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

PCR and FISH Detection Extends the Range of Pfiesteria piscicida in Estuarine Waters

PCR and fluorescent in situ hybridization probes were used to assay for the presence of the dinoflagellate Pfiesteria piscicida in 170 estuarine water samples collected from New York to northern Florida. 20% of samples tested positive for the presence of P. piscicida, including sites where fish kills due to Pfiesteria have occurred and sites where there was no historical evidence of such events. The results extend the known range of P. piscicida northward to Long Island, New York. The results also suggest that P. piscicida is common, and normally benign, inhabitatant of estuarine waters of the eastern US

Sensors for ceramic components in advanced propulsion systems

This report includes: (1) a survey of the current methods for the measurement of surface temperature of ceramic materials suitable for use as hot section flowpath components in aircraft gas turbine engines; (2) analysis and selection of three sensing techniques with potential to extend surface temperature measurement capability beyond current limits; and (3) design, manufacture, and evaluation of the three selected techniques which include the following: platinum rhodium thin film thermocouple on alumina and mullite substrates; doped silicon carbide thin film thermocouple on silicon carbide, silicon nitride, and aluminum nitride substrates; and long and short wavelength radiation pyrometry on the substrates listed above plus yttria stabilized zirconia. Measurement of surface emittance of these materials at elevated temperature was included as part of this effort

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

The survival probability, S_N(t), of a diffusing prey (``lamb'') in the proximity of N diffusing predators (a ``pride of lions'') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S_N(t) is proportional to t^{-beta_N}, with the decay exponent beta_N proportional to ln N. The crossover behavior as a function of the relative diffusivities of the lions and the lamb is also discussed. When N--->oo, the lamb survival probability exhibits a log-normal decay, exp(-ln^2 t).Comment: 12 pages, no figures, macro files prepended, to be submitted to J. Phys.

Asymmetric Upwarp of the Asthenosphere beneath the Baikal Rift Zone, Siberia

In the summer of 1991 we installed 27 seismic stations about lake Baikal, Siberia, aimed at obtaining accurately timed digital seismic data to investigate the deep structure and geodynamics of the Baikal rift zone and adjacent regions. Sixty-six teleseismic events with high signal-to-noise ratio were recorded. Travel time and Q analysis of teleseisms characterize an upwarp of the lithosphere-asthenosphere boundary under Baikal. Theoretical arrival times were calculated by using the International Association of Seismology and Physics of the Earth\u27s interior 1991 Earth model, and travel time residuals were found by subtracting computed arrival times from observed ones. A three-dimensional downward projection inversion method is used to invert the P wave velocity structure with constraints from deep seismic sounding data. Our results suggest that (1) the lithosphere-asthenosphere transition upwarps beneath the rift zone, (2) the upwarp has an asymmetric shape, (3) the velocity contrast is -4.9% in the asthenosphere, (4) the density contrast is -0.6%, and (5) the P wave attenuation contrast t* is 0.1 s