Diffraction of a plane electromagnetic wave by a parallel plate grating with dielectric loading: the case of transverse magnetic incidence

1985 ◽  
Vol 63 (4) ◽  
pp. 453-465 ◽  
Author(s):  
Kazuya Kobayashi
Keyword(s):  
Cross Sections ◽  
Parallel Plate ◽  
Plane Electromagnetic Wave ◽  
Approximate Solutions ◽  
Transverse Magnetic ◽  
Transform Domain ◽  
Wave Scattering And Diffraction ◽  
Decomposition Procedure ◽  
Dielectric Loading ◽  
The Fourier Transform

Wave scattering and diffraction problems concerning objects with complex cross sections have been widely investigated so far with the advance of electronic computers. In this paper, a periodically placed parallel plate grating with dielectric loading is considered, and the problem of diffraction of a TM polarized plane wave is analyzed with the aid of the Wiener–Hopf technique. Introducing the Fourier transform pair for the unknown scattered field and applying boundary conditions in the transform domain, one can formulate this problem as the single Wiener–Hopf equation. This functional equation is then solved by a decomposition procedure and a rigorous solution is obtained. Furthermore, approximate solutions are derived by applying the modified residue calculus technique. Based on the above analysis, several numerical examples are given and the characteristics of this grating are discussed.

Multiple scattering by a linear array of conducting spheres

1990 ◽  
Vol 68 (10) ◽  
pp. 1157-1165 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Multiple Scattering ◽  
Cross Sections ◽  
Linear Array ◽  
Plane Electromagnetic Wave ◽  
Spherical Wave ◽  
Approximate Solutions ◽  
Addition Theorem ◽  
Wave Functions ◽  
Coordinate Systems ◽  
Conducting Spheres

The problem of multiple scattering of a plane electromagnetic wave incident on N closely spaced perfectly conducting spheres is solved analytically by expanding the incident and scattering fields in terms of an appropriate set of vector spherical wave functions. To impose the boundary conditions, the scattered field from one sphere is expressed in coordinate systems attached to the others by using the translation addition theorem. An approximate solution is obtained to solve for the scattering by N small spheres. Numerical results for the normalized backscattering and bistatic cross sections for systems of spheres show that the agreement between the analytic and approximate solutions is better for larger electrical distances between neighbouring spheres.

scholarly journals Polyurethane Composite Foams Synthesized Using Bio-Polyols and Cellulose Filler

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3474
Author(s):  
Katarzyna Uram ◽  
Milena Leszczyńska ◽  
Aleksander Prociak ◽  
Anna Czajka ◽  
Michał Gloc ◽  
...  
Keyword(s):  
Cross Sections ◽  
Raw Materials ◽  
Polyurethane Foams ◽  
Degree Of Crystallinity ◽  
X Ray Diffraction ◽  
Polyurethane Composite ◽  
Composite Foams ◽  
Closed Cell ◽  
Ft Ir ◽  
The Fourier Transform

Rigid polyurethane foams were obtained using two types of renewable raw materials: bio-polyols and a cellulose filler (ARBOCEL® P 4000 X, JRS Rettenmaier, Rosenberg, Germany). A polyurethane system containing 40 wt.% of rapeseed oil-based polyols was modified with the cellulose filler in amounts of 1, 2, and 3 php (per hundred polyols). The cellulose was incorporated into the polyol premix as filler dispersion in a petrochemical polyol made using calenders. The cellulose filler was examined in terms of the degree of crystallinity using the powder X-ray diffraction PXRD -and the presence of bonds by means of the fourier transform infrared spectroscopy FT-IR. It was found that the addition of the cellulose filler increased the number of cells in the foams in both cross-sections—parallel and perpendicular to the direction of the foam growth—while reducing the sizes of those cells. Additionally, the foams had closed cell contents of more than 90% and initial thermal conductivity coefficients of 24.8 mW/m∙K. The insulation materials were dimensionally stable, especially at temperatures close to 0 °C, which qualifies them for use as insulation at low temperatures.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

V.—Bifurcation of a Parallel-Plate Waveguide by a Unidirectionally Conducting Screen

1965 ◽  
Vol 67 (1) ◽  
pp. 50-68
Author(s):  
R. K. Arora
Keyword(s):  
Slow Wave ◽  
Parallel Plate ◽  
Transverse Electric ◽  
Transverse Magnetic ◽  
Hybrid Wave ◽  
Parallel Plate Waveguide ◽  
Hopf Method ◽  
Conducting Screen ◽  
Electric Mode ◽  
Transverse Electric Mode

SynopsisThe types of modes which may exist in an infinite parallel-plate waveguide with a centrally-placed unidirectionally conducting screen are studied. The effect of bifurcating an infinite parallel-plate waveguide by such a screen in the region x>O is investigated when a transverse electric mode is incident on the bifurcated region. The problem is solved by the Wiener-Hopf method, and expressions are derived for the amplitudes and phases of the reflected and transmitted modes. It is found that the transmitted field contains a hybrid wave and a slow wave, and the reflected field contains transverse electric and transverse magnetic waves.

An Asymptotic Analysis of Three-Dimensional Extrusion

1989 ◽  
Vol 56 (3) ◽  
pp. 519-526 ◽  
Author(s):  
N. Aravas ◽  
R. M. McMeeking
Keyword(s):  
Asymptotic Analysis ◽  
Cross Sections ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Approximate Solutions ◽  
The Finite Element Method ◽  
Wide Range ◽  
Metal Extrusion ◽  
Asymptotic Perturbation ◽  
Generalized Plane Strain

A new method of analysis of three-dimensional metal extrusion using asymptotic perturbation methods is presented in this paper. The plasticity model used depends on the first and second invariants of the stress tensor and covers a wide range of constitutive models commonly used for the analysis of metal-forming operations. It is shown that the three-dimensional extrusion problem can be approximated, to leading order, by a problem of generalized plane-strain. The results of the asymptotic analysis together with the finite element method are used to obtain approximate solutions for extrusions of elliptic or square cross-sections from round billets.

The General theory of Cylindrical and Conical Tubes Under Torsion and Bending Loads

1949 ◽  
Vol 53 (461) ◽  
pp. 461-483 ◽  
Author(s):  
J. Hadji-Argyris ◽  
P. C. Dunne
Keyword(s):  
General Theory ◽  
Cross Sections ◽  
Approximate Solutions ◽  
Torsional Stiffness ◽  
Numerical Example ◽  
Bending Loads ◽  
Present Part

SummaryParts 1 to 5 of this paper (February, September and November 1947 issues of the JOURNAL) investigated the stresses and deformations of closed tubes in which the thicknesses were governed by the ts* and t* laws. In the present part, the analysis is extended to multi-cell tubes with openings, open tubes with or without St. Venant torsional stiffness, and to tubes formed by joining elements of different cross-sections. To illustrate the theory a numerical example of the stressing of a four-boom wing consisting of seven joined elements is fully worked out. Finally, an appendix gives practical methods of dealing with tubes which do not conform to the ts* and t* laws, and of finding approximate solutions for four-boom tubes with direct stress carrying covers.

scholarly journals The practice of using the fourier transform in processing the results of mathematical modeling of the hydrodynamics of getaways

2021 ◽  
Vol 2131 (3) ◽  
pp. 032029
Author(s):  
I Lipatov ◽  
M Molchanova ◽  
O Lebedev
Keyword(s):  
Mathematical Modeling ◽  
Fourier Transform ◽  
Cross Sections ◽  
Reference Data ◽  
Fourier Transforms ◽  
Scientific Analysis ◽  
Engineering Measures ◽  
The Fourier Transform ◽  
Lock In

Abstract The article deals with the actual aspects of practical mathematical modeling of hydro-dynamic processes in the chambers of navigational locks. The use of direct and inverse Fourier transforms has been tested to obtain the representations of non-stationary graphs acceptable for analysis. Cross-sections of the water flow filling the chamber of a typical lock in the Volga-Don shipping channel were used as reference data (VDSC). The control sections in the flow were selected with a qualitatively different hydrodynamic nature of motion. A two-dimensional array of non-stationary data results were decomposed into Fourier series. The resulting graph of the amplitude-frequency spectrum was analyzed by the harmonics forming it. Its amplitude was taken as the criterion for the harmonics’ selection. After zeroing the insignificant harmonics, the inverse Fourier transform was performed. The quality of the data array approximation was controlled by visual overlay of the original graphs on the processed one. In all cases, it was possible to obtain the acceptable approximation results. This created a reliable basis for the scientific analysis and development of engineering measures for the implementation of safe ship passage through gateways. At the end of the article, a number of the data processing specific features are presented, caused by a variety of hydrodynamic features of the flow in various sections.

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