Spectral Green's Function Research Articles

Unified solution of various dielectric-loaded ridge waveguides with a mixed spectral-domain method

A mixed spectral-domain method is developed and applied to the analysis of various dielectric-loaded ridge waveguides. Magnetic surface currents at apertures are identified as unknowns in auxiliary structures. Spectral Green's functions are formulated for these structures using the spectral immittance approach. Mixing different spectral domains existing on the two sides of an aperture in a spectral Galerkin approach then leads to the characteristic equations required for the dispersion analysis. The simplicity and numerical efficiency of the conventional spectral-domain immittance approach, which cannot be applied directly to the present structures, are maintained. Representative results are obtained to illustrate the application of the method. >

Spectral dyadic Green's function formulation for planar integrated structures

The problem of the complete determination of the dyadic spectral Green's function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field. The reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral Green's function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source. Furthermore, an equivalent circuit representation of the structure, allowing a noteworthy simplification in the determination of the total power, has been obtained. These equivalent circuits and the derived spectral Green's function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading, such as matched or unmatched loads, parasitic, and shorting pins. >

Analysis of MMIC structures using an efficient iterative approach

A class of two-dimensional and three-dimensional monolithic microwave integrated circuit (MMIC) structures is analyzed theoretically using an efficient iterative technique. The transfer-matrix approach to constructing the spectral Green's functions of multilayered structures is adopted. Discretization of the continuous functions and utilization of the periodicity of the MMIC structures enclosed by sidewalls lead to a discrete convolution operation, which is carried out efficiently using the FET (fast Fourier transform) algorithm. The spectral Green's functions are modified for both the periodic and aperiodic structures to improve the numerical efficiency of the iterative algorithm. Numerical results are presented and compared with available data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the singularity of the full spectral Green's dyad

The full 3 \times 3 spectral dyadic Green's function exhibits certain properties that its popular 2 \times 2 transversal portion does not. In particular, it is shown that the dyad is identically singular, the singularity being a manifestation of the plane wave properties of each spectral component. This singularity has an impact on the use of certain computational algorithms which in general would require an inversion of the dyad. Other plane wave properties, being dual to Maxwell's equations, are also discussed.

On the spectral dyadic Green's function for stratified linear media. Application to multilayer MIC lines with anisotropic dielectrics

On the spectral dyadic Green's function for stratified linear media. Application to multilayer MIC lines with anisotropic dielectrics

Three-dimensional free boundary calculations using a spectral Green's function method

The plasma energy W p = ∫ ω p ( 1 2 B 2 +p dV is minimized over a toroidal domain ω p using an inverse representation for the cylindrical coordinates R = ΣR mn ( S) cos( mθ − nζ) and Z = ΣZ mn ( s) sin( mθ − nζ), where ( s, θ, ζ) are radial, poloidal and toroidal flux coordinates, respectively. The radial resolution of the MHD equations is significantly improved by separating R and Z into contributions from even and odd poloidal harmonics which are individually analytic near the magnetic axis. A free boundary equilibrium results when ω p is varied to make the total pressure 1 2 B 2 + p continuous at the plasma surface Σ p and when the vacuum magnetic field B v satisfies the Neumann condition B v ·d Σ p = 0 . The vacuum field is decomposed as B v = B 0 + ∇φ , where B 0 is the field arising from plasma currents and external coils and φ is an single-valued potential necessary to satisfy B v d Σ p = 0 when p ≠ 0. A Green's function method is used to obtain an integral equation over Σ p for the scalar magnetic potential φ = Σφ mn sin( mθ − nζ). A linear matrix equation is solved for φ mn to determine 1 2 B 2 v on the boundary. Real experimental conditions are simulated by keeping the external and net plasma currents constant during the iteration. Applications to l = 2 stellarator equilibria are presented.

A mechanism for tectonic deformation on Venus

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface‐density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.

Green's function in the spectral domain for biaxial and uniaxial anisotropic planar dielectric structures

Green's function solutions of the biaxial and uniaxial anisotropic layered-medium planar-structure is formulated in terms of Maxwell's equations. Diagonalized biaxial and uniaxial permittivity tensors in the coordinate system of interest are treated. The Green's function is found in the double Fourier transformed domain for three longitudinal-to-an-axis coupled electric-magnetic field sets applied to a simple layered structure. The approach is applicable to structures having discontinuities in two orthogonal planar directions such as patch radiators or resonators. Spectral Green's function is usable in method-of-moment calculations assisted by Galerkin's method.

Shear waves due to cracks in an isotropic rectangular strip

A mathematical formulation of the shear waves due to the presence of a crack, loaded in an opening mode, in an isotropic and elastic rectangular strip is presented. An analytical solution based on application of spectral representation and Green's functions methods is developed. Numerical presentations of the solution demonstrate the effect of crack length on the amplitude of these waves at any given position along the sides of the rectangular strip. The solution provides a quantitative analysis on means of detection of shear waves emitted due to the presence of a loaded crack.

MIC Overlay Coupler Design Using Spectral Domain Techniques

A quasi-TEM analysis of dielectric overlay microstrip is described for an overlay extending several conductor Iinewidths beyond the coupled lines. This method permits the analysis of numerous variations of overlay coupler geometries. The relevant spectral domain Green's function is given and used to generate a set of design curves when the overlay is identical in thickness and dielectric constant to the main substrate. A trial 8.34-dB coupler was built. Significant improvement in isolation was noted with the overlay when compared to the equivalently designed uncompensated coupler. The measured values of isolation agree very well with predicted values.

PHONON DISPERSION RELATION OF MASS DEFECT CONCENTRATED ALLOY Ni-Pt AND ITS INTERPRETATION BY CPA

By means of inelastic scattering of neutrons, the phonon dispersion relations of 00ζ T branch have been measured for Ni-Pt alloys with various concentrations. For Ni95Pt5 and Ni70Pt30, double peaks were found in the neutron scattering spectra obtained by constant q method at about q = 0.5. The dispersion relation has an energy gap corresponding to the appearance of the double peaks. The gap with is about 3 meV and 6 meV for Ni95Pt5 and Ni70Ni30, respectively. Taylor has calculated the spectral Green function of phonons in mass defect concentrated alloy AuCu under CPA. From the positions and widths of the peaks of the Green function, one can construct the dispersion curves of phonon mode as well as width. The theoretical dispersion relation, thus obtained has an energy gap corresponding to the localized vibrations. The similarity of the theoretical and experimental dispersion relations indicates that the nature of phonons in highly concentrated mass defect alloys can be well interpreted by the theory under CPA. The reason of the appearance of the double phonons corresponding to a single wave number can be understood by considering that the vibration frequency of an atom changes in time or in space from higher one which is a localized mode around light atoms to lower one which is a localized mode around heavy atoms.

Standard-Basis Operator Method in the Green's-Function Technique of Many-Body Systems with an Application to Ferromagnetism

A new formalism, using standard-basis matrix operators, is presented for the study of the collective excitations and the thermodynamic properties of an ensemble of identical interacting quantum-mechanical systems subsequently called ions, each ion having discrete energy levels. A model Hamiltonian is formulated in terms of these operators. The Hamiltonian contains terms which express the interaction of the ion with the crystal field and the external fields as well as terms which arise from the mutual interaction of ions. Using the doubletime temperature-dependent Green's-function technique, the equations of motion of the Green's functions of standard-basis operators are developed in the random-phase decoupling approximation. It is demonstrated that the temperature-dependent correlation functions of standard-basis operators, which are obtained from associated spectral Green's functions, lead to a set of equations that can be solved for the occupation probabilities of the single-ion energy levels. Hence, one can calculate the thermal-average expectation value of any quantum-mechanical operator representing a microscopic observable of a single ion, or a pair of ions (correlations). An important feature of the standard-basis matrix-operator formalism is that the single-ion terms, such as crystal field, molecular field, or external fields, are always treated exactly in any Green's-function decoupling scheme. In contrast, Green's-function methods which use angular momentum operators often necessarily treat single-ion terms in a decoupling approximation. As an example, the general standard-basis operator theory is applied to the Heisenberg ferromagnet in the presence of uniaxial single-ion crystal-field anisotropy, which has received extensive theoretical attention previously, with widely varying results.

The Spectral Matrix and Green's Function for Singular Self-Adjoint Boundary Value Problems

Let L denote the formal ordinary differential operator,where we assume the pk are complex-valued functions with n-k continuous derivatives on an open real interval a &lt; x &lt; b (a = — ∞, b = + ∞, or both may occur), p0(x) ≠ 0 on a &lt; x &lt; b, and L coincides with its Lagrange adjoint L+ given by.