Using the Kirchhoff integral for approximate calculation of angular characteristics of sound scattering by elastic shells of nonanalytical form

Предложен новый приближенный метод расчета угловых характеристик рассеяния звука на упругих телах неаналитической формы при различных геометрических параметрах стыкуемых фрагментов аналитической формы. Метод базируется на использовании интегральной формулы Кирхгофа и известных строгих решениях задач дифракции звука на упругих аналитических телах. Совместное использование методов динамической теории упругости и разделения переменных с помощью потенциалов Дебая и «типа Дебая» позволяет получить решения задач дифракции звука на изотропных оболочках неаналитической формы, составленных из компонентов сфероидальной, цилиндрической и сферической форм. Вычислены и проанализированы угловые характеристики рассеяния при различных волновых размерах, геометрических и физических параметрах оболочек. Применение рассматриваемого метода имеет особенно актуально в диапазонах низких и средних звуковых частот, где упругие тела являются эффективными рассеивателями звука, что повышает вероятность определения их индивидуальных признаков. A new approximate method for calculating the angular characteristics of sound scattering on elastic bodies of non-analytical form for various geometric parameters of the joined fragments of the analytical shape we proposed. The method they based on the use of the Kirchhoff integral formula and well-known rigorous solutions of sound diffraction problems on elastic analytical bodies. The combined use of methods of the dynamic theory of elasticity and separation of variables using Debye potentials and "Debye type" potentials allows us to obtain solutions to problems of sound diffraction on isotropic shells of non-analytical form composed of components of spherical, cylindrical and spherical forms. Angular scattering characteristics are calculated and analyzed for various wave sizes, geometric and physical parameters of the shells are calculated. The application of this method is particularly relevant in the low and medium sound frequency ranges, where elastic bodies are effective sound diffusers, which increases the probability of determining their individual characteristics.

Validation of Fresnel–Kirchhoff Integral Method for the Study of Volume Dielectric Bodies

In this work, we test a nondestructive optical method based on the Fresnel–Kirchhoff integral, which could be applied to different fields of engineering, such as detection of small cracks in structures, determination of dimensions for small components, analysis of composition of materials, etc. The basic idea is to apply the Fresnel–Kirchhoff integral method to the study of the properties of small-volume dielectric objects. In this work, we study the validity of this method. To do this, the results obtained by using this technique were compared to those obtained by rigorously solving the Helmholtz equation for a dielectric cylinder of circular cross-section. As an example of the precision of the method, the Fresnel–Kirchhoff integral method was applied to obtain the refractive index of a hair by fitting the theoretical curve to the experimental results of the diffraction pattern of the hair measured with a CCD camera. In a same manner, the method also was applied to obtain the dimensions of a crack artificially created in a piece of plastic.

Transparent boundary condition for the calculation of eigenmodes in transversely infinite waveguides

Waveguides play one of the key figures in today's electronics and optics for signal transmission. Corresponding simulations of electromagnetic wave transportation along these waveguides are accomplished by discretization methods such as the Finite Integration Technique (FIT) or the Finite Element Method (FEM). For longitudinally homogeneous and transversely unbounded waveguides these simulations can be approximated by closed boundaries. However, this distorts the original physical model and unnecessarily increases the size of the computational domain size. In this article we present a boundary condition for transversely open waveguides based on the Kirchhoff integral which has been implemented within the framework of FIT. The presented solution is compared with selected conventional methods in terms of computational effort and memory consumption.

Experimental Investigation of Diffraction caused by Transparent Barriers

In addition to wave-particle duality, the contributions of Kirchhoff-Helmholtz are fundamental to the scalar theory of diffraction. The mathematical results of their formulae help predict the maximum intensity of light at the center of the far-field diffraction pattern that coincides with the optical axis. This study demonstrates, via a series of the single-slit experiments, that the Helmholtz–Kirchhoff integral is invalid for transparent barriers. In fact, the experimental results show that the main factors determining the appearance of the diffraction pattern are the refractive index contrast between the barrier and the medium, including the physical invariance of the medium in response to factors such as temperature and pressure, and the dimensions of the barriers.

NEW APPROACHES IN OPTIMIZATION OF CALCULATION OF WAVE FIELDS DIRECTLY RELATED TO THE SELECTED TARGET AREA OF SEISMIC RESPONSE

The article describes the method of calculating the wave field of reflected waves of a certain type of re-reflection from localized target objects. A special feature of the method is the combination of the wave field continuation operator calculated by means of layer-by-layer recalculation based on the Kirchhoff integral and the finite-difference operator of reflected waves. Parameterization of the wave field continuation operator type is determined on the basis of the frame effective depth-velocity model. The research is carried out by Seismotech, Ltd under the grant support of "Skolkovo" Foundation.

Kirchhoff Approximations for the Forward-Scattering Target Strength of Underwater Objects

Kirchhoff approximations for the forward-scattering target strength of underwater objects are developed by combining Babinet’s principle and the Kirchhoff integral, where theoretical formulations and a numerical implementation are given in detail. The Kirchhoff approximation is found to be a high-frequency physical acoustic approximation. The forward-scattering target strength versus frequency and the spatial angles for spherical objects, prolate spheroids and the Benchmark Target Strength Simulation Submarine (BeTSSi-Sub) model are obtained by the Kirchhoff approximation and compared with results from theory, the deformed cylinder method (DCM) and the boundary element method (BEM). The Kirchhoff approximation shows considerable agreement with the theoretical and numerical approaches in a region of [Formula: see text] from the rigorous forward-scattering direction. The forward-scattered field contour and the corresponding directivity for the BeTSSi-Sub model are also calculated as a demonstration. Mode coupling caused by the simulated target is clearly revealed. The results indicate that the Kirchhoff approximation can predict the forward-scattering target strength of complex underwater objects.

Statistical image analysis for information system

The surface Kirchhoff integral is numerically calculated by the fourth-order Newton – Cotes method with high accuracy. The intensity is normalized. Implemented quantization of the signal with a unit step for different distances of observation is carried out. The cross section of the central topological object intensity and its characteristics are shown. Variation curves and cumulates are constructed for intensity distributions at different observation distances. The basic statistical parameters of distributions are determined, such as, the mode, the mean, the median and the standard deviation.