Related papers: Numerical formulation of three-dimensional scatter…
We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the…
The Faddeev equation for three-body scattering below the three-body breakup threshold is directly solved without employing a partial wave decomposition. In the simplest form it is a three-dimensional integral equation in four variables.…
We extend the Finite-Difference Time-Domain method to treat dispersive magnetic media by incorporating magneto-optical effects through a frequency-dependent permittivity tensor. For benchmarking our method, we consider the light scattering…
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in…
Electromagnetic scattering in moving structures is a fundamental topic in physics and engineering. Yet, no general numerical solution to related problems has been reported to date. We introduce here a generalized FDTD scheme to remedy this…
We analyze electromagnetic waves propagation in one-dimensional periodic media with single or periodic defects. The study is made both from the point of view of the modes and of the diffraction problem. We provide an explicit dispersion…
A formalism is introduced for the non-perturbative, purely numerical, solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we apply this formalism to study the…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
The formal scattering theory is developed for the three-particle differential Faddeev equations. The theory is realised along the same line as in the standard two-body case. The solution of the scattering problem is expressed in terms of…
In this tutorial paper, we formulate a two-dimensional integral-equation based method of moments approach for numerically computing the electromagnetic fields scattered from an azimuthally-rough dielectric cylinder or an axially-rough…
Mathematical models and computer algorithms are developed to calculate dynamic stress concentration and fracture wave propagation in a reinforced composite sheet. The composite consists of a regular system alternating extensible fibers and…
A recently developed formulation for a direct treatment of the equations for two- and three-nucleon bound states as set of coupled equations of scalar functions depending only on vector momenta is extended to three-nucleon scattering.…
Acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered. While the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density…
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation…
We outline specific features of numerical simulations of metamaterial wedges and interfaces. We study the effect of different positioning of a grid in the Yee method, which is necessary to obtain consistent convergence in modeling of…
This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an…
Due to the nonlocal feature of fractional differential operators, the numerical solution to fractional partial differential equations usually requires expensive memory and computation costs. This paper develops a fast scheme for fractional…
A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…
We use lattice QCD calculations of the finite-volume spectra of systems of two and three mesons to determine, for the first time, three-particle scattering amplitudes with physical quark masses. Our results are for combinations of $\pi^+$…
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…