# Scattering of a spherical wave by a small ellipsoid

@article{Charalambopoulos1999ScatteringOA, title={Scattering of a spherical wave by a small ellipsoid}, author={Antonios Charalambopoulos and George Dassios}, journal={Ima Journal of Applied Mathematics}, year={1999}, volume={62}, pages={117-136} }

A point generated incident "eld impinges upon a small triaxial ellipsoid which is arbitrarily oriented with respect to the point source. The point source "eld is so modi"ed as to be able to recover the corresponding results for plane wave incidence when the source recedes to in"nity. The main dif"culty in solving analytically this low-frequency scattering problem concerns the "tting of the spherical geometry, which characterizes the incident "eld, with the ellipsoidal geometry which is…

## Figures from this paper

## 19 Citations

On spherical-wave scattering by a spherical scatterer and related near-field inverse problems

- Mathematics, Physics
- 2001

A spherical acoustic wave is scattered by a bounded obstacle. A generalization of the 'optical theorem' (which relates the scattering cross-section to the far-field pattern in the forward direction…

On the Low-Frequency Interaction between a Central Dyadic Wave and a Spherical Cavity

- Mathematics
- 2004

The dyadic fundamental solution of the linearized theory of elasticity in a homogeneous and isotropic medium is considered as a point-generated incident dyadic field. This central field is disturbed…

On spherical-wave scattering by a spherical scatterer and related near-field inverse problems

- Mathematics, Physics
- 2010

A spherical acoustic wave is scattered by a bounded obstacle. A generalization of the ‘optical theorem’ (which relates the scattering cross-section to the far-field pattern in the forward direction…

Scattering of a Spherical Dyadic Field by a Small Rigid Sphere

- Mathematics
- 2002

A complete dyadic field, which is generated at a point and propagates within a homogeneous and isotropic elastic medium, is disturbed by a small rigid sphere. Analytic solutions for this complicated…

On the scattering of spherical electromagnetic waves by a layered sphere

- Mathematics
- 2006

A spherical electromagnetic wave is scattered by a layered sphere. The exact expressions of the scattered and interior fields are obtained by solving the corresponding boundary-value problem, by…

Conductive masses in a half-space Earth in the diffusive regime: fast hybrid modeling of a low-contrast ellipsoid

- GeologyIEEE Trans. Geosci. Remote. Sens.
- 2000

In this paper, the response of a conductive ellipsoid buried at shallow depth in a half-space Earth is investigate by a novel hybrid approach combining the localized nonlinear approximation and the low frequency scattering theory.

Scattering of a point generated field by a multilayered spheroid

- Materials Science
- 2001

SummaryThe point source excitation acoustic scattering problem by a multilayer isotropic and homogeneous spheroidal body is presented. The multilayer spheroidal body is reached by an acoustic wave…

2D elastic scattering of a plane dyadic wave by a small rigid body and cavity

- Mathematics
- 2008

In this paper the scattering problem of the disturbance of a plane dyadic wave by a rigid body or a cavity, in two‐dimensional elastodynamics is considered. The direct scattering problems are…

A Conditioned Probabilistic Method for the Solution of the Inverse Acoustic Scattering Problem

- MathematicsMathematics
- 2022

In the present work, a novel stochastic method has been developed and investigated in order to face the time-reduced inverse scattering problem, governed by the Helmholtz equation, outside connected…

## References

SHOWING 1-10 OF 18 REFERENCES

Point source excitation in direct and inverse scattering

- Mathematics
- 1995

A spherical wave emanating from a point source is scattered by either a soft or a hard body. The incident spherical wave has a wavelength which is much larger than the characteristic dimension of the…

Direct and inverse scattering for point source fields. The penetrable small sphere

- Mathematics
- 1999

A point source field is disturbed by the presence of a small penetrable scatterer which is either lossless or lossy. The point generated incident field is normalized in such a way as to be able to…

THE IMPEDANCE SCATTERING PROBLEM FOR A POINT-SOURCE FIELD. THE SMALL RESISTIVE SPHERE

- Mathematics
- 1997

A small resistive scatterer disturbs a spherical time-harmonic field emanating from a point source. The incident point-source field is normalized in such a way as to be able to recover the…

The Ultimate Image Singularities for External Ellipsoidal Harmonics

- Mathematics, Physics
- 1974

The image system of singularities of an arbitrary exterior potential field within a triaxial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over…

Second order low-frequency scattering by the soft ellipsoid

- Mathematics
- 1980

We consider low-frequency (small k) scattering of a plane wave by a triaxial ellipsoid for the case where the field vanishes on its surface. The terms up to order $k^2 $ for the field and $k^4 $ for…

Electromagnetic and Acoustic Scattering by Simple Shapes

- Physics
- 1969

Abstract : The book represents an exhaustive study of the scattering properties of acoustically soft and hard bodies and of perfect conductors, presented for 15 geometrically-simple shapes. Such…

Maneuvering Hydrodynamics of Ellipsoidal Forms

- Engineering, Mathematics
- 1977

The hydrodynamical forces and moments acting on a triaxial ellipsoid moving in an incompressible and inviscid fluid are analyzed. The rigid ellipsoid is allowed to move in the most general manner…

「レイリー散乱」(Rayleigh Scattering)

- Physics, Mathematics
- 1983

• Rayleigh scattering is an approximation used to predict scattering from particles much smaller than an electromagnetic wavelength • The approximation is based on quasi-static ideas: in regions of…

Seismic waves and sources

- Geology
- 1981

1 Classical Continuum Dynamics.- 1.1. The Stress Dyadic and Its Properties.- 1.2. Geometry of Small Deformations.- 1.3. Linear Elastic Solid.- 1.4. The Field Equations.- 1.5. Lagrangian Formulation.-…

The Theory of Spherical and Ellipsoidal Harmonics

- Mathematics
- 1955

Preface 1. The transformation of Laplaces's equation 2. The solution of Laplace's equation in polar coordinates 3. The Legendres associated functions 4. Spherical harmonics 5. Spherical harmonics of…