相关论文: Modified Rayleigh Conjecture and applications

Modified Rayleigh conjecture (MRC) in scattering theory was proposed and justified by the author (J.Phys A, 35 (2002), L357-L361). MRC allows one to develop efficient numerical algorithms for solving boundary-value problems. It gives an…

This paper contains a self-contained brief presentation of the scattering theory for periodic structures. Its main result is a theorem (the Modified Rayleigh Conjecture, or MRC), which gives a rigorous foundation for a numerical method for…

The Rayleigh conjecture on the representation of the scattered field in the exterior of an obstacle $D$ is widely used in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture…

A numerical algorithm is presented for solving the direct scattering problems by the Modified Rayleigh Conjecture Method (MRC) introduced by A.G.Ramm. Some numerical examples are given. They show that the method is numerically efficient.

The Rayleigh conjecture about convergence up to the boundary of the series representing the scattered field in the exterior of an obstacle $D$ is widely used by engineers in applications. However this conjecture is false for some obstacles.…

Some novel numerical approaches to solving direct and inverse obstacle scattering problems (IOSP) are presented. Scattering by finite obstacles and by periodic structures is considered. The emphasis for solving direct scattering problem is…

The small perturbations method has been extensively used for waves scattering by rough surfaces. The standard method developped by Rice is difficult to apply when we consider second and third order of scattered fields as a function of the…

In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

Multiple scattering of polarised electromagnetic waves in diffusive media is investigated by means of radiative transfer theory. The method becomes exact in several situations of interest, such as a thick-slab experiment (slab thickness L…

The problem of an electromagnetic wave scattering by a slab with two rough boundaries is solved by a small-perturbation method under the Rayleigh hypothesis. In order to obtain a perturbative development, we use a systematic procedure which…

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…

We consider the inverse cracks scattering problems from the far field patterns with a fixed incident direction. We firstly show that the sound-soft cracks can be uniquely determined by the multi-frequency far field patterns with a fixed…

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

We study the inverse problem of locating point sources from far-field data under plane wave incidence. A direct computational method is developed based on multiple scattering theory, using a novel indicator function to avoid iterative…

Scattering properties of a material are changed when the material is injected with small acoustically soft particles. It is shown that its new scattering behavior can be understood as a solution of a potential scattering problem with the…

Radiative transfer (RT) simulations are a powerful tool that enables the calculation of synthetic images of a wide range of astrophysical objects. These simulations are often based on the Monte Carlo (MC) method, as it provides the needed…

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…