Modelling of soft and hard surfaces using ideal perfect electric conducting/perfect magnetic conducting strip grids

Strip-loaded surfaces and corrugated surfaces can be efficiently analysed using asymptotic boundary conditions that are valid in the limit of vanishing strip and corrugation period, respectively. An even simpler boundary condition is obtained by assuming that the surfaces are ideally soft or hard. This corresponds to a curvilinear grid of quasi-parallel perfect electric conducting (PEC) and perfect magnetic conducting (PMC) strips of incremental width and period, referred to as a PEC/PMC strip grid. Such a simple model for soft/ hard surfaces speeds up the design process and provides the proper object parameters under the ideal soft or hard conditions. After reaching the designed characteristics, one can study the bandwidth of realisations of the surface using the asymptotic boundary conditions and finally make a complete and detailed study of all characteristics of the realisations by including even the finite period of the strips and corrugations. The ideal PEC/PMC strip model is used here as an example applied to bodies of revolution (BOR) such as soft horns with transverse corrugations and hard horns with longitudinal corrugations. The longitudinally corrugated horn is not a BOR, but both the asymptotic boundary condition and the ideal PEC/PMC strip model make it possible to analyse it as a BOR with an anisotropic wall and this reduces the computer time enormously compared to a full wave analysis for a finite corrugation period. It is shown that the PEC/PMC strip grid can predict the radiation patterns well at the centre frequency, but the bandwidth cannot be determined.     

Study of the evolution of temperature in the core of a high voltage electric cable

The core of the electric cable is a heterogeneous medium; the conducting wires are periodically distributed and the period is small compared with the diameter of the core. Moreover, the insulating medium is not perfectly thermally insulating but its thermic conductivity is small. We study the evolution of the global temperature in the core and find two different types of results, depending upon how small are the two small parameters.     

Scattering of electromagnetic waves by a coated not perfectly conducting sphere

We consider the low-frequency scattering problem of a plane electromagnetic wave by a sphere, which is covered by a penetrable concentric spherical shell. The medium, occupying the shell, is lossless while on the surface of the core an impedance boundary condition is satisfied. The impedance boundary condition was introduced by Leontovich (Investigations of Radiowave Propagation. Part II, Academy of Science, Moscow, 1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first orders while in the far field we derive the leading non-vanishing terms for the scattering amplitude and the scattering cross-section. Spherical coated obstacles are very important in applications. Small particles in biological suspensions, cells, some human organs, atmospheric particles and granules within composite materials are only a few examples of applied interest in science and technology.     

Modeling and Analysis of a Long Thin Conducting Stripline

A long thin conducting stripline embedded in a dielectric and centered between two large conducting plates, i.e., the stripline environment, is considered. The stripline is modeled as infinitely long, infinitely thin, and perfectly conducting by first considering a stripline of finite length, thickness, and conductivity in a dielectric layer. Starting from Maxwell's equations and assuming that the current on the stripline is a propagating wave in length direction, asymptotic expressions for the fields inside and in the neighbourhood of the stripline are deduced. These expressions are used to model the stripline in the stripline environment, which leads to a boundary-value problem for the electric potential. This problem is solved by two different approaches, leading to integral equations for the current and for an auxiliary function describing the electric potential. A relation between the current and the auxiliary function is deduced, which is used to obtain asymptotic expressions for current and impedance. Results are compared with a numerical solution of the integral equation for the current and with results in literature.     

Shielded electronic current transformer

A current transformer with nominal ratio 10 A to 10 mA, intended for low-frequency applications, was developed. It includes an electronic device to reduce the magnetizing current, and a continuous shield in the secondary winding (coaxial cable) in order to eliminate the effect of stray capacitances. No guard-source is connected to the shield. It is proposed in this paper to leave the cable-shield-potential floating. This leads to high-accuracy results (ratio errors and phase-displacements in the order of few parts in 10/sup 6/ from 50 Hz to 1 kHz).     

Beam implementation in a nonorthogonal coordinate system: application to the scattering from random rough surfaces

The C method is known to be one of the most efficient and versatile tools established for modeling diffraction gratings. Its main advantage is the use of a coordinate system in which the boundary conditions apply naturally and are, ipso facto, greatly simplified. In the context of scattering from random rough surfaces, we propose an extension of this method in order to treat the problem of diffraction of an arbitrary incident beam from a perfectly conducting (PEC) rough surface. For that, we were led to revisit some numerical aspects that simplify the implementation and improve the resulting codes.     

Symmetry properties of the field transmitted by inductive grids

Abstract

Following an analysis of the modes inside a perfectly conducting rectangular grid, we design diffractive elements that can split an incident beam into four beams with equal intensities. This property is obtained under Bragg mounting for a wide domain of grating parameters (dimensions of the through-holes, height, period). Extension to finite conductivity is also addressed.     

Numerical analysis of low-frequency electromagnetic scattering from axially symmetric bodies using an inductance matrix

We have proposed a numerical method for calculating low-frequency electromagnetic scattering from axially symmetric conducting bodies with and without apertures. The surface of the perfectly conducting scatterer is modeled by a set of inductively coupled coil elements, and the current in each coil element is computed by solving an inductance matrix equation. A disadvantage of a conventional method for a scatterer with apertures is discussed. Scattering from various axially symmetric conducting bodies with or without apertures is calculated and the resulting fields are in good agreement with those obtained by finite-element method.     

TE-impedance of a coated right-angled wedge

The surface impedance observed by a plane TE-wave impinging on a coated right-angled perfectly conducting wedge is derived for a high contrast dissipative coating. The impedance proves to be constant ove rmost of the surface of the coating. The value of the constant agrees with that obtained when the coating is placed on an infinite perfectly conducting plane. Near the edge of the coating, however, the impedance is not invariable. Both the magnitude and phase can deviate substantially from their asymptotic values; also they change with the angle of incidence of the irradiating wave. The region of variability depends on the amount of absorption but does not exceed a free-space wavelength for the cases considered.     

Time-domain analysis of multiple straight thin wires in a non-homogeneous medium

Time-domain analysis of the transient current distribution along parallel wires located at different heights above a real ground is presented. The numerical solution is carried out via time-domain variant of the Galerkin–Bubnov indirect boundary element method (GB-IBEM) of solution extended to handle the case of arbitrary array of parallel wires located in a homogenous lossless medium, above a perfectly conducting (PEC) ground, or above a dielectric half-space. The mathematical formulation is based on the set of coupled space-time integral equations of the Hallen type. Some illustrative numerical results being compared to the results obtained via other methods wherever possible are presented.     

Diffraction of homogeneous and inhomogeneous plane waves by a planar junction between perfectly conducting and impedance half-planes

The problem of diffraction of homogeneous and inhomogeneous plane waves at the discontinuity formed by perfectly conducting and impedance half-planes is examined by the method of modified theory of physical optics (MTPO). The MTPO integral of the reflected scattered waves by the perfectly conducting half-plane is reconstructed in order to include the effect of the diffracted wave coming from the edge of the impedance half-plane. The integrals are evaluated by a uniform asymptotic method. The results are plotted numerically and compared with the literature.     

Boundary element modeling of radio base station antennas

The paper presents an accurate and efficient boundary element procedure for the analysis of radiation from base station antennas. The base station antenna system is represented by the vertical antenna array in front of perfectly conducting (PEC) ground plane reflector.The formulation of the problem is based on a set of coupled Pocklington integro-differential equations for vertical antenna array. This set of coupled equations has been numerically treated by the indirect Galerkin–Bubnov boundary element method (GB-IBEM). The numerical results for the currents induced along the wires obtained via GB-IBEM are compared to the results computed via numerical electromagnetic code (NEC).Knowing the current distribution along the antenna array the corresponding radiated field is calculated. Some illustrative numerical results are presented in the paper.     

Analytical solutions of fully plastic crack-tip higher order fields under antiplane shear

Analytical solutions of higher order fields in a fully plastic power-law hardening material are presented. By the use of hodograph transformation and asymptotic analysis the stress and strain exponents, angular distributions of shear stresses and strains are analytically determined. Special cases, such as linearly elastic, perfectly plastic materials are discussed. Similar characteristics between mode III and mode I plane strain, and mode II plane stress are examined. Comparison of four-term asymptotic solutions with exact and leading term solutions in an infinite strip with a semi-infinite crack under constant displacements along its edges is provided.     

Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics

The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly conducting surface with roughness and autocorrelation width comparable with the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a nonspecular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.     

Calculating in-plane frequencies of multispan cables using the Exterior-Matrix Method

The Exterior-Matrix Method (EMM) is applied to the in-plane dynamical equations of a shallow elastic catenary. The transfer matrices of the composite system are expanded so that asymptotic analysis can be done for the general case. The main idea is to find the 4-by-4 transfer matrices for each span of the cable system, and the transfer matrices for the joint, which could be an insulated pole. Then, by using the exterior matrices, the 6-by-6 matrices which correspond to the transfer matrices can be found. At first it seems surprising to use 6-by-6 matrices instead of the 4-by-4 transfer matrices, but with the exterior matrices, the determinant of the product need not be taken. This allows one to immediately take approximations of the matrices without worry that the highest-order terms will cancel. As a bonus to using the exterior matrices, an angle for the insulator will be allowed, which generalizes the work done by Simpson (Proc IEE 113(5):870–878, 1966). The practical use of this method is illustrated by finding the normal frequencies of a symmetrical 3-span system.     

Hiemenz flow in hydromagnetics

Summary The laminar flow of an incompressible, viscous, electrically conducting fluid impinging normal to a plane in the presence of a transverse magnetic field is investigated. Using finite-differences and quasilinearization, an exact numerical solution is presented which takes into account the asymptotic boundary condition. It is demonstrated that iff denotes the dimensionless stream function, the value off(0) increases monotonically withM, the Hartmann number, where a prime denotes the derivative normal to the plane.This conclusion is supported by deriving a perturbation solution valid for smallM. Also, an analytical solution is obtained valid for largeM. Finally, an approximate solution is given which is simple and sufficiently accurate for the entire range of values ofM.     

Nanotubes of boron nitride filled with molybdenum clusters

Carbon nanotubes are known to be metallic or semiconducting, depending on their helicity and diameter. However, boron nitride (BN) nanotubes are the only nanotubular product known to date that are predicted to have stable insulating properties that are independent of their atomic structure and morphology. Thus, the BN tube has attracted prime attention as an advanced nanoinsulating shield for all types of encapsulated conducting material, i.e., metal wires, clusters, etc. However, so far there have been no successes in controlled one-dimensional filling of BN nanotubes with conductive material. We report the first experimental results on the synthesis, high-resolution transmission electron microscopy, energy dispersion X-ray analysis, and electron energy loss spectroscopy of BN nanotubes that are filled with Mo clusters over their entire length. This was accomplished by means of two-step thermochemical treatment of chemically vapor-deposited C nanotubes with B2O3, CuO, and MoO3 oxides in a flowing N2 atmosphere. The first examples of BN nanotubes filled with molybdenum clusters are reported and the formation of the first nanocable (approximately 10 nm in length), consisting of a conductive metal core and an insulating BN nanotubular shield is demonstrated.     

Shape identification by physical optics: the two-dimensional TE case

A method is provided for reconstruction of the shape of perfectly conducting objects in a homogeneous space starting from knowledge of the scattered far field under the incidence of TE-polarized plane waves. The Kirchhoff model of scattering permits linearization of the inverse problem, which is further simplified by adopting an asymptotic approximation. Thus the problem is tackled with an approach based on singular-value decomposition already developed for the TM case.     

Theory to boil-off gas cooled shields for cryogenic storage vessels

An intermediate refrigeration with boil-off gas cooled shields using the boil-off gas stream is an alternative method to the conventional intermediate refrigeration with a cryogenic liquid.By using an analytical calculation method relations are derived, which enable complete predictions about the effectiveness of an intermediate refrigeration with boil-off gas cooled shields as a function of the number of shields for the different stored cryogenic liquids. For this theoretical derivation however, the restrictive assumption must be made that the thermal conductivity of the used insulation material has a constant value between the considered temperature boundaries.For purposes of a more exact calculation a numerical method is therefore suggested, which takes into consideration that the thermal conductivity is temperature-dependent. For a liquid hydrogen storage vessel with a perlite-vacuum insulation e.g., the effectiveness of one shield and its equilibrium temperature are given as a function of the position of the shield in the insulation space.     

Asymptotic behavior of the Langevin equation for a nonhomogeneous medium

The Langevin equation has gained renewed interest through its role in modeling turbulent, reacting flow, and turbulent dispersion. Such applications often require an understanding of its long term, asymptotic behavior. The asymptotic, Smoluchowsky, equation is derived by constructing a uniformly valid bound on the velocity variance. Extra drift terms arise in the asymptotic equation when the coefficients are not constant.