A Modified Hybrid Integral Equation to Electromagnetic Scattering from Composite PEC-Dielectric Objects Containing Closed-Open PEC Junctions

To efficiently analyze the electromagnetic scattering from composite perfect electric conductor (PEC)-dielectric objects with coexisting closed-open PEC junctions, a modified hybrid integral equation (HIE) is established as the surface integral equation (SIE) part of the volume surface integral equation (VSIE), which employs the combined field integral equation (CFIE) and the electric field integral equation (EFIE) on the closed and open PEC surfaces, respectively. Different from the traditional HIE modeled for the objects whose closed and open PEC surfaces are strictly separate, the modified HIE can be applied to the objects containing closed-open junctions. A matrix equation is obtained by using the Galerkin’s method of moments (MoM), which is augmented with the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA), improved by the mixed-potential representation and the triangle/tetrahedron-based grouping scheme. Because in the improved SE-MLFMA, the memory usage for storing the radiation patterns of basis functions is independent of the SIE type in the VSIE, it is highly appropriate for the fast solution of the VSIE that contains the HIE. Various numerical experiments demonstrate that during the calculation of composite objects containing closed-open PEC junctions, the application of the modified HIE in the VSIE can give reliable results with fast convergence speed.

SIMULATION AND PARAMETERS-IDENTIFICATION METHODS OF HETEROGENEOUS ABNORMAL NEUROLOGICAL MOVEMENTS IN MULTICOMPONENT NEURO-BIOSYSTEMS WITH COGNITIVE FEEDBACK

The foundations of mathematical modeling and identification of parameters of heterogeneous abnormal neurological movements (ANM) in multicomponent neuro-biosystems with cognitive feedback have been developed. Based on the methods of integral transformations and spectral analysis developed by the authors for heterogeneous media, a new approach to the construction of hybrid models of wave signal propagation is proposed that describes unwanted tremors of the patient's arm (T-object) as a result of an unconstrained contraction of skeletal muscles due to the cognitive effects of a certain group of neural nodes in the cortex cerebral (CC). A hybrid model of a neuro-biosystem is developed, which describes the state and behavior, namely, the segment-by-segment description of 3D elements of the ANM trajectories of the T-object, taking into account the matrix of cognitive influences of the groups of neuro nodes of the CC. On the basis of hybrid integral Fourier transforms a high-speed analytical vector solution of the model is obtained, which describes the elements of the trajectories on each AND-segment. A new method for calculating of hybrid spectral function, spectral values and matrix of cognitive influences of CC neuronodes is proposed, which determine hybrid integral transformation of solution construction. New non-classical problems of multi-parameter identification of neuro-feedback systems in heterogeneous media based on minimization of the residual functional between observation trajectories and their model analogs are formulated and solved. High-performance algorithms of the amplitude-frequency characteristics identifying of a feedback-system in analytical expressions for the gradients of the residual functional have been constructed, which allow parallel-computations on multicore computers. Computer modeling and identification of ANM trajectories of the studied neuro-feedback-system have been performed.

3-D Integral Formulation for Thin Electromagnetic Shells Coupled with an External Circuit

The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air regions, and at the same time helps to take care of the skin effect. By integrating the system of circuit equations, the method presented in this paper can also model the conductor structures. In addition, the equations describing the interaction between the conductors and the thin shell are also developed. Finally, the formulation is validated via an axisymmetric finite element method and the obtained results are compared with those implemented from another shell formulation.

Autodyne – a Multifunctional Element of Devices for the Formation and Processing of Radio Signals

The information about the history of invention and the development of autodyne topics related to the use of autodyne in devices for the formation and processing of radio signals is presented. This paper contains brief information about the English inventor of the autodyne H. Round, the inventor of the theremin L.S. Termene and others. The stages of formation and development of the field of autodyne application in transceiver devices are considered. The prospects of this direction of radio engineering associated with the practical use of autodyne in hybrid-integral and monolithic transceiver modules made by using modern CMOS technology are demonstrated. These modules, combined with active antennas, are in demand in last mile communication systems for the needs of the Internet and other services.

PARABOLIC BOUNDARY VALUE PROBLEMS IN A PIECEWISE HOMOGENEOUS WEDGE-SHAPED SOLID CYLINDER

The unique exact analytical solutions of parabolic boundary value problems of mathematical physics in piecewise homogeneous wedge-shaped solid cylinder were constructed at first time by the method of integral and hybrid integral transforms in combination with the method of main solutions (matrices of influence and Green matrices). The cases of assigning on the verge of the wedge the boundary conditions of Dirichlet and Neumann and their possible combinations (Dirichlet – Neumann, Neumann – Dirichlet) are considered. Finite integral Fourier transform by an angular variable $\varphi \in (0; \varphi_0)$, a Fourier integral transform on the Cartesian segment $(-l_1;l_2)$ by an applicative variable $z$ and a hybrid integral transform of the Hankel type of the first kind on a segment $(0;R)$ of the polar axis with $n$ points of conjugation by an radial variable $r$ were used to construct solutions of investigated initial-boundary value problems. The consistent application of integral transforms by geometric variables allows us to reduce the three-dimensional initial boundary-value problems of conjugation to the Cauchy problem for a regular linear inhomogeneous 1st order differential equation whose unique solution is written in a closed form. The application of inverse integral transforms restores explicitly the solution of the considered problems through their integral image. The structure of the solution of the problem in the case of setting the Neumann boundary conditions on the wedge edges is analyzed. Exact analytical formulas for the components of the main solutions are written and the theorem on the existence of a single bounded classical solution of the problem is formulated. The obtained solutions are algorithmic in nature and can be used (using numerical methods) in solving applied problems.