Related papers: On resonances generated by conic diffraction
Optical resonances spanning the Near and Short Infra-Red spectral regime were exhibited experimentally by arrays of plasmonic nano-particles with concave cross-section. The concavity of the particle was shown to be the key ingredient for…
Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties…
For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under…
The Minneart resonance is a low frequency resonance in which the wavelength is much larger than the size of the resonators. It is interesting to study the interaction between two adjacent bubbles when they are brought close together.…
The propagation of elastic waves in soft materials plays a crucial role in the spatio-temporal transmission of mechanical signals, e.g. in biological mechanotransduction or in the failure of marginal solids. At high Reynolds numbers $Re \gg…
We investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smooth manifold and a cone over a compact fiber. For the…
Low energy scattering amplitudes for two atoms in one- and two-dimensional atomic wave guides are derived for short range isotropic and resonant interactions in high partial wave channels. Taking into account the finite width of the…
A waveguide coincides with a strip having two narrows of diameter $\epsilon$. Electron motion is described by the Helmholtz equation with Dirichlet boundary condition. The part of waveguide between the narrows plays the role of resonator…
Let $(X,g)$ be a compact manifold with conic singularities. Taking $\Delta_g$ to be the Friedrichs extension of the Laplace-Beltrami operator, we examine the singularities of the trace of the half-wave group $e^{- i t \sqrt{…
We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold. This extends the classical notion of asymptotic directions usually defined on smooth submanifolds. We…
In the weak field approximation the gravitational wave is approximated as a linear wave, which ignores the nonlinear effect. In this paper, we present an exact general solution of the cylindrical gravitational wave. The exact solution of…
We use matched asymptotics to derive analytical formulae for the acoustic impedance of a subwavelength orifice consisting of a cylindrical perforation in a rigid plate. In the inviscid case, an end correction to the length of the orifice…
We address the two-dimensional band-structure of graphene above the vacuum level in the context of discrete states immersed in the three-dimensional continuum. Scattering resonances are discovered that originate from the coupling of the…
We study resonances for the generator of a diffusion with small noise in $R^d$ :$ L_\epsilon = -\epsilon\Delta + \nabla F \cdot \nabla$, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F…
We deal with the scattering of an acoustic medium modeled by an index of refraction $n$ varying in a bounded region $\Omega$ of $\mathbb{R}^3$ and equal to unity outside $\Omega$. This region is perforated with an extremely large number of…
The waves (including acoustic, electromagnetic and elastic ones) propagating in the presence of a cluster of inhomogeneities undergo multiple interactions between them. When these inhomogeneities have sub-wavelength sizes, the dominating…
We have carried out axisymmetric numerical simulations of a spatially developing hypersonic boundary layer over a sharp 7$^{\circ{}}$-half-angle cone at $M_\infty=7.5$ inspired by the experimental investigations by Wagner (2015).…
A phenomenon analogous to the conical refraction well-known in the crystalooptics and crystaloacoustics is considered for the magnetohydrodynamical waves in a collisionless plasma with anisotropic thermal pressure. Imposing the most general…
We investigate the elastic normal modes of two-dimensional media with broken time-reversal and parity symmetries due to a Lorentz term. Our starting point is an elasticity theory that captures the low-energy physics of a diverse range of…
Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential of simplest shape giving rise to resonances (metastable states) in one dimension: $x \in(-\infty, \infty)$. In such a potential, there are…