Related papers: The reduced wave equation in layered materials

Consider the differential operator H = -(1/m(x))L, where L is the N-dimensional Laplacian, in the weighted Hilbert space of square integrable functions on N-dimensional Euclidean space with weight m(x)dx. Here m(x) is a positive step…

We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…

Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…

Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…

Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint. Consider the corresponding wave equations &(1) \quad \ddot{w}+ Lw=0, \quad w(0)=0,\quad \dot{w}(0)=f, \quad \dot{w}=\frac{dw}{dt}, \quad…

Elastic scattering governed by the Lame system associated with the third-type or fourth-type boundary condition is considered. It was shown in [8] by two of the authors that under suitable geometric conditions on the boundary surface of the…

We first establish the presence of a diffractive front in the fundamental solution of the wave operator with a diract delta intial condition in two dimensional euclidean space caused by the potentials perturbation on the spherical…

We consider rotating wave solutions of the nonlinear wave equation \[ \left\{ \begin{aligned} \partial_{t}^2 v - \Delta v + m v & = |v|^{p-2} v \quad && \text{in $\mathbb{R} \times \textbf{B}$} \\ v & = 0 && \text{on $\mathbb{R} \times…

We study propagation of electromagnetic surface waves on a metal-air interface in the case when the wave frequency is below the plasma frequency. We derive a reduced wave equation for a metal cylinder with a given radius of curvature. Using…

Let $-\Delta_{\cal S}$ be the Laplace operator in ${\cal S} \subset \mathbb{R}^3$ on a waveguide shaped surfaces, i.e., ${\cal S}$ is built by translating a closed curve in a constant direction along an unbounded spatial curve. Under the…

We investigate quantitative (or effective) versions of the limiting absorption principle, for the Schr\"odinger operator on asymptotically conic manifolds with short-range potentials, and in particular consider estimates of the form $$ \|…

Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible to reduce an…

Theoretical and interpretative study on the subject of photodetachment of H$^{-}$ near a partial reflecting surface is presented, and the absorption effect of the surface is investigated on the total and differential cross sections using a…

This work presents a new design for broadband absorption of low-frequency acoustic waves using a thin coating made of subwavelength acoustic resonators arranged periodically on a reflective surface. We first study the associated scattering…

We consider the Dirichlet Laplacian in the half-plane with constant magnetic field. Due to the translational invariance this operator admits a fiber decomposition and a family of dis- persion curves, that are real analytic functions. Each…

We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…

A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit…

We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…

It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. Our proof is based on the Schwarz…

We realized and experimentally tested a conceptually new kind of electrically thin absorbers of electromagnetic waves. The idea is to utilize a single layer of precisely designed meta-atoms. This allows one to design an absorber with…