Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width

A hybrid asymptotic-modal analysis of the EM scattering by an open-ended S-shaped rectangular waveguide cavity

The electromagnetic fields (EM) backscatter from a 3-dimensional perfectly conducting S-shaped open-ended cavity with a planar interior termination is analyzed when it is illuminated by an external plane wave. The analysis is based on a self-consistent multiple scattering method which accounts for the multiple wave interactions between the open end and the interior termination. The scattering matrices which described the reflection and transmission coefficients of the waveguide modes reflected and transmitted at each junction between the different waveguide sections, as well at the scattering from the edges at the open end are found via asymptotic high frequency methods such as the geometrical and physical theories of diffraction used in conjunction with the equivalent current method. The numerical results for an S-shaped inlet cavity are compared with the backscatter from a straight inlet cavity; the backscattered patterns are different because the curvature of an S-shaped inlet cavity redistributes the energy reflected from the interior termination in a way that is different from a straight inlet cavity

High-frequency asymptotic methods for analyzing the EM scattering by open-ended waveguide cavities

Four high-frequency methods are described for analyzing the electromagnetic (EM) scattering by electrically large open-ended cavities. They are: (1) a hybrid combination of waveguide modal analysis and high-frequency asymptotics, (2) geometrical optics (GO) ray shooting, (3) Gaussian beam (GB) shooting, and (4) the generalized ray expansion (GRE) method. The hybrid modal method gives very accurate results but is limited to cavities which are made up of sections of uniform waveguides for which the modal fields are known. The GO ray shooting method can be applied to much more arbitrary cavity geometries and can handle absorber treated interior walls, but it generally only predicts the major trends of the RCS pattern and not the details. Also, a very large number of rays need to be tracked for each new incidence angle. Like the GO ray shooting method, the GB shooting method can handle more arbitrary cavities, but it is much more efficient and generally more accurate than the GO method because it includes the fields diffracted by the rim at the open end which enter the cavity. However, due to beam divergence effects the GB method is limited to cavities which are not very long compared to their width. The GRE method overcomes the length-to-width limitation of the GB method by replacing the GB's with GO ray tubes which are launched in the same manner as the GB's to include the interior rim diffracted field. This method gives good accuracy and is generally more efficient than the GO method, but a large number of ray tubes needs to be tracked

Riesz transform characterization of Hardy spaces associated with Schr\"odinger operators with compactly supported potentials

Let L=-\Delta+V be a Schr\"odinger operator on R^d, d\geq 3. We assume that V is a nonnegative, compactly supported potential that belongs to L^p(R^d), for some p>d/2. Let K_t be the semigroup generated by -L. We say that an L^1(R^d)-function f belongs to the Hardy space H_L^1 associated with L if sup_{t>0} |K_t f| belongs to L^1(R^d). We prove that f\in H_L^1 if and only if R_j f \in L^1(R^d) for j=1,...,d, where R_j= \frac{d}{dx_j} L^{-1/2} are the Riesz transforms associated with L.Comment: 6 page

60 GHz indoor propagation studies for wireless communications based on a ray-tracing method

This paper demonstrates a ray-tracing method for modeling indoor propagation channels at 60 GHz. A validation of the ray-tracing model with our in-house measurement is also presented. Based on the validated model, the multipath channel parameter such as root mean square (RMS) delay spread and the fading statistics at millimeter wave frequencies are easily extracted. As such, the proposed ray-tracing method can provide vital information pertaining to the fading condition in a site-specific indoor environment

60 GHz indoor propagation studies for wireless communications based on a ray-tracing method

This paper demonstrates a ray-tracing method for modeling indoor propagation channels at 60 GHz. A validation of the ray-tracing model with our in-house measurement is also presented. Based on the validated model, the multipath channel parameter such as root mean square (RMS) delay spread and the fading statistics at millimeter wave frequencies are easily extracted. As such, the proposed ray-tracing method can provide vital information pertaining to the fading condition in a site-specific indoor environment

Immunoglobulin-A distribution in glomerular disease: Analysis of immunofluorescence localization and pathogenetic significance

Immunoglobulin-A distribution in glomerular disease. Analysis of immunofluorescence localization and pathogenetic significance. Renal biopsies from 470 patients with various glomemlonephropathies were studied for patterns and frequency of glomerular bound IgA. Correlations of IgA with IgG, IgM, C3, and C4 were made. Glomerular deposits of IgA were observed in five of six cases of Henoch-Schoenlein anaphylactoid nephritis (83%), stalk proliferative glomerulonephritis (73%), lupus nephritis (60%), and focal proliferative glomerulonephritis (57 %). In addition, IgA was less frequently observed in diffuse (acute) proliferative (33%), membranoproliferative (42%), membranous (32%), focal sclerosing (25%) crescentic (26%), and chronic glomerulonephritides (23%) as well as malignant arterionephrosclerosis, amyloidosis, and a group of patients with minimal glomerular alteration and no determinable diagnosis (40%). IgA was not specifically associated with IgG or IgM in any one diagnostic category but was often present with both. Deposits containing C3 and C4 most closely paralleled those of IgG and/or IgM. Presence of IgA appeared to correlate with variable degrees of increased glomerular mesangial cellularity in “minimal”, stalk proliferative, and focal-segmental glomerular lesions. The cause and immunopathogenetic significance of mesangial or peripheral glomerular capillary localization of IgA is unknown. Though a number of apparent examples of what has been referred to as IgA-IgG nephropathy were observed in this study, this entity, characterized by mesangial deposits of IgA, IgG, and C3, could not always be specifically identified or differentiated on histopathologic criteria alone from a variety of other glomerulopathies in which variable proportions of IgA, IgG, IgM, C3, and C4 globulins were localized

Local Time Asymmetry of Saturn\u27s Magnetosheath Flows

Using gross averages of the azimuthal component of flow in Saturn\u27s magnetosheath, we find that flows in the prenoon sector reach a maximum value of roughly half that of the postnoon side. Corotational magnetodisc plasma creates a much larger flow shear with solar wind plasma prenoon than postnoon. Maxwell stress tensor analysis shows that momentum can be transferred out of the magnetosphere along tangential field lines if a normal component to the boundary is present, i.e., field lines which pierce the magnetopause. A Kelvin‐Helmholtz unstable flow gives rise to precisely this situation, as intermittent reconnection allows the magnetic field to thread the boundary. We interpret the Kelvin‐Helmholtz instability acting along the magnetopause as a tangetial drag, facilitating two‐way transport of momentum through the boundary. We use reduced magnetosheath flows in the dawn sector as evidence of the importance of this interaction in Saturn\u27s magnetosphere