Related papers: Bound States in the Continuum in Elasticity
Systems with space-periodic Hamiltonians have unique scattering properties. The discrete translational symmetry associated with periodicity of the Hamiltonian creates scattering channels that govern the scattering process. We consider a…
The phenomenon of selective diffraction is extended to in-plane elastic waves and we design surface corrugated periodic laminates that incorporate crystal momentum transfer which, due to the rich physics embedded within the vector elastic…
The spectrum of electromagnetic waves in periodic linear structures, such as periodic waveguides or chains of microelements i.e. spheres, cavities, exhibit the sequence of stop bands for propagating waves. Breaking the translational…
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest…
We consider E polarized bound states in the radiation continuum (BICs) in circular periodical arrays of $N$ infinitely long dielectric rods. We find that each true BIC which occurs in an infinite linear array has its counterpart in the…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
The theory of acoustic wave scattering by many small bodies is developed for bodies with impedance boundary condition. It is shown that if one embeds many small particles in a bounded domain, filled with a known material, then one can…
This is a review of Glauber's asymptotic diffraction theory, in which diffractive scattering is described in terms of interference between semiclassical amplitudes, resulting from a stationary-phase approximation. Typically two such…
We consider the nonlinear scattering and transmission of an atom laser, or Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The nonlinearity inherent in this problem leads to several new physical features beyond the…
Photonic bound states in the continuum (BICs) are special localized and non-decaying states of a photonic system with a frequency embedded into the spectrum of scattered states. The simplest photonic structure displaying a single BIC is…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry…
The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel…
Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are…
Theory of scattering by many small bodies is developed under various assumptions concerning the ratio $\frac{a}{d}$, where $a$ is the characteristic dimension of a small body and $d$ is the distance between neighboring bodies $d =…
Thirty years ago, theorists showed that a properly designed combination of incident waves could be fully transmitted through (or reflected by) a disordered medium, based on the existence of propagation channels which are essentially either…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…
We consider light scattering by two dimensional arrays of high-index dielectric spheres arranged into the triangular lattice. It is demonstrated that in the case a triple degeneracy of resonant leaky modes in the Gamma-point the scattering…
Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the…