Related papers: On the Regularity of Non-Scattering Anisotropic In…
In this paper we examine necessary conditions for an inhomogeneity to be non-scattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditions are formulated in terms of the regularity of the boundary…
This paper investigates the possible scattering and non-scattering behavior of an anisotropic and inhomogeneous Lipschitz medium at a fixed wave number and with a single incident field. We connect the anisotropic non-scattering problem to a…
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We examine isotropic as well as anisotropic media. Part of the…
We consider the scattering of waves by a penetrable inclusion embedded in some reference medium. We exhibit examples of materials and geometries for which non-scattering frequencies exist, i.e., for which at some frequencies there are…
We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024] and using free boundary techniques from [arXiv:2506.22328].…
This paper continues the study initiated in [30] on nonscattering phenomena for inhomogeneous media. We investigate star-shaped domains in $\mathbb{R}^2$ and establish finiteness results for nonscattering wavenumbers associated with…
This paper investigates the asymptotic behaviors of time-harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high-contrast material parameters. We derive sharp asymptotic estimates and…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…
We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
Eigenvalues arising in scattering theory have been envisioned as a potential source of target signatures in nondestructive testing of materials, whereby perturbations of the eigenvalues computed for a penetrable medium would be used to…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
The geometry of mesoscopic inhomogeneities plays an important role in determining the macroscopic propagation behaviors of elastic waves in a heterogeneous medium. Nonequiaxed inhomogeneities can lead to anisotropic wave velocity and…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary…
Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions…
In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
It is shown that natural boundary conditions for non-relativistic wave functions are of periodic or of homogeneous Robin type. Using asymptotic central symmetry of Hamiltonian and theory of singular differential equations the many-electron…
We present a simple model of the interface between a local homogeneous medium and a potentially nonlocal metamaterial/photonic crystal. This model allows us to calculate the scattering matrix elements of the interface for a plane wave of…