Integral Representations of a Pulsed Signal in a Waveguide

Acoustical Physics - The problem of pulsed excitation of an acoustic waveguide with a constant cross section is considered. Absorption is ignored. As the most general model of such a waveguide,...     

Acoustical estimation of parameters of porous road pavement

In the simplest case, porous road pavement of a known thickness is described by such parameters as porosity, tortuosity, and flow resistance. The problem of estimating these parameters is investigated in this paper. An acoustic signal reflected by the pavement is used for this. It is shown that this problem can be solved by an experiment conducted in the time domain (i.e., the pulse response of the media is recorded). The incident sound wave is thrown at a grazing angle to the surface between the pavement and the air to improve penetration into the porous medium. The procedure of computing of the pulse response using the Morse-Ingard model is described in detail.     

Resonances in a discrete system of variable length

Resonance properties of a finite discrete chain with a periodically varying length are investigated. The evolution equation describing a wave profile in continual approximation is derived. Splitting of the resonance peak is revealed. Wave profiles near the resonances are considered. It is shown that wave profiles formed near different resonances differ from each other in spectral composition. This result is theoretically substantiated.     

Precision Resonator Microwave Spectroscopy in Millimeter and Submillimeter Range

By the use of Fabry–Perot resonator with quality factor 600 000 and fast precision (down to one Hertz) frequency control of coherent millimeterwave radiation source the 20 Hz accuracy in measurements of the width of resonance curve is obtained. This accuracy corresponds to the detection of 1.8 × 10^–3 dB/km absorption in the sample filling the resonator and exceeds the before known sensitivity more than by an order of magnitude. The example of precise measurement of 60 GHz oxygen absorption band in the real atmosphere is presented. The new possibilities of application of precision resonator microwave spectroscopy to the atmospheric problems as well as to the ultra-low absorptions measurements in dielectrics and metal surfaces up to Terahertz frequencies are discussed.     

The modified kontorovich-lebedev transform and its application to solving canonical problems of diffraction

The aim of this work is to fill the gap between three-dimensional embedding formulas for problems of diffraction by cones and the modified Smyshlyaev formulas. The three-dimensional embedding formulas express the diffraction effect in the form of iterated integrals over spatial variables. The modified Smyshlyaev formulas express it in the form of a single contour integral with respect to the parameter ν of separation of variables. This situation resembles the theorem of convolution for the Fourier transform: repeated convolutions are expressed by a single integral with respect to frequency. In [1], where the modified Smyshlyaev formulas were introduced for the first time, these formulas were hypothesized and then proved. No regular method for deriving them has been proposed. The extension of the analogy with the Fourier transform to the case of conical problems of diffraction enables one to construct a technique for transformation of contour integrals that can be used for deriving the modified Smyshlyaev formulas directly from the three-dimensional embedding formulas. This extension is performed by introducing an integral transform similar to the Kontorovich-Lebedev transform, for which analogs of the theorem of convolution and the Plancherel formulas can be successfully proved.     

Embedding formulae for Laplace-Beltrami problems on the sphere with a cut

We consider the problem of diffraction of a plane wave by a quarter-plane (a flat cone) with Dirichlet boundary conditions. The most efficient approach to this problem is the technique of Smyshlyaev’s formulae or a modified Smyshlyaev’s formula, both of which are representations of the diffraction coefficient as contour integrals over a complex parameter. These representations have been proven independently. Here we are demonstrating a link between these classes of formulae. The link is established by developing an embedding procedure (in the very special sense of diffraction theory) on the unit sphere.     

Nonlinear phenomena accompanying the development of oscillations excited in a layer of a linear dissipative medium by finite displacements of its boundary

A method of describing oscillations in resonators on the basis of evolution equations is proposed. The latter are obtained by simplifying the functional equations under the assumption that the distortions of travelling waves within the resonator length are small, that the Mach number for the moving boundary oscillations is small, and that the frequency is close to one of the natural frequencies of the resonator. The problems of nonstationary oscillations of a layer with a moving boundary are solved. The law that should govern the wall oscillations to provide the development of steady-state linear resonance oscillations is determined. The shape of the resonance curve formed in the presence of a boundary nonlinearity is calculated. The method of matching of asymptotics is applied to the singularly perturbed problem with small dissipation. It is shown that a boundary nonlinearity leads to a distortion of the temporal profile of the standing wave and to the generation of higher harmonics in the process of the development of steady-state oscillations. In contrast to the classical linear problems where the resonance occurs at the coincidence of the external force frequency with one of the natural frequencies, in the case under study the resonance behavior is observed in frequency bands, which are wider the higher the amplitude of the boundary oscillations is.     

Embedding formulae for diffraction by non-parallel slits

Embedding formulae for diffraction theory encode the diffractioncoefficients for some given wave incidence on a scatterer interms of the directivity from a single or reduced number ofscattering problems. If one deduces the relation between thesedirectivities, then the resulting formulae enable rapid computationsand allow one to concentrate computational resources accordingly.Unfortunately, the range of applicability of embedding formulaeis currently rather restricted. In this article, we demonstratehow embedding is applied to plane-wave scattering by non-parallelstrips or slits. Primarily, we concentrate upon the problemof a line crack, or strip, inclined to a flat infinite surfaceand we derive and implement the embedding formula. Various othergeneralizations are possible given these formulae and we outlinethem.