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In this work we compare the electromagnetic fields calculated in two approaches: using a linear current model and using the superposition of the individual electron fields.
This report sets out a method of calculation of ray formulae for a phase jump caused by the geometrical spreading turning to zero on the caustics. It is based on the Morse index computation, i.e. the number of focal points on the ray between the source and observation points.
In the framework of DOM (Discrete Orientation Model) the movement of a magnetic moment looks like a Markov chain with a finite number of states coinciding with points (edges) of lattice. It is possible to get asymmetrical spectrum within a discrete approximation corresponding to non-potential drift field by introducing a non-symmetric stochastic matrix as a generator of dynamics. This leads to precession...
We are concerned with the scalar interference head wave introduced first by V. S. Buldyrev in 1960-s in the course of considering exact solutions for diffraction by transparent obstacles. Our goal is to describe this wave by a heuristic approach based upon the locality principle.
Deformed Heun class equations or more precise Heun class equations with added apparent singularity are considered. It is proved that any deformed Heun class equation realizes under antiquantization the transfer from a Heun class equation to the corresponding Painlevé equation.
Metamaterials are artificial periodic structured materials with unique electromagnetic properties that are not observed in nature. Wire metamaterials represent periodic arrays of parallel conducting wires which allow one to manipulate, enhance and redistribute electromagnetic fields. In this work we present the annular wire metamaterial resonator in order to improve characteristics of Magnetic Resonance...
We solve the magnetostatics equations for convex domains, bounded by a thin heterogeneous isotropic ferromagnetic layer. The problem reduces to determining the internal and external solutions of a system of Laplace equations with mixed boundary conditions on a surface. Potential theory allows us to reduce the problem to a system of Fredholm equations of the second kind. Analytical solution for an...
In this paper, we propose an analytic method capable of describing time truncated Airy-type pulses in material media with quadratic dispersion. The method is based on the superposition of exponentially apodized Airy pulses and provides a simple, elegant and fast way to obtain the pulse evolution and its characteristic resistance to the dispersion effects for long distances.
A new method is suggested for the simplification of analytical calculation of the axisymmetric elastic wave propagation in systems of several infinite coaxial cylindrical shells with various filling of gaps. The reflection coefficients similar to those known in the theory of transmission lines are introduced. Four coefficients are required at each cylindrical boundary.
In this paper we study the resonant transmission through a waveguide formed by a periodically placed high-index dielectric nanoparticles with a side-coupled resonator. We show that a resonator with high enough Q-factor allows control of the signal transmission through a waveguide. We suggest a practical realization of such scheme that employs a multipole resonance of a dielectric particle with large...
We consider two families of monic polynomials P = {Pn(x)}∞n=0 and Q = {Qn(x)}∞n=0 orthogonal with respect to probability measures μ and v on the real line, respectively. Let {Qn(x)}∞n=0 and {Pn(x)}∞n=0 be connected by the relations Qn(x) = Pn(x) + a1Pn−1(x). We consider a generalized oscillator algebras Ap and Aq associated with the sequences P and Q. In the article we describe all the pairs (P, Q)...
The mathematical model and exact analytical solution of the forced axisymmetric vibrations of semiin-finite cylindrical shell partially submerged into the liquid is constructed. The protruding part of the shell is infinite. The source of the vibrations in the system shell-liquid is incident wave propagating from the infinite side of the shell. The joint oscillations of the shell and ideal compressible...
In this study, we simulate propagation of a Gaussian wavepacket through a two-dimensional quantum waveguide. The model is based on Schrödinger equation, which is solved by original matrix formulation of an alternating direction implicit (ADI) method. The approach is suitable for parallelization and execution on modern graphics accelerators.
The problem of controllability for 2D-tunnel bifurcations in systems with quantum molecules in a dielectric matrix of a metamaterial in the external electric field at finite temperature has been investigated. Usage of the theory of quantum tunneling with dissipation to study the interaction of quantum molecules (QM) with contact medium is productive, because, in spite of usage of the instanton approach,...
The study and design of electronic components, based on ballistic electron transport in nanowires, recently show steep increase of interest. The components can be field effect transistors, resonant tunneling, diodes, lasers, cubits, etc. Previously we carried out numerical simulations of electron transport for energies far from the thresholds (in the case of multichannel scattering). Here we present...
New dielectric metamaterial based on the Bragg filter comprising ten dielectric bilayers was investigated. Each bilayer is the thin films of silicone dioxide (SiO2) and another film of zirconium dioxide (ZrO2). The surface of the multilayer film is profiled. It has a form of periodic system of rectangles separated by the open gaps. We use the computer simulation as well as analytical solution to find...
In this article, a simple computational scheme to numerical solution of quasi-linear hyperbolic equation is considered. The idea of the following technique is to approximate the spatial derivative by using of some interpolant, for example, the well-known cubic B-spline or cha, n interpolant. The time derivative is approximated by the first-order forward derivative for simplicity.
We review recent progress of the mid-range applications of wireless power transfer (WPT) technology and introduce its main standards. In the last decade, extensive research has been carried out on magnetic coupling wireless power transfer with the transmission distance comparable or greater than the coil dimension. Metamaterials show great abilities to increase the WPT efficiency by controlling the...
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