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EN
Hydrodynamic forces on a submerged cylinder in uniform finite depth ice-covered water is formulated by using the method of multipoles, the ice-cover being modelled as an elastic plate of very small thickness. The forces (vertical and horizontal) are obtained analytically as well as numerically and depicted graphically for various values of flexural rigidity of the ice-cover to show the effect of its presence. When the flexural rigidity and surface density of the ice-cover are taken to be zero, then the curves for the forces almost coincide with the curves for the case of uniform finite depth water with free surface.
EN
An original model based on first principles is constructed for the temporal correlation of acoustic waves propagating in random scattering media. The model describes the dynamics of wave fields in a previously unexplored, moderately strong (mesoscopic) scattering regime, intermediate between those of weak scattering, on the one hand, and diffusing waves, on the other. It is shown that by considering the wave vector as a free parameter that can vary at will, one can provide an additional dimension to the data, resulting in a tomographic-type reconstruction of the full space-time dynamics of a complex structure, instead of a plain spectroscopic technique. In Fourier space, the problem is reduced to a spherical mean transform defined for a family of spheres containing the origin, and therefore is easily invertible. The results may be useful in probing the statistical structure of various random media with both spatial and temporal resolution.
3
Content available A spectral-based method for tissue characterization
EN
Quantitative ultrasound methods are widely investigated as a promising tool for tissue characterization. In this paper, a novel quantitative method is developed which can be used to assess scattering properties of tissues. The proposed method is based on analysis of oscillations of the backscattered echo power spectrum. It is shown that these oscillations of the power spectrum are connected with the distances between scatterers within the medium. Two techniques are proposed to assess the scatterer’s distribution. First, we show that the inverse Fourier transform of the backscattered echo power spectrum corresponds to a histogram of the distances between scatterers. Second, the Hilbert-Huang transform is used to directly extract the power spectrum oscillations. Both methods are examined by means of a numerical experiment. A cellular gas model of a biological medium is considered. Results are presented and discussed. Both methods can be used to evaluate the scatterer’s distribution by means of the power spectrum oscillations.
EN
The problem of plane electromagnetic wave scattering by periodic system of semi-infinite thick plates of rectangular shape is solved in this paper. The case of TM-polarization is considered in this paper. The field distribution in the free space region above the plates is found in the form of series of spatial harmonics in accordance with the Floquet's theorem. In the plate region the field is found in the form of parallel-plate waveguide modes. The continuity condition for tangential components of electric and magnetic field vectors is applied in order to find unknown partial wave amplitudes. To satisfy the boundary conditions and the singular behavior of the electric field vector near the plate edges, the use is made of the known properties of certain Fourier expansion with corresponding coefficients being properly chosen Legendre functions. The final rigorous solution is given in the form of infinite series of spatial harmonics with unknown coefficients being the solution of the corresponding doubly infinite system of linear equations which can be solved only numerically.
PL
W pracy przeanalizowano zagadnienie rozpraszania fal harmonicznych na niejednorodnościach porowatego materiału modelowanych jako periodyczny ośrodek złożony z naprzemiennie ułożonych dwóch rodzajów warstw o różnych własnościach mechanicznych. Otrzymano równanie dyspersyjne oraz amplitudowy współczynnik odbicia od półprzestrzeni takiego ośrodka przy prostopadłym padaniu fal. Pokazano występowanie ujemnej dyspersji fal w ośrodku warstwowym oraz zakresów częstotliwości, dla których staje się on nieprzeźroczysty.
EN
The problem of wave scattering at inhomogeneities of porous material is analyzed. The model of periodic medium is considered. The structure is formed by alternately arranged two kinds of layers with different mechanical properties. The dispersion relation and reflection coefficient for perpendicular wave incidence at halfspace of layered medium are derived. It was shown the existence of negative dispersion and the ranges of wave frequencies for which the total reflection is observed.
EN
The paper is focussed on the development of the method of analytical regularization (MAR) in electromagnetic wave scattering and absorption by imperfect scatterers shaped as thin screens.
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