Numerical solution of scattering problems using pseudo-differential impedance operators

Direct numerical solutions of scattering problems based on boundary-integral equations are computationally costly at high frequencies. A numerical method is presented that efficiently computes accurate approximations to unknown surface quantities given known surface data (an approximate Dirichlet-to-Neumann map). The method is based on a pseudo-differential impedance operator (PIO) numerically implemented using rational approximations. An example of a PIO is the so-called on-surface radiation condition (OSRC) method. For a convex obstacle, the method can be viewed as applying a parabolic equation directly on the surface of a scatterer. In contrast to past OSRCs, the use of rational approximations provides accuracy for wide scattering angles which is needed for grazing angles of incidence. Generalization to impedance operators for two-dimensional acoustic scatterers with concave parts is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microwave heating of ceramic composites

The microwave heating of a ceramic composite is modelled andanalysed. The composite consists of many small ceramic particlesembedded in a ceramic cement. The composite is assumed to bewell insulated, and each particle is assumed to be in imperfectthermal contact with the surrounding cement. Based on thesetwo assumptions an asymptotic theory exploiting the small Biotnumber and small non-dimensional contact conductance is developed.Our asymptotic theory yields a set of nonlinear partial differentialequations which govern the temperature in the composite. Theseare reduced to a set of coupled nonlinear ordinary differentialequations in which the surface area of each particle entersas a parameter. Recent experiments with such composites haveshown that the steady-state temperature of the composite isstrongly dependent upon the radii of the embedded particles.Our model captures this effect. In fact, our analysis showsthat the assumption of imperfect thermal contact between theparticles and the ceramic cement is essential for this trendto be established.     

The Interaction of the Supersonic Plasma-Jet with the Substrate in the RF Plasma-Chemical Reactor

Although the plasma-chemical processes and properties of the deposited thin film can strongly depend on the interaction of the supersonic plasma jet channel with the substrate, up to now the study of this phenomenon has not yet been done. We decided to study this interaction by means of CCD camera. The presented results indicate that the light intensity recorded close to the substrate can be used as a measure of the intensity of plasma-chemical deposition processes on the substrate surface.     

Backscatter from a limestone seafloor at 2-3.5 kHz: measurements and modeling

Physics-based interface scattering models for the seafloor [H.-H. Essen, J. Acoust. Soc. Am. 95, 1299-1310 (1994); Gragg et al., ibid. 110, 2878-2901 (2001)] exhibit features in their predicted grazing angle dependence. These features have a strong dependence on the assumed composition and roughness of the bottom. Verifying such predictions requires data that cover a wide range of grazing angles and involve minimal sub-bottom penetration. Such measurements were performed in the frequency band 2-3.5 kHz over an exposed limestone bottom off the Carolina coast during the second Littoral Warfare Advanced Development Focused Technology Experiment of 1996 (LWAD FTE 96-2). Direct-path bottom scattering strengths were obtained in shallow water (198-310 m deep) for grazing angles from 8 degrees to 75 degrees using data fusion from multiple experimental geometries coupled with careful signal processing. The processing included corrections for the surface-reflected path, other multipaths, and characteristics of the reverberation decay observed over the pulse duration at higher grazing angles. The resulting frequency and grazing-angle dependences exhibit trends consistent with theoretical predictions, and geoacoustic parameters obtained by inversion are consistent with values expected for limestone.     

Optical colours and polarization of a model reflection nebula

Simple models of a reflection nebula in the form of a plane-parallel slab containing smooth spherical solid particles in submicron size range have been considered. Single scattering has been assumed. The effect of varying the composition and size distribution function of the grains have been brought out in the calculations using Mie theory of scattering. The analytical part of the geometry of the problem has been treated quite rigorously and the resulting expression for nebular intensity has been presented in a somewhat new form. In this paper, the case of the star behind the nebula has been examined. A comparison of the theoretical results with the observations of the Merope nebula shows that the dirty ice grains with index of refraction about 1·3–0·1i and size parametera ₀ = 0·5μ give reasonable agreement with the colours. Simultaneously, the polarization in the visual and blue wavelength bands agree approximately up to offset angle of 6 minutes of arc. The larger offset angles pose an intriguing problem. The general trends of nebular colours and polarization with variation of real and imaginary parts of index of refraction and the size distribution parameter have been tabulated to serve as a guide for further study of reflection nebulae with the star in the rear. A part of this work was presented at the first scientific meeting of the Astronomical Society of India, held on 27 and 28 February 1974 at Hyderabad. An erratum to this article is available at .     

Über 3,3,6,9,9-Pentamethyl-2,10-diaza-bicyclo-[4.4.0]-1-decen und einige seiner Derivate. Über synthetische Methoden. 13. Mitteilung

3,3,6,9,9-Pentamethyl-2,10-diaza-bicyclo[4.4.0]-1-decen and some of its derivatives A simple synthesis for the bicyclic amidine 1 (Scheme 3) is described. This base and the salts which were prepared from it show solubility characteristics which make the amidine a potentially useful reagent for salt formation of carboxylic acids and related proton complexes of bidentate ligands. Among the derivatives made from 1 are the sterically strongly hindered N-alkylated amidines 11 , 12 and 14 (Scheme 5), as well as the stable crystalline N¹-oxidoamidine-N²-oxyl radical 2 (Scheme 6). The ability of the latter to serve as a paramagnetic chelating ligand for metal ions is illustrated by the preparation of a corresponding nickel(II) complex. The radical is also a source for the α-nitronyl-nitrosonium cation 4 which shows in its reactivity towards conjugated dienes and olefines some of the expected resemblance to singlet oxygen.     

Ca0．80Zn0．20Te晶体的生长及性能研究

用本实验室合成的Ca0．80Zn0．20Te多晶料为原料，采用改进的布里奇曼法在镀碳和未镀碳的石英安瓿中生长出Ca0．80Zn0．20Te晶锭。使用X射线衍射仪对合成产物及晶锭进行了分析，生长晶体的X射线衍射峰尖锐，摇摆谱对称，表明晶锭的结晶性能较好；用IRPrestige-21红外光谱仪分析了晶体的红外透射光谱，测试结果表明安瓿镀碳后生长的晶体位错密度小，均匀性较好，电阻率优于未镀碳安瓿生长的晶体；晶体的蚀坑密度在10^3-10^4cm^-2之间，比未镀碳安瓿生长的晶体低1个数量级。     

Superatomic Boolean algebras constructed from strongly unbounded functions

Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ^{++ +} ≤ λ, κ^<κ = κ and 2^κ = κ⁺, and η is an ordinal with κ⁺ ≤ η < κ⁺⁺ and cf(η) = κ⁺. Then, in some cardinal‐preserving generic extension there is a superatomic Boolean algebra $\mathcal BUsing Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ^{++ +} ≤ λ, κ^<κ = κ and 2^κ = κ⁺, and η is an ordinal with κ⁺ ≤ η < κ⁺⁺ and cf(η) = κ⁺. Then, in some cardinal‐preserving generic extension there is a superatomic Boolean algebra $\mathcal B$ such that $\mathrm{ht}(\mathcal B) = \eta + 1$, $\mathrm{wd}_{\alpha }(\mathcal B) = \kappa$ for every α < η and $\mathrm{wd}_{\eta }(\mathcal B) = \lambda$(i.e., there is a locally compact scattered space with cardinal sequence 〈κ〉_η^??〈λ〉). Especially, $\langle {\omega }\rangle _{{\omega }_1}{}^{\smallfrown } \langle {\omega }_3\rangle$ and $\langle {\omega }_1\rangle _{{\omega }_2}{}^{\smallfrown } \langle {\omega }_4\rangle$ can be cardinal sequences of superatomic Boolean algebras.     

Transient vibration of thin viscoelastic orthotropic plates

This article deals with solutions of transient vibration of a rectangular viscoelastic orthotropic thin 2D plate for particular deformation models according to Flu¨gge and Timoshenko-Mindlin.The linear model,a general standard viscoelastic body,of the rheologic properties of a viscoelastic material was applied.The time and coordinate curves of the basic quantities displacement,rotation,velocity,stress and deformation are compared.The results obtained by an approximate analytic method are compared with numerical results for 3D plate generated by FEM application and with experimental investigation.