Related papers: Essential spectrum in vibrations of thin shells in…
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…
We revisit the problem of extraordinary transmission of acoustic (electromagnetic) waves through a slit in a rigid (perfectly conducting) wall. We use matched asymptotic expansions to study the pertinent limit where the slit width is small…
We investigate the transmission of scalar, electromagnetic, and linearized odd-parity gravitational waves in a static spacetime characterized by a spherical distribution of matter in the form of thin concentric equidistant shells of equal…
We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a…
We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order $ h >0$. The essential spectrum of the problem is…
This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform…
We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with flexural resonances at low frequencies able to…
The problem of electromagnetic pulses propagation in plasma was studied in connection with various problems of radio engineering and radar systems. The description of propagation such signals is based on exactly solvable problems for…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
A typical singularity of elastic wave propagation, often termed a shear-wave singularity, takes place when the Christoffel equation has a double root or, equivalently, two out of three slowness or phase-velocity sheets share a common point.…
A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as…
The in-plane acoustic behavior of non-centrosymmetric lattices having nodes endowed with mass and gyroscopic inertia and connected by massless ligaments with asymmetric elastic properties has been analysed through a discrete model and a…
Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke…
We investigate in a quantitative way the plasmon resonance at eigenvalues and the essential spectrum (the accumulation point of eigenvalues) of the Neumann-Poincar\'e operator on smooth domains. We first extend the symmetrization principle…
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…
The thermal fluctuation spectrum of a fluid membrane coupled harmonically to a solid support by an array of tethers is calculated. For strong tethers, this spectrum exhibits non-monotonic, anisotropic behavior with a relative maximum at a…
In the recent years we have shown that cylindrical biological membranes such as nerve axons under physiological conditions are able to support stable electromechanical pulses called solitons. These pulses share many similarities with the…
We investigate an influence of the random external electric field on the 2D extremely short optical pulses propagation in the silicene. The random electric field is perpendicular to the silicene plane. An effective equation has the form of…
An exact analytical solution of the decaying wave function of two identical noninteracting particles, which are entangled by spatial symmetry, is used to analyze the effect of the resonance spectra in the propagation of the decaying…
This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation,…