Scattering by a thin multicoated perfectly conducting spherical shell with a circular aperture

1992 ◽  
Vol 70 (2-3) ◽  
pp. 164-172 ◽  
Author(s):  
R. A. Said ◽  
M. Hamid
Keyword(s):  
Spherical Shell ◽  
Cross Sections ◽  
Spherical Wave ◽  
Least Square ◽  
Circular Aperture ◽  
Modal Expansion ◽  
Scattering Coefficients ◽  
Expansion Coefficients ◽  
Scattered Fields ◽  
Scattering Cross Sections

An analytic solution is presented for the problem of an infinitely thin perfectly conducting spherical shell with a circular aperture of arbitrary angle cut into the shell, filled with a dielectric, and coated by different thicknesses of spherical dielectric layers. The fields in all regions are expanded in terms of spherical wave functions and the boundary conditions of the continuity of the tangential fields at the dielectric–dielectric and dielectric–free-space boundaries are applied to express the expansion coefficients of the first dielectric layer in terms of the scattering coefficients. To approximate the modal expansion coefficients, the least-square error method is applied to the equations resulting from matching the fields through the aperture. Different numerical results for the simple case of a single coating layer are obtained in the form of amplitude patterns for the aperture and scattered fields versus angle as well as the backward- and forward-scattering cross sections for different loadings as functions of cavity size.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

ICSC: a program for calculating inelastic scattering cross sections for fast electrons incident on crystals

2003 ◽  
Vol 36 (3) ◽  
pp. 940-943 ◽  
Author(s):  
M. P. Oxley ◽  
L. J. Allen
Keyword(s):  
Inelastic Scattering ◽  
Cross Sections ◽  
Dark Field ◽  
Fast Electrons ◽  
Scattering Coefficients ◽  
Einstein Model ◽  
Annular Dark Field ◽  
Inner Shell Ionization ◽  
Scattering Cross Sections ◽  
Shell Ionization

A computer program which calculates inner-shell ionization and backscattering cross sections for fast electrons incident on a crystal is presented. The program calculates the inelastic scattering coefficients for inner-shell ionization, pertinent to electron energy loss spectroscopy and energy dispersive X-ray analysis, using recently presented parameterizations of the atomic scattering factors. Orientation-dependent cross sections, suitable for atom location by channelling enhanced microanalysis, may be calculated. Inelastic scattering coefficients that allow the calculation of orientation-dependent annular dark-field and Rutherford backscattering maps are calculated using an Einstein model. In all cases, absorption due to thermal diffuse scattering, also calculated using an Einstein model, can be included.

Acoustic Scattering Field Reconstruction Using Truncated Total Least Square Algorithm

2018 ◽  
Vol 27 (04) ◽  
pp. 1850055
Author(s):  
Haitao Yu ◽  
Yingmin Wang ◽  
Qi Wang
Keyword(s):  
Acoustic Scattering ◽  
Reconstruction Algorithm ◽  
Least Square ◽  
Modal Expansion ◽  
Field Reconstruction ◽  
Scattering Field ◽  
Wave Numbers ◽  
Total Least Square ◽  
Simulation Results ◽  
Expansion Coefficients

Acoustic scattering-field reconstruction of structures with arbitrary shape is the research basis of the scattering characteristics for underwater targets. Firstly, using boundary element method (BEM) and acoustic radiation modes (ARMs) solution in fluid domain, it is proved that the scattering pressures can be expressed by ARMs. Secondly, the acoustic field distribution modes (AFDMs) are constructed by ARMs and a new acoustic transfer matrix (ATM) which is acquired by the simplification of the traditional ATM. At the same time, the scattering pressures can be expressed as the product of the AFDMs and the modal expansion coefficients. Thus, the scattering reconstruction problem is converted into the exact solution problem of the modal expansion coefficients. Aiming at the existing noise of both the pressures at measuring point and AFDMs, the total least square (TLS) algorithm is introduced to acquire the accurate solution. Further, considering the ill-conditioned AFDMs matrix, the truncated total least square (TTLS) algorithm is introduced to solve the modal expansion coefficients. Simulation results show that the capability of resisting noise contamination is limited for the reconstruction algorithm based on TLS and that the reconstruction algorithm based on TTLS has a better denoising performance than the TLS one. At the same time, for smaller wave numbers, the modal orders for reconstruction at different noise levels are approximately equal and the reconstruction errors are small. The simulation results also demonstrate that the reconstruction algorithm based on TTLS has a better denoising performance at smaller wave numbers than at higher wave numbers. For the higher wave numbers, the modal orders for reconstruction decrease and the reconstruction errors increase with the decrease of the signal-to-noise ratio (SNR). For the backward reconstruction at smaller wave numbers, the influence to reconstruction results, which arises from structure complexity ascending and evanescent waves existing, should be considered when the reconstruction surfaces are near the structures.

Elastic wave scattering by a circular crack

1982 ◽  
Vol 308 (1502) ◽  
pp. 167-198 ◽  
Keyword(s):  
Cross Sections ◽  
Circular Crack ◽  
Integral Equation Method ◽  
Infinite Matrix ◽  
Far Field ◽  
Direct Integral ◽  
Elastic Wave Scattering ◽  
The Matrix ◽  
Expansion Coefficients ◽  
Scattering Cross Sections

The scattering of waves by a circular crack in an elastic medium is solved by a direct integral equation method. The solution method is based on expansion of stresses and displacements on the crack surface in terms of trigonometric functions and orthogonal polynomials. The expansion coefficients are related through an infinite matrix, and by contour integration the matrix elements are expressed in terms of finite integrals. The scattered far field is expressed explicitly in terms of simple functions and the displacement expansion coefficients. The system of equations is solved numerically, and extensive results are given both in the form of maps of the scattered far field and as scattering cross sections. Neither the method nor the specific results are restricted by any assumptions of symmetry.

scholarly journals Two-Dimensional Scattering by a Homogeneous Gyrotropic-Type Elliptic Cylinder

2016 ◽  
Vol 5 (3) ◽  
pp. 106
Author(s):  
A. K. Hamid ◽  
F. Cooray
Keyword(s):  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Separation Of Variables ◽  
Elliptic Cylinder ◽  
Wave Functions ◽  
Two Dimensional ◽  
Vector Wave ◽  
Expansion Coefficients ◽  
Scattering Cross Sections ◽  
Uniform Plane

The separation of variables procedure has been employed for solving the problem of scattering from an infinite homogeneous gyrotropic-type (G-type) elliptic cylinder, when a uniform plane electromagnetic wave perpendicular to its axis, illuminates it. The formulation of the problem involves expanding each electric and magnetic field using appropriate elliptic vector wave functions and expansion coefficients. Imposing suitable boundary conditions at the surface of the elliptic cylinder yields the unknown expansion coefficients related to the scattered and the transmitted fields. To demonstrate how the various G-type materials and the size of the cylinder affects scattering from it, plots of scattering cross sections are given for cylinders having different permittivity/permeability tensors and sizes.

scholarly journals Covariance Matrices for Differential and Angle-Integrated Neutron-Induced Elastic and Inelastic Scattering Cross Sections of 56Fe

2019 ◽  
Vol 211 ◽  
pp. 07002 ◽  
Author(s):  
Shengli Chen ◽  
David Bernard ◽  
Pascal Archier ◽  
Cyrille De Saint Jean ◽  
Gilles Noguere ◽  
...  
Keyword(s):  
Cross Sections ◽  
Uncertainty Propagation ◽  
Least Square Method ◽  
Nuclear Data ◽  
High Energy ◽  
Least Square ◽  
Angular Distributions ◽  
Model Parameters ◽  
Nuclear Data Library ◽  
Scattering Cross Sections

Correlations between neutron inelastic scatterings angular distributions are not included in the Joint Evaluated Fission and Fusion (JEFF) nuclear data library, while they are key quantities for uncertainty propagation of nuclear data. By reproducing the angle-integrated cross sections and uncertainties of JEFF-3.1.1, the present work obtains covariance matrix between high energy model parameters using the least square method implemented in the CONRAD code. With this matrix, it is possible to generate correlations between angle-integrated cross sections and angular distributions, which are usually presented by Legendre coefficients. As expected, strong correlations are found, for example, between the Legendre coefficients of elastic and first-level-inelastic scatterings and the angle-integrated total, elastic, total inelastic cross sections.

Absolute inner-shell cross section determination for EELS analysis

1988 ◽  
Vol 46 ◽  
pp. 534-535
Author(s):  
P.A. Crozier
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Absolute Cross Section ◽  
Specimen Thickness ◽  
Mass Thickness ◽  
Scattering Cross ◽  
Before And After ◽  
Estimated Error ◽  
Scattering Cross Sections ◽  
Electron Microscopist

Absolute inelastic scattering cross sections or mean free paths are often used in EELS analysis for determining elemental concentrations and specimen thickness. In most instances, theoretical values must be used because there have been few attempts to determine experimental scattering cross sections from solids under the conditions of interest to electron microscopist. In addition to providing data for spectral quantitation, absolute cross section measurements yields useful information on many of the approximations which are frequently involved in EELS analysis procedures. In this paper, experimental cross sections are presented for some inner-shell edges of Al, Cu, Ag and Au.Uniform thin films of the previously mentioned materials were prepared by vacuum evaporation onto microscope cover slips. The cover slips were weighed before and after evaporation to determine the mass thickness of the films. The estimated error in this method of determining mass thickness was ±7 x 107g/cm2. The films were floated off in water and mounted on Cu grids.

scholarly journals Partial Energy Transfer Model of Lamb Waves Scattering in Materially Isotropic Waveguides

2021 ◽  
Vol 11 (10) ◽  
pp. 4508
Author(s):  
Pavel Šofer ◽  
Michal Šofer ◽  
Marek Raček ◽  
Dawid Cekus ◽  
Paweł Kwiatoń
Keyword(s):  
Energy Transfer ◽  
Lamb Waves ◽  
Hybrid Approach ◽  
Wave Mode ◽  
Transfer Model ◽  
Material Interface ◽  
Modal Expansion ◽  
Scattering Coefficients ◽  
Expansion Technique ◽  
Partial Energy

The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique.

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