Related papers: Isotropic Scattering in a Flatland Half-Space
We present an accurate, stable and efficient solution to the Lippmann-Schwinger equation for electromagnetic scattering in two dimensions. The method is well suited for multiple scattering problems and may be applied to problems with…
We investigate the defocusing inhomogeneous nonlinear Schr\"odinger equation $$ i \partial_tu + \Delta u = |x|^{-b} \left({\rm e}^{\alpha|u|^2} - 1- \alpha |u|^2 \right) u, \quad u(0)=u_0, \quad x \in \mathbb{R}^2, $$ with $0<b<1$ and…
Scattering of a time harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so called zero-offset case of scattering due to a…
We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility…
In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the…
We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.
The model problem of scattering of a sound wave by an infinite plane structure formed by a semi-infinite acoustically hard screen and a semi-infinite sandwich panel perforated from one side and covered by a membrane from the other is…
Partially gated two-dimensional electron systems (2DES) represent the basic building block of prospective optoelectronic devices, including electromagnetic detectors and sources. At the same time, the electrodynamic properties of such…
In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.
In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…
For problems of time-harmonic scattering by polygonal obstacles, embedding formulae provide a useful means of computing the far-field coefficient induced by any incident plane wave, given the far-field coefficient of a relatively small set…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
We consider in this paper space-cutoff charged $P(\varphi)_{2}$ models arising from the quantization of the non-linear charged Klein-Gordon equation: \[ (\p_{t}+\i V(x))^{2}\phi(t, x)+ (-\Delta_{x}+ m^{2})\phi(t,x)+…
The Klein-Gordon equation in the presence of a spatially one-dimensional Hulth\'en potential is solved exactly and the scattering solutions are obtained in terms of hypergeometric functions. The transmission coefficient is derived by the…
Analytical methods are fundamental in studying acoustics problems. One of the important tools is the Wiener-Hopf method, which can be used to solve many canonical problems with sharp transitions in boundary conditions on a plane/plate.…
It is studied the scattering of magnons by the 2d topological Belavin-Polyakov soliton in isotropic ferromagnet. Analytical solutions of the scattering problem are constructed: (i) exactly for any magnon wave vectors for the partial wave…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
L\"uscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…