Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.     

The effect of carbon nanotubes on epoxy matrix nanocomposites

The paper concerns thermal properties of epoxy/nanotubes composites for aircraft application. In this work, influence of carbon nanotubes on thermal stability, thermal conductivity, and crosslinking density of epoxy matrix was determined. Three kinds of nanotubes were used: non-modified with 1- and 1.5-μm length, and 1-μm length modified with amino groups. Scanning electron microscopy observations were done for examining dispersion of nanotubes in the epoxy matrix. Glass transition temperature (T _g) was readout from differential scanning calorimetry. From dynamic mechanical analysis, crosslinking density was calculated for epoxy and its composites. Also, thermogravimetric analysis was done to determine influence of nanotubes addition on thermal stability and decomposition process of composites. Activation energy was calculated from TGA curves by Flynn–Wall–Ozawa method. Thermal diffusivity was also measured. SEM images proved the uniform dispersion of carbon nanotubes without any agglomerates. It was found that nanotubes modified with amino groups lead to the increase of epoxy matrix crosslinking density. The significant increase in T _g was also observed. On the other hand, addition of carbon nanotubes leads to the decrease of thermal stability of polymer due to the increase of thermal diffusivity.     

Positive-Part Moments via the Fourier–Laplace Transform

Integral expressions for positive-part moments E X₊^pmathsf{E},X_{+}^{p} (p>0) of random variables X are presented, in terms of the Fourier–Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-part moments.     

Prevalence of Antimicrobial Resistant Bacteria from Conjunctival Flora in an Eye Infection Prone Breed (Saint Bernard)

The conjunctival bacterial resident and opportunistic flora of dogs may represent a major source of dissemination of pathogens throughout the environment or to other animals and humans. Nevertheless, contamination with bacteria from external sources is common. In this context, the study of the antimicrobial resistance (AMR) pattern may represent an indicator of multidrug resistant (MDR) strains exchange. The present study was focused on a single predisposed breed—Saint Bernard. The evaluated animals were healthy, but about half had a history of ocular disease/treatment. The swabs collected from conjunctival sacs were evaluated by conventional microbiological cultivation and antimicrobial susceptibility testing (AST). The most prevalent Gram-positive was Staphylococcus spp.; regardless of the history, while Gram-negative was Pseudomonas spp.; exclusively from dogs with a history of ocular disease/treatment. Other identified genera were represented by Bacillus, Streptococcus, Trueperella, Aeromonas and Neisseria. The obtained results suggest a possible association between the presence of mixed flora and a history of ocular disease/treatment. A high AMR was generally observed (90%) in all isolates, especially for kanamycin, doxycycline, chloramphenicol and penicillin. MDR was recorded in Staphylococcus spp. and Pseudomonas spp. This result together with a well-known zoonotic potential may suggest an exchange of these strains within animal human populations and the environment.     

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl’s law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients of the proof include the wave equation parametrix, a pretrace formula and the Dirichlet box principle. Our results develop and extend the unpublished thesis of A. Karnaukh [Ka]. The first author was supported by NSERC, FQRNT, Alfred P. Sloan Foundation Fellowship and Dawson Fellowship. The second author was supported by NSERC and FQRNT. Received: April 2006 Revision: October 2006 Accepted: October 2006     

Explicit Constructions of Universal R-Trees and Asymptotic Geometry of Hyperbolic Spaces

This paper presents explicit constructions of universal R-treesas certain spaces of functions, and also proves that a -universal R-tree can be isometricallyembedded at infinity into a complete simply connected manifoldof negative curvature, or into a non-abelian free group. Incontrast to asymptotic cone constructions, asymptotic spacesare built without using the axiom of choice. 2000 MathematicsSubject Classification L53C23, 20F67.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.