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The problem of electromagnetic (EM) wave scattering in the presence of one single body is considered in the assumption of its smallness. The integral equation method is applied for its solving. The respective integral equation is used for determination of an auxiliary function to find the explicit form of solution to the initial problem. The corresponding to this equation linear algebraic system (LAS)...
The numerical approach to determine the shape of scattering body by the known scattering amplitude has been developed. The inverse scattering problem is formulated for 3-D case. The system of equations regarding the function describing form of body and normal derivative of field on the body is derived. The system is ill-posed because of equation for finding the form of body shape. The specification...
The problem of electromagnetic (EM) wave scattering on the small particle is reduced to solving the Fredholm integral equation of the second kind. Integral representation of solution to the scattering problem implies in determination of some unknown function which contains in integrand of this equation. The respective linear algebraic system (LAS) for the components of this unknown vector function...
Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective EM field in the limiting medium, in the limit a→0, where a is the characteristic size of a particle and the number M(a) of the particles...
A variational formulation of the synthesis problem for plane antenna systems according to the prescribed power radiation pattern (RP) is considered. The functional representing the mean-square deviation of the prescribed and synthesized power RPs and containing the additional term with squared norm of the current or field in the antenna aperture is considered as criterion of optimization. Freedom...
A short overview of the results obtained by the authors and their colleagues for a long time in the field of the antenna synthesis theory and the related problems of the field transformation is presented. The main common subject in all problems are the free phase functions ascribed to the given amplitude patterns of the antennas, or appearing as the phase corrections in the quasi-optical field transformers...
The antenna synthesis problem according to the prescribed power radiation pattern (RP) is generalized by taking into account an additional restriction on the norm of the synthesized RP. The variational approach supplemented by the Lagrange method of multipliers is applied for the formulation of problem. The modified Newton method is used for numerical solving the respective Euler equation. Numerical...
The theory of scattering of the acoustic waves on the small bodies is applied to solution of problem related to the non-destructive testing of materials with defects. The change of the refraction coefficient of the acoustic wave passing through the steel pattern testifies to presence of microdefects in material. The numerical results are presented for several kinds of steel and they confirm the possibility...
The variational approach for investigation of solution to nonlinear synthesis problem of plane rectangular equidistant array is used. The functional representing the mean-square deviation of the given and received power radiation patterns including the term with norm of currents is minimized. The nonlinear equation is obtained and the bifurcation of its solutions is studied numerically.
Scattering of electromagnetic (EM) waves by many small impedance particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedance. The limiting equation is obtained for the effective EM field in the limiting medium, at a → 0, where a is the characteristic size of a particle and the number M(a) of the particles tends to...
The synthesis problem of waveguide array according to the prescribed amplitude radiation pattern is considered. The mutual coupling of the separate elements of array is taken into account in the process of solution of a direct problem (analysis problem). Variational statement of the synthesis problem and application of the aperture orthogonal polynomials (AOP) method, are considered as alternative...
The synthesis problem of the waveguide array according to the prescribed amplitude radiation pattern is considered. The mutual coupling of the separate elements of array is taken into account in the process of solution of a direct problem (analysis problem). Variational statement of the synthesis problem and application of the aperture orthogonal polynomials (AOP) method, are considered as alternative...
A version of generalized eigenoscillation method is applied to the problem about resonant effects in metallic nanoparticles. An approach is proposed, that permits to avoid calculating all higher eigenoscillations except the resonant one. An algorithm for determination of the resonant eigenoscillation, based on the Galerkin procedure, is described in details for the case of bodies of revolution. Model...
The problem of electromagnetic wave scattering by many small bodies is reduced to solving a Fredholm second-kind integral equation. This equation is solved asymptotically as the characteristic size a of the small bodies tends to zero. The numerical solution of this Fredholm equation is compared with asymptotic solution. Numerical results are presented in the case of single body. The difference between...
The synthesis problem of the waveguide array according to the prescribed amplitude radiation pattern is considered. The mutual coupling of the separate elements of array is taken into account in the process of solution of a direct problem (analysis problem). Variational statement of the synthesis problem and application of the R-function method, are considered as alternative approaches to solve the...
The problem of electromagnetic wave scattering by many small bodies is reduced to solving a Fredholm second-kind integral equation. This equation is solved asymptotically as the characteristic size a of the small bodies tends to zero. The numerical calculations concern the investigation of applicability of the asymptotic formulas depending on the parameters of problem. Numerical results are presented...
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption ka<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary conditions are assumed on the boundaries of small particles. The results of numerical simulation show good agreement with the theory. They open a way to...
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