The application of a modified method of discrete sources for solving the problem of wave scattering by group of bodies

A new universal and effective algorithm for solving the problems of wave diffraction on complicated structures composed of bodies of revolution is presented. The method is applied to diffraction on a group made of two impedance bodies of revolution. The method permits to get the pattern and the field with high accuracy.     

A new method for solving the problem of diffraction by a compact obstacle in a layered medium

We propose a new method for solving the two-dimensional problem of diffraction by a cylindrical body in a layered medium. Unlike the traditional methods, the boundary-value problem is reduced to solving the integral equation for the scattering pattern of the body. As an illustration of this method, we consider the problem of scattering by a round cylinder located in a dielectric layer between two homogeneous half-spaces. Technical University of Communication and Information Science, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 874–888, July, 1998.     

A modified version of the Methfessel‒Paxton method

A modified version of the method for calculating integrals over the Brillouin zone, which relies on the use of the orthogonal function series, is discussed. It is shown that adoption of the system of Chebyshev’s polynomials makes it possible, while retaining all the advantages of the original scheme, to overcome a number of its disadvantages and to improve the numerical stability in the case of high-degree polynomial approximation, to reduce the number of parameters in the method, and to rule out the development of regions with negative values of the density of states.     

High-frequency diffraction by a narrow hyperboloid of revolution

High-frequency diffraction of a plane acoustic wave incident at a small angle to the axis of a narrow hyperboloid of revolution is considered. By the parabolic equation method in spheroidal coordinates, the leading term of field asymptotics in the near-surface boundary layer is constructed in the form of an integral involving Whittaker functions. Difficulties associated with its calculation are considered. Results obtained for the field at the surface of a perfectly rigid hyperboloid are presented. They reproduce the predicted high-frequency diffraction effects.     

Investigation of plasmon resonances in local structures by the discrete sources method

The modification of the Discrete Sources Method, which allows one to perform effective numerical analysis of plasmon resonances in local structures, is proposed and realized. The numerical algorithm allows computation of the near field with a high degree of accuracy and tracking resonances that cause an increase of the near-field intensity by several orders of magnitude.     

Analysis of radiative transport in a cylindrical enclosure—An application of the modified discrete ordinate method

Application of the modified discrete ordinate method (MDOM) proposed by Mishra et al. [Mishra SC, Roy HK, Misra N. Discrete ordinate method with a new and simple quadrature scheme. J Quant Spectrosc Radiat Transfer 2006;101:249-262.] has been extended for calculation of volumetric radiative information in a cylindrical enclosure. Radiatively, the medium inside a diffuse gray 1-D concentric cylinder is absorbing, emitting and scattering. Three types of problems, viz., an isothermal medium representing non-radiative equilibrium case, a non-isothermal medium representing radiative equilibrium situation and the case of a combined mode conduction and radiation heat transfer have been used to test the robustness of the MDOM. Temperature/emissive power and heat flux/energy flow rate distributions in the medium have been found for the effects of various parameters like the extinction coefficient, the scattering albedo, the boundary emissivity and the conduction-radiation parameter. To check the accuracy of the results of the MDOM, results have been compared with those available in the literature and also by obtaining the radiative information using the finite volume method. MDOM has been found to provide accurate results.     

A new solution to the problem of an acoustically transparent body

The method of active impedance matching is applied to the well-known problem of an acoustically transparent body. Two laws of active force control, by velocity and by pressure, are obtained for solving the problem.     

Effective-dielectric-constant method for the problem of wave diffraction by a close-spaced dielectric grating

A simple method for determination of effective dielectric constants is proposed that allows a close-spaced two-dimensionally periodic dielectric layer with rectangular elements to be replaced by a homogeneous and anisotropic layer of the same thickness. The method makes it unnecessary to solve the complicated problem of determination of the fields within the elements for calculation of the plane-wave reflection and transmission coefficients in a long-wave approximation, which considerably simplifies the calculations. Comparison with known solutions obtained by rigorous methods for one-dimensionally periodic gratings shows exact agreement of the results. The method is easily extended to magnetodielectric media as well as to multicomponent media, including those whose dielectric constants are functions of the coordinate perpendicular to the layer.Academician A. L. Mints Radio-Engineering Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-4, pp. 286–294, March–April, 1993.     

Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water

Empirical potential structure refinement (EPSR) is a method for developing a structural model of a liquid for which diffraction measurements are available. The EPSR technique involves refining a starting interatomic potential energy function in a way that produces the best possible agreement between the simulated and measured site-site partial structure factors. Here a series of test simulations are performed to establish how well the EPSR method can recover the interatomic potential for a single component fluid of Lennard-Jones particles, and for a binary fluid consisting of charged atoms interacting at short range by a Lennard-Jones potential. Special attention is given to the problem of developing an accurate interatomic potential for water using these procedures. An alternative method for perturbing the starting potential is used to obtain the best possible fit to the diffraction data. The resulting parametrization of the water potential is in contrast to many existing effective potentials for water, and indicates that water molecules in the liquid at ambient conditions are highly polarized, as has been suggested in recent ‘first-principles’ simulations of water. Three-body correlation functions and spatial density functions derived from the EPSR simulations show excellent agreement with those obtained with the model potential simulations. However, the potentials extracted by EPSR are found to depend on the constraints applied to the hardness of the core potential and the energy and pressure of the simulation, even when the fits to the data are equally good. It is concluded that performing EPSR on diffraction data can be used as a good test for interatomic potentials and to derive reliable many-body structures in the liquid state, but cannot on its own be used to derive a reliable set of site-site pair potentials for a particular system.     

Shortwave asymptotic behavior of the solution of the problem of diffraction by a convex body. III

Based on an integral representation found previously for the shortwave asymptotic behavior of the solution of the problem of diffraction by a smooth convex cylinder, the author derives asymptotic estimates for the diffraction field in the illuminated region and in a shadow region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 98–111, January, 1972.     

Diffraction by a strongly elongated body of revolution

A high-frequency acoustic field in a penumbra domain on the surface of a strongly elongated body is investigated. A new asymptotic formula expressing the field in the form of inverse Mellin transform of an expression containing Whittaker functions is derived. Presented numerical results show that the increase of the transverse curvature of the body increases field attenuation on a hard surface and decreases it on an acoustically soft surface. This effect agrees to previous results.     

A finite-element method for solving a scalar problem of diffraction by two-dimensional scatterers of complex structure

A scalar problem of diffraction by two-dimensional domains of complex form is solved by the finite-element method. The good agreement of the numerical results with the exact solution to the problem of plane wave diffraction by an infinite cylinder is demonstrated. In conclusion, examples of the capabilities of the program are demonstrated.     

Analysis of scattering properties of optical antennas by discrete sources method

Based on the discrete sources method, a mathematical model of the optical antenna is developed. Scattering properties of antennas as clusters of nanodimensional particles in a film on a substrate were analyzed. The results of computer simulation of the scattered intensity are presented.     

一种新的求解脑磁逆问题的搜索方法

给出一种新的求解真实头模型下脑磁逆问题的搜索方法.通过不同位置的源的相互关系，由上一个搜索源的计算结果通过简单计算，直接得到下一个搜索源的结果，避免了繁琐耗时的边界元积分方法，简化了求解过程，提高了求解速度. 关键词： 脑磁图 逆问题 搜索方法