Coupled Integral Equations Research Articles

Analysis of a dielectric resonator antenna in a cylindrical conducting cavity: HEM modes

Numerical modelling has been performed for the hybrid HEM modes of a flush-mounted dielectric resonator antenna in a cylindrical conducting cavity. The antenna is formed by a conducting cavity with a dielectric post and radiates through an annular slot in the upper ground plane. Coupled aperture magnetic current integral equations are used to model the slot and the effect of the post resonator and the cavity are included via Green's function techniques. The moment method is applied to the coupled integral equations and the complex resonant frequencies for the antenna structure are found by searching for the zeros of the determinant of the impedance matrix in the complex frequency plane. The radiation Q factor, slot field distribution and radiation field are subsequently computed at the resonant frequency. The HEM modes with the lowest resonant frequencies have been investigated for different geometrical configurations.

Analysis of a cylindrical antenna in a circular aperture in a screen

An analysis is presented of a finite-length cylindrical antenna which extends through the center of a circular aperture in a perfectly conducting screen separating two dissimilar half-spaces. The screen is planar and of infinite extent while the half-spaces are homogeneous, of semi-infinite extent, and possibly lossy. The screen and the cylinder are perpendicular. The cylinder is excited by the traditional slice generator. Coupled integral equations for the cylinder current and aperture electric field are derived and solved numerically. The effect of the PEC screen on the antenna current distribution is investigated as is the effect of the dissimilar properties of the two half-spaces. It is also pointed out that, for a sufficiently large aperture, the cylinder current is a good approximation of that on the ground stake antenna. Data are presented for cases of interest and are compared with special-case results available in the literature.

Improved Hybrid Lumped-Differential Formulation for Double-Pipe Heat Exchanger Analysis

Based on recent developments in the so-called Coupled Integral Equation Approach for the approximate solution of heat and mass diffusion problems, the classical lumped-differential formulation for double-pipe heat exchangers is extended and significantly improved in terms of overall accuracy. The energy equation for the outer annular channel is formally integrated and temperature gradients approximately taken into account, in contrast to the conventional lumped system analysis. The resulting partial differential equation for the inner stream, involving a more general type of boundary condition, is analytically handled through the generalized integral transform technique. A critical accuracy analysis is then performed in order to demonstrate the improvement over the plain lumped-differential formulation.

Full-wave boundary integral equation method for suspended planar transmission lines with pedestals and finite metallization thickness

A boundary integral equation method is proposed for the full-wave analysis of suspended planar transmission lines with pedestals and/or finite metallization thickness. Coupled boundary integral equations are formulated on equivalent magnetic currents only on the apertures of subregions using the Green's identity of the second kind. Because it is possible to take a large number of terms in the series expansion of Green's functions in each subregion independently from the order of resulting matrices, this approach can avoid the relative convergence problem. Numerical results for suspended coplanar waveguides are found to have a stable convergence property and to be in excellent agreement with other available theoretical results. Numerical data reveal the effects of conductor thickness and aperture width on the transmission properties of suspended planar transmission lines with pedestals. >

Theoretical and experimental studies of cavity-backed slot antenna excited by a narrow strip

Theoretical and experimental studies of a cavity-backed slot antenna excited internally by a suspended narrow strip are undertaken. Coupled integral equations are developed to compute the electric field distribution in the slot and the surface current distribution on the strip. The input impedance of the cavity at the feeding point on the strip has been computed theoretically and measured experimentally. The impedance data, being a function of cavity dimension, slot length, strip length, and frequency, can be polyfitted and used to implement a systematic design procedure to construct a planar array of these slots.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of a wide radiating slot in the ground plane of a microstrip line

An analysis of a wide rectangular radiating slot excited by a microstrip line is described. Coupled integral equations are formulated to find the electric current distribution on the feed line and the electric field in the aperture. The solution is based on the method of moments and using the space domain Sommerfeld-type Green's function. The information about the input impedance or reflection coefficient is extracted from the electric current distribution on the microstrip line utilizing the matrix pencil technique. The theoretical analysis is described and data are presented and compared with other theoretical and experimental results. >

A Hybrid Integral Equation Solution of Scattering of TE Excitation by Inhomogeneous Cylinders Near a Medium Interface

An analysis of scattering of transverse electric (TE) illumination by inhomogeneous lossy dielectric/ferrite cylinders near a planar media interface by employing the hybrid surface/volume integral equation method is presented. The inhomogeneous cylinders are of general cross section, of infinite extent, and their axes are parallel to the interface. Coupled hybrid integral equations are formulated and a numerical method is developed for solving them. In the formulation of the hybrid integral equations, both the surface equivalence principle and the volume equivalence theorem are employed, and attention is focused on minimizing the computation of Sommerfeld integrals and on reducing the number of unknowns. From the numerical solution of the equivalent surface current, the far-zone scattered field is calculated. Data depicting the equivalent current distribution and the far-zone field patterns are presented and discussed for various cylinder and half-space parameters.

Scattering of TM Excitation by Inhomogeneous Cylinders Near a Media Interface-A Hybrid Integral Equation Approach

In this paper we present a hybrid surface/volume integral equation method solution of scattering from inhomogeneous lossy dielectric/ferrite cylinders near the planar interface separating two semi-infinite, homogeneous half-spaces. The inhomogeneous cylinders of general cross section are of infinite extent, their axes are parallel to the interface, and the excitation is transverse magnetic to their axes. Coupled hybrid integral equations are formulated by employing both surface equivalence principle and volume equivalence theorem. In the formulation, attention is focused on minimizing the computation of Sommerfeld integrals which is often encountered in dealing with buried objects, and on reducing the number of unknowns. A moment method numerical solution technique is developed for solving the formulated hybrid integral equations. From the calculated equivalent surface current, the far-zone scattered field is determined. Data showing the equivalent current distribution and the scattered field patterns are...

General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers

Coupled volume integral equations and the long-wavelength approximation have been used to generalize the Purcell-Pennypacker technique (PPT) and the method of moments (MOM) for inhomogeneous bianisotropic scatterers. The interrelationship between the generalized PPT and the MOM has been established. The dyadic functions employed throughout can be easily interpreted in terms of matrices or as Cartesian tensors of the second rank

Transient scattering from two-dimensional dielectric cylinders of arbitrary shape

The problem of transient scattering by arbitrarily shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time technique. The dielectric problem is approached via the surface equivalence principle. Two coupled integral equations are derived by enforcing the continuity of the electric and magnetic fields which are solved by using the method of moments. Numerical results are presented for two cross sections, viz. a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution. >

Radiation transfer in a diffuse and specular reflecting slab with Rayleigh scattering

A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source.

Slotted parallel-plate waveguide coupled to a conducting cylinder

The problem of electromagnetic scattering from a perfectly electrically conducting cylinder in the presence of a slot in a parallel-plate waveguide is considered. A two-dimensional slot in one of the walls of the parallel-plate guide opens into a half-space in which the twodimensional conducting cylinder resides. The excitation for this structure is an incident TEM wave from within the waveguide, and/or a magnetic line source which produces an incident TEy wave in the exterior half-space. Coupled integral equations for the aperture electric field and the cylinder current are derived from first principles and are solved numerically for cylinders of various cross-section, size, and location relative to that of the slot aperture. From knowledge of the aperture electric field and cylinder current, all other quantities of interest may be determined. For TEM excitation from within the guide, the reflection coefficient and radiation pattern data are presented along with the aperture electric field and cylinder current. For external excitation, data are presented that illustrate how the cylinder serves as a shield for the aperture. From this data one can assess the effectiveness of a conducting shield placed over, but not in contact with, the guide aperture.

Relativistic three-fermion wave equations

Coupled integral eigenvalue equations are derived variationally, within theHamiltonian formalism of QED, for a relativistic two-fermion-one-antifermion bound system, each of arbitrary mass and charge. The ansatz employed is sensitive to all terms of the Hamiltonian. These equations are uncoupled approximately and their applications are discussed.

Electromagnetic response of two crossing, infinitely long, thin wires

The electromagnetic coupling of two crossed thin wires of infinite length is considered. Two coupled integral equations are obtained, given in terms of generalized impedance functions, for the spectral currents flowing in each wire. The wires may be in a homogeneous medium or over a half-space. The numerical implementation focuses, however, only on the former. The numerical solution may be obtained by either applying moment or multiple scattering methods. The solution obtained from the method of moments is applicable for any wire spacing. Obversely, the multiple scattering method leads to a convenient matrix series solution, which shows that the coupling between wires is proportional to 1/d/sup 2/ (where d is the wire separation) plus higher order scattering terms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Oblique scattering from inhomogeneous cylinders using a coupled integral equation formulation with triangular cells

A novel method of moments formulation for scattering from penetrable two-dimensional cylinders illuminated by an obliquely incident excitation is presented. The permittivity and permeability profiles may have arbitrary piecewise-constant dependence on the transverse variables. Regardless of the polarization of the incident field, the response of the scatterer is a combination of transverse electric (TE) and transverse magnetic (TM) waves. Coupled integral equations for the longitudinal electric and magnetic fields are used in conjunction with a triangular-cell discretization, a piecewise linear representation for E/sub z/ and H/sub z/, and point-matching. Numerical results for the internal fields and scattering cross-section are presented to illustrate the accuracy of the approach. >

Flanged parallel-plate waveguide coupled to a conducting cylinder

The characteristics of a flanged parallelplate waveguide coupled to a conducting cylinder are investigated in general. The parallel-plate guide opens, through a slot aperture in an infinite screen, into a semi-infinite half-space in which resides a perfectly conducting cylinder of arbitrary cross-section whose axis is parallel to that of the slot. The excitations considered for this structure are (a) a TEM wave in the guide and (b) a line source in the region exterior to the guide, which when sufficiently remote creates a local plane wave. Coupled integral equations for the aperture electric field (or equivalent magnetic current) and the cylinder current are derived from first principles and are solved numerically for cylinders of various cross-section, size and location relative to that of the slot aperture. From knowledge of aperture electric field and cylinder current, all other quantities of interest may be determined: voltage received in the guide, guide reflection coefficient and far-zone radiation. Data are presented that illustrate how the cylinder loads the guide, modifies its radiation pattern and serves as a shield for the aperture. From the data, one can assess the effectiveness of a conducting shield placed over, but not in contact with, the guide aperture.

Thermal conductivity enhancement of solid-solid phase-change materials for thermal storage

0.6 Nc = 4.0 Frankel, J. I., and Wang, 1 P., Radiative Exchange Between Gray Fins Using a Coupled Integral Equation Formulation, Journal of Thermophysics and Heat Transfer, Vol. 2, No. 4, Oct. 1988, pp. 296-302. Frankel, J. I., Function Solution to Heat Transfer of a Transparent Gas through a Tube, Numerical Heat Transfer, Part B, No. 2, 1989, pp. 231-244. Frankel, J. I., NASA-Marshall Spaceflight Center, Progress Rept. NAG8-109, Jan. 12, 1988. Stakgold, I., Green's Functions and Boundary Value Problems, Wiley, New York, 1979, pp. 86-184.

Relativistic wave equations for bound states of two scalar particles from scalar quantum electrodynamics.

Coupled integral equations for bound states of two spin-0 bosons are derived variationally from scalar quantum electrodynamics, using an ansatz which incorporates the transverse photon degrees of freedom of the electromagnetic field. The equations are decoupled approximately and then solved perturbatively as well as numerically. A perturbative eigenenergy formula for particles of arbitrary masses, including all the corrections of order ${\mathrm{\ensuremath{\alpha}}}^{4}$, is obtained. A variational solution of the wave equation is used to determine eigenvalues and eigenfunctions at arbitrary coupling for the 1s and 2p states of the equal-mass and ${\mathit{m}}_{\mathit{K}}$/${\mathit{m}}_{\mathrm{\ensuremath{\pi}}}$ cases. Radial s-state excitations are calculated using the basis-state expansion method. In the limit where one particle becomes infinite our equation turns out to be the same as the weak-field limit of the Klein-Gordon-Coulomb equation.

A variational treatment of the relativistic two-fermion bound-state system in quantum electrodynamics

Coupled integral equations for a relativistic two-fermion system of masses m and M are derived variationally within the Hamiltonian formalism of quantum electrodynamics, using an improved ansatz that is sensitive to all terms in the Hamiltonian. The equations are solved approximately to determine the eigenvalues and eigenfunctions, at arbitrary coupling, for various states of the two-particle system.

An electromagnetic model for multiconductor connectors

An electromagnetic model for the response of multiconductor connectors is presented. The model is based on the canonical problem of the electromagnetic response of a thin circumferential slot in the shield of a cylindrical multiconductor transmission line (MTL). The problem is formulated for a shielded MTL of arbitrary cross section with impressed sources driving the interior of the MTL. The problem of interior-to-exterior coupling is solved by treating the slot as a thick aperture in the shield. The equivalence principle is used to divide the original problem into three separate parts. Two coupled integral equations are obtained for the equivalent surface magnetic currents, which are solved by the method of moments, and equivalent networks are presented. The equivalent networks consist of three generalized admittances, one of which is interpreted in terms of a connector admittance. >