相关论文: Dynamical diffraction in sinusoidal potentials: un…
The dynamical scattering theory is developed for the Laue diffraction of the M\"{o}ssbauer rays and x-rays, whose angular distribution is comparable with the diffraction angular range. Both the Rayleigh and the resonant nuclear scattering…
We consider the two-dimensional advection-diffusion equation on a bounded domain subject to either Dirichlet or von Neumann boundary conditions and study both time-independent and time-periodic cases involving Liouville integrable…
The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics. We focus on the case when…
This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…
Two-dimensional scattering by homogeneous and layered dielectric elliptical cylinders is analyzed following an analytical approach using Mathieu functions. Closed-form relations for the expansion coefficients of the resulting electric field…
For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…
We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in…
We present several applications of mode matching methods in spectral and scattering problems. First, we consider the eigenvalue problem for the Dirichlet Laplacian in a finite cylindrical domain that is split into two subdomains by a…
We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
In this paper, we propose a new spectral decomposition method to simulate waves propagating in complicated waveguides. For the numerical solutions of waveguide scattering problems, an important task is to approximate the…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…
Consider the scattering of a time-harmonic elastic plane wave by a bi-periodic rigid surface. The displacement of elastic wave motion is modeled by the three-dimensional Navier equation in an open domain above the surface. Based on the…