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We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, $\theta$, obeys the dynamics $\Ddot{\theta} + \omega^{2} \sin{\theta} = H\cos{\omega t}$. The linearized approximation gives…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
The quantum optical problem of the propagation of electromagnetic waves in a nonlinear waveguide is related to the solutions of the classical nonstationary harmonic oscillator using the method of linear integrals of motion [ Malkin et.al.,…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
We consider a family of cylindrical spacetimes endowed with angular momentum that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixing adapted to…
The plasmon resonance has found important application in various systems, e.g., nanoantennas, solar panels, refractive index sensors. Unfortunately, a few analytical solutions for such systems are known. The work aims to find a solution for…
We explore the problem of scattering in a medium modulated by a superluminal rectangular pulse, with the pulse modulation realized through transverse excitations. We solve this problem in the moving frame where the modulation appears purely…
Various aspects of axion electrodynamics in the presence of a homogeneous and isotropic dielectric medium are discussed. 1. We consider first the "antenna-like" property of a planar dielectric surface in axion electrodynamics, elaborating…
We consider a quite general problem concerning a linear free oscillation of a discrete mass-spring-damper system. This discrete sub-system is embedded into a one-dimensional continuum medium described by the linear telegraph equation. In a…
Small differential conductance oscillations as a function of source-drain bias were observed and systematically studied in an asymmetric quantum point contact (QPC). These oscillations become significantly suppressed in a small in-plane…
Superscatterers are known to expand the rigid boundary of an object thereby enhancing the scattering cross section of the object. The design philosophy of the acoustic superscatterers is based on partially-resonant systems in which a…
In this paper, we establish the full-wave electromagnetic scattering theory to study the electromagnetic scattering from infinitely long cylinders with radially anisotropic coatings. We show that the total effective scattering width can be…
Scattering of nonstationary electromagnetic fields from axially symmetrical bodies is numerically investigated. Simulations are performed using the time- and frequency-domain approaches. Computational results obtained for a finite perfectly…
The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…
In this Letter, we present a theoretical analysis of the acoustic transmission through two-dimensional arrays of straight rigid cylinders placed parallelly in the air. Both periodic and completely random arrangements of the cylinders are…
We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…
This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time…
The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of…
A broad-band reflectionless channel which supports unidirectional wave propagation originating from the interplay between gyrotropic elements and symmetrically placed gain and loss constituents is proposed. Interchange of the active…
Dense arrays can facilitate the integration of multiple antennas into finite volumes. In addition to the compact size, sub-wavelength spacing enables superdirectivity for endfire operation, a phenomenon that has been mainly studied for…