The scattering of a time-harmonic plane wave in an inhomogeneous medium is modeled by the scattering problem for the Helmholtz equation. A transmission eigenvalue is a wavenumber at which the scattering operator has a non-trivial kernel or cokernel. Because many sampling methods for locating scatterers succeed only at wavenumbers that are not transmission eigenvalues, they have been studied for...

Magnetic structures of epitaxial Cr(001)/Sn multilayers, where monatomic Sn layers are periodically embedded in a Cr(001) film, were studied using neutron diffraction and Mössbauer spectroscopy. It was found that spin-density-wave (SDW) antiferromagnetic structures with the modulation along the perpendicular direction to the film plane are stabilized at low temperatures. The wavelength of the S...

Consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open crack Γ and a bounded domain D in R2 as cross section. We assume that the crack Γ is divided into two parts, and one of the two parts is possibly coated on one side by a material with surface impedance λ. Different boundary conditions are given on Γ and ∂D. Applying potential theory, th...

Multi-centre molecular integrals over spherical Gaussian-type orbitals modified with plane-wave phase factors, which arise in the close-coupling treatment of ion–atom collisions as well as in some molecular structure calculations, are evaluated analytically in closed form by means of the Fourier transform and the addition theorem of harmonic polynomials. The resulting integral formulae for sphe...

We consider the electromagnetic scattering from a convex polyhedral PEC or PMC obstacle due to a time-harmonic incident plane wave. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior. Using the local maximum indicating phenomena, one can determine the exterior unit normal directions, as well as the face areas, of the f...

This work is concerned with a time harmonic scattering problem of electromagnetic waves from a two-dimensional open cavity embedded in the infinite ground plane. Because of the highly oscillatory nature of the solution for large or deep cavity, the model scattering problem is challenging both mathematically and computationally. A variational formulation reduces the scattering problem into a bou...

Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the primitive translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such features as neg...

The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T),...

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a tim...