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An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the M\"uller equations and an impedance boundary condition for a…
In this paper the validity of the diffusion approximation for multiple scattering of classical waves in random medium in different regimes is investigated, with emphasize to weak localization effects. Many principle topics are discussed…
We study the propagation of surface waves across structured surfaces with random, localized inhomogeneities. A discrete analogue of Gurtin-Murdoch model is employed and surface elasticity, in contrast to bulk elasticity, is captured by…
By a computer simulation approach we study the scattering of $p$- or $s$-polarized light from a two-dimensional, randomly rough, perfectly conducting surface. The pair of coupled inhomogeneous integral equations for two independent…
This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
The analysis of scattering from complex objects using surface integral equations is a challenging problem. Its resolution has wide ranging applications- from crack propagation to diagnostic medicine. The two ingredients of any integral…
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…
This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -- \zs\cite{zhao03} \& \pz\cite{zhao15}. An actual rough surface is (incompletely) described…
This document takes existing derivations of scattering loss from rough surfaces, and makes them more accessible as a tool to derive the total scattering loss from a rough mirror given its true surface profile. It does not contain any new…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
Remote sensing measurements have been an important data source of ocean surface roughness. Scatterometers operating at moderate and high incidence angles provide information on the Bragg resonance spectral components of the ocean surface…
Electromagnetic wave scattering from a perfectly reflecting self-affine surface is considered. Within the framework of the Kirchhoff approximation, we show that the scattering cross section can be exactly written as a function of the…
The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearised shallow-water model of the mixed layer. Modelling the flow as a homogeneous and stationary random process with spatial scales…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
A general approach for the calculation of the incoherent intensity scattered by a random medium with rough boundaries has been developed using a Green function formalism. The random medium consists of spherical particles whose physical…
A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the…
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 limiting case is considered, when the size…