We investigate the diffraction of TM mode at an open-ended deeply corrugated cylindrical waveguide. We analyze the case when wavelengths and the waveguide radius are much greater than the corrugation period. In this case, equivalent boundary conditions (EBC) can be used. The approach applied uses the solution of the corresponding Wiener–Hopf–Fock equation. Typical radiation patterns are presented and analyzed.
Far-field asymptotics for the quasi-spherical body waves generated in an arbitrarily anisotropic elastic half-space by a surface source is derived from the Green’s matrix based integral representation for the solution to the corresponding elastodynamic problem. The asymptotics is validated by numerical integration and illustrated with several numerical examples.
In this work, we study dipolar oscillations in infinite and finite one-dimensional arrays of scatterers supporting dipole resonances. We show that the presence of two dipolar responses of different types in a single scatterer can induce a change of the dispersion of an infinite chain from monotonic to non-monotonic one. In turn, the non-monotonic dispersion leads to the interaction between two collective modes in the corresponding finite chain. This results in a strong suppression of the radiative losses of one of the modes for a certain distance between the scatterers. Moreover, by tuning the ratio of the resonant frequencies in a single scatterer the optimal period can be shifted to the values that can be realized in feasible optical designs.
Given a semiclassical distribution f h microlocalized on a Lagrangian manifold Λ 0 , H ∈ C ∞ (T ∗ ℝ n ), and H = E a regular energy surface, we find asymptotic solutions of the PDE (H(x,$\hat p$)−E)u h (x,E) = f h (x) in terms of the Maslov canonical operator, when the Hamilton vector field v H fails to be transverse to Λ 0 at some points.
We deal with the ultrahyperbolic equation in ℝ d × ℝ n . Our goal is to construct its fundamental solutions that satisfy a certain support condition. In the particular case n = 1, they coincide with either the advanced or the retarded fundamental solution of the wave equation. Such fundamental solutions provide Volterra type transformations which can be utilized in the study of perturbed ultrahyperbolic equations.
A possibility of achieving high efficiencies of high number diffraction orders is considered for blaze gratings working in the X-ray range. The diffraction efficiency depends on the flatness of the reflecting facet of grooves, characterized by the average blaze angle and camber. A phenomenological formula was obtained for the relationship between these groove parameters and the modulus of the maximum order number, at which the grating efficiency is still maximum. Using the PCGrate™ code, this formula is confirmed by the results of numerical simulation of the diffraction efficiency of unique X-ray echelles. The obtained theoretical estimate makes it possible to classify a manufactured grating according to its maximum achievable diffraction efficiency, i.e., before efficiency measurements or calculus.
Solving the light scattering problem for axisymmetric particles with a mid-plane symmetry, e.g., spheroids, by the exact methods (SVM, EBCM, etc.), leads to linear systems with half matrix elements equal to zero. We suggest an approach that allows one to reduce such a system to two smaller ones, which significantly speeds up the calculations. We apply the approach to the recently derived solution to the problem for layered spheroids with non-confocal internal boundaries.
Wave processes in layered specimens (phantoms) mimicking the waveguide properties of tubular bones are studied to identify signs of developing osteoporosis in the results of ultrasound bone examination. In continuation of the research discussed at last year’s DD meetings, the present work is focused on extracting guided wave (GW) characteristics from received surface signals and studying the sensitivity of GW resonance frequencies to the elastic properties of the internal diseased bone sublay-ers. The monotonic dependence of resonance frequencies on the elastic property degradation in both coated and uncoated phantoms, revealed by these studies, is considered as a promising diagnostic indicator.
We show a new example of the mechanical system where the phenomenon of the anti-localization of non-stationary (quasi)-waves can be observed. This is a 1D semi-infinite harmonic chain subjected to an impulse loading at the free end. The anti-localization of non-stationary waves is zeroing of the non-localized propagating component of the wave-field in a neighbourhood of an inclusion or defect. The known examples of systems, where this wave phenomenon occurs, are a 1D infinite harmonic chain with an isotopic defect (Shishkina, Gavrilov, 2023, Continuum Mech. Thermodyn. 35, 431–456), and an infinite string on the Winkler foundation with a discrete oscillator (Shishkina, et al., 2023, J. Sound Vib. 553, 117673).
Waveguides with dielectric filling and a vacuum channel for the passage of bunches are of interest for the development of new methods of wakefield acceleration in accelerating structures. Excitation of waveguides by relativistic electron bunches makes it possible to achieve accelerating field with a longitudinal component of strength E of the order of 100 MV/m and higher when using subterahertz and terahertz structures. The problem of ensuring beam stability in such waveguides is solved analytically and numerically based on an analysis of the self-consistent beam dynamics. The efficiency of energy transfer from the accelerating beam to the accelerated one is optimized on the bases of charge and energy profiling in one or multi-beam accelerating schemes. The possibility of transforming the parasitic effect of generating deflecting fields in dielectric accelerating wakefield structures into a useful effect for creating a wakefield undulator based on waveguides with periodic asymmetric dielectric filling is considered.
The application of elastic surface waves for analysis of water contents of layered poroelastic soil is considered in this investigation. Mathematical and computer models based on the integral Fourier transform, Green’s matrix technique and mode analysis are employed and briefly described here. The dried top layer of soil and its thickness change the characteristics of surface elastic waves. The results of numerical analysis of this influence are presented.
In this paper a method for expressing the field amplitude in the 3D space in the parabolic approximation, based on the amplitude's values on the outer surface of a rectangular computational domain (prism), is proposed. The connection of the method to the 3D exact transparent boundary condition in a rectangular computational domain is considered and it is demonstrated that the amplitude outside the domain can be found by a series of 1D integrations over boundary values of the same auxiliary function, which is used in the transparent boundary condition. The numerical experiments with free space Gaussian b eams demonstrate the validity of the proposed method and its relative errors.
An inverse problem for quasi-linear equations of complex heat transfer is considered, which consists in finding the intensities of internal sources from the integral overdetermination. The existence of a unique solution of the problem is proved and an optimization algorithm for its solution is proposed.
An inverse extremum problem for quasilinear equations of complex heat transfer simulating the process of endovenous laser ablation is studied. It is required to provide a desired temperature distribution in a specific subdomain, while the temperature in another subdomain cannot exceed a critical value. The solvability of the inverse extremum problem is proved. An algorithm for finding its solution by minimizing the objective functional with a penalty is proposed and implemented.
The resonance interaction of low frequency waves guided by cylindrical duct with decreased plasma density in a uniform magnetized plasma is considered. The parametric instability of the guided waves propagating in the opposite directions is analyzed in the case of resonant magnetoplasma. The instability growth rates and threshold are determined. The numerical results illustrating the wave interaction under conditions of the upper ionosphere are presented.
The paper considers two main applications of the transducers in the form of a piezoelectric disk with two metal plate end-caps, which are usually called cymbal transducers. The first variant of the cymbal transducer is an energy harvesting device. Here, the cymbal transducer is located inside the asphalt pavement and generates electric fields under low-frequency oscillatory mechanical action on the pavement. The second version of the transducer is located in a liquid medium and, under the electrical influence oscillating at the first resonant frequency, generates acoustic waves. For both cases, we investigate the efficiency of transducers for four types of piezoceramic materials: solid piezoceramics, conventional porous piezoceramics, and porous piezoceramics with thin and thick layers of metallization of the pore surfaces. The studies were carried out numerically using the finite element method in the ANSYS package. The calculation results showed that the use of porous piezoceramics or porous piezoceramics without or with metallized pore surfaces can increase the efficiency of electromechanical transformations compared to dense ones. Moreover, the fact whether the transducer is excited by the electric potential difference or by the electric current plays a significant role for actuator applications.
The propagation of elastic plane waves in a 2D model of a weakly cohesive powder is numerically simulated by the discrete element method (DEM). Isotropic samples of disks interacting by elasticity, friction and cohesion in their contacts are first assembled in equilibrium states under isotropic pressure. Contact laws are linearized in elastic form, with fixed normal (K N ) and tangential (K T ) stiffness constants, to model the response to a sine-shaped impulse (main frequency ω) imparted to the sample boundary. The shape of this disturbance depends on the value of ω, relative to basic frequency ${{\mathbf{\omega }}^{\ast}} \equiv \sqrt {{{\mathbf{K}}_N}/m} $ (m denoting the grain mass). Longitudinal and transverse waves triggered at low ω/ω ∗ propagate with a coherent wavefront followed by an incoherent tail, with the classical velocity deduced from static moduli. Higher values of ω/ω ∗ result in much smaller coherent signals and a strong localization of the energy near the source. Longitudinal waves are accompanied by disordered rotations, travelling with another velocity, induced at all times during propagation. Transverse waves contain both rotational and translational components. It is speculated that reduced Cosserat theories could be relevant for such materials on the continuum scale.
The paper deals with the fractional modification of the Landau–Khalatnikov model to describe diffusion-wave polarization processes in ferroelectrics. The problem is formalized as an initial-boundary value problem for a semilinear time-fractional partial differential equation. To solve the problem numerically, an implicit computational scheme was derived using the Grünwald–Letnikov derivative. The constructed numerical scheme was implemented in Matlab. The designed computer program was used to conduct simulations of the spatial-temporal polarization distributions and hysteresis loops for ferroelectrics with the second-order phase transitions. This approach allows one to provide more adequate modelling of polarization processes in complex physical systems due to the variation of regimes by means of changes in the dynamical dimension.
Additive technologies show promising results in 6G antennas operating in W-band. However, quality of additive manufacturing strongly depends on many crucial factors related to the manufacturing process. In this work we perform electromagnetic simulations to study an impact of surface roughness to the performance of some conventional antennas suitable for 6G applications. Finally, we could define the surface roughness requirements for the additive antennas.
We study the guided propagation of whistler waves along an enhanced density duct in a nonresonant magnetoplasma. Conditions are revealed under which an approximate approach based on perturbation theory can be applied for determining characteristics of the guided modes in the case of a smooth monotonic variation of plasma density across the duct. A good agreement is shown to exist between the results of the developed approximate approach and a rigorous full-wave analysis.
