plate waveguide with two-layer material loading and impedance boundaries is rigorously analyzed for E polarization using the Wiener-Hopf technique. Introducing the Fourier transform for the scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations, which are solved via the factorization and decomposition procedure. The scattered field is evaluated by taking the inverse Fourier transform and applying the saddle point method. The numerical examples of the radar cross section (RCS) are represented for various physical parameters and backscattering characteristics, of considered geometry for open ended cavity and discussed in detail.

The analysis of wave scattering and diffraction problems involving canonical objects is one of the important subjects in electromagnetic theory and radar cross section (RCS) studies. Various analytical and numerical methods have been developed so far and the scattering problems have been investigated for many kinds of two- and three-dimensional structures. Among a number of analysis methods, the Wiener-Hopf technique is known as a rigorous, function-theoretic approach for electromagnetic wave problems related to canonical geometries. In this chapter, we shall consider a thin material strip that is important from both the theoretical and engineering viewpoints, and analyze the electromagnetic wave diffraction by means of the Wiener- Hopf technique. It is shown that our final solutions are valid over a broad frequency range. Numerical examples are presented for various physical parameters, and the far field scattering characteristics are discussed in detail. Some comparisons with other existing methods are also given.

Visual rules and schemas play a crucial role in formally representing visual reasoning in design. The indeterminacy inherent in shapes within visual computation fosters creative discoveries, as shapes can be perceived differently in various contexts. Design, however, often transcends visual aspects, involving creative processes rooted in material engagement and making. This chapter explores the integration of visual and material reasoning in creative processes by employing material shapes in shape computation. We exemplify how material shapes, particularly those generated through basket weaving, contribute to a dynamic interplay between abstract representations and physical outcomes. Triaxial basket weaving serves as a case study, demonstrating basic rules and showcasing the use of abstract shapes and material shapes in computational making processes in tandem. The iterative nature of an “abstraction–materialization–abstraction” cycle is exemplified through the bending and twisting of thin linear strips of flexible material in basket weaving, highlighting the emergence of forms shaped by the physical system during the weaving process.

The diffraction of a spherical acoustic wave by a half plane in an infinite plane, porous barrier is considered. The barrier is modeled as a rigid material filled with narrow pores, more or less normal to the plane, that provide sound damping. However, the compressibility of the gas in the pores is also considered so that some sound transmission takes place. An approximate boundary condition is derived that models both these effects. The principal purpose of the barrier is to reduce the transmitted sound so that the flow resistance of the pores is large. This consideration is important in the sense that point sources are also regarded as reasonable substitutes for real sources. The far field is calculated using integral transforms, the Wiener-Hopf technique and asymptotic methods.

A uniform asymptotic solution is presented for the diffraction of Ez polarized plane waves by a resistive strip residing between two impedance half-planes. The analysis proceeds from triple integral equations approach which leads to a system of uncoupled modified Wiener-Hopf equations (MWHE). This system is then reduced to two pairs of Fredholm integral equations of the second kind which are solved by successive approximations. Diffracted field expressions are derived up to the third order terms which include the surface wave field effects in a uniform manner.

Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain

Two basic refinements of the finite-difference method for 3-D dc resistivity modeling are presented. The first is a more accurate formula for the source singularity removal. The second is the analytic computation of the source terms that arise from the decomposition of the potential into the primary potential because of the source current and the secondary potential caused by changes in the electrical conductivity. Three examples are presented: a simple two-layered model, a vertical contact, and a buried sphere. Both accurate and approximate Dirichlet boundary conditions are used to compute the secondary potential. Numerical results show that for all three models, the average percentage error of the apparent resistivity obtained by the modified finite-difference method with accurate boundary conditions is less than 0.5%. For the vertical contact and the buried sphere models, the error caused by the approximate boundary condition is less than 0.01%.

The solution of exterior interface problems using a variational method with Lagrange multipliers