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.

Elastic Wave Scattering from an Interface Crack: Antiplane Strain

1987 ◽  
Vol 54 (3) ◽  
pp. 503-508 ◽  
Author(s):  
A. Bostro¨m
Keyword(s):  
Interface Crack ◽  
Crack Opening ◽  
Plane Waves ◽  
Integral Equation Method ◽  
Far Field ◽  
Antiplane Strain ◽  
Opening Displacement ◽  
Direct Integral ◽  
The Matrix ◽  
Scattering Of Elastic Waves

The two-dimensional scalar problem of scattering of elastic waves under antiplane strain from an interface crack between two elastic half-spaces is considered. The method used is a direct integral equation method with the crack-opening displacement as the unknown. Chebyshev polynomials are used as expansion functions and the matrix in the resulting equations is simplified by contour integration techniques. The scattered far field is expressed explicitly in simple functions and the expansion coefficients. The consequences of energy conservation are explored and are used as a check in the numerical implementation. For incoming plane waves numerical results are given for the total scattered energy and the far field amplitude.

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.

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.

Effect of Interface Layers on Scattering of Elastic Waves

1988 ◽  
Vol 55 (4) ◽  
pp. 871-878 ◽  
Author(s):  
R. Paskaramoorthy ◽  
S. K. Datta ◽  
A. H. Shah
Keyword(s):  
Cross Sections ◽  
Elastic Waves ◽  
Interface Layer ◽  
Scattering Cross ◽  
Expansion Technique ◽  
The Matrix ◽  
Scattering Of Elastic Waves ◽  
Elastic Inclusions ◽  
Interface Layers ◽  
Scattering Cross Sections

Scattering of elastic waves by spheroidal elastic inclusions has been studied in this paper. Particular attention has been focused on the effect of interface layers between the inclusions and the matrix on the scattering cross-sections. It has been assumed that properties of each layer is constant through its thickness. For spheroidal inclusion this problem cannot be solved by exact means. We have used a hybrid finite element and wave function expansion technique to analyze the problem. It is shown that solutions thus obtained for spherical inclusions and cavities agree well with analytical solutions. For spheroidal inclusions we show that when the interface layer properties are intermediate between those of the particles and the matrix the scattering cross-section increases. These results can be useful in characterizing interface layer properties.

ELECTRON – HYDROGEN ATOM SCATTERING IN BORN APPROXIMATION

1960 ◽  
Vol 38 (12) ◽  
pp. 1654-1660 ◽  
Author(s):  
Ta-You Wu
Keyword(s):  
Hydrogen Atom ◽  
Cross Sections ◽  
Born Approximation ◽  
Matrix Elements ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Atom Scattering ◽  
The Matrix ◽  
Scattering Cross Sections

The elastic (1s–1s) and the inelastic (1s–2s, 1s–2p) scattering cross sections in the Born approximation at energies of 1, 4, 9, 16 rydbergs have been calculated exactly from the closed formulas of the matrix elements for these transitions. Both the differential and the total cross sections are given here.

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.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

scholarly journals Towards fully nonperturbative computations of inelastic ℓN scattering cross sections from lattice QCD

2020 ◽  
Vol 102 (11) ◽  
Author(s):  
Hidenori Fukaya ◽  
Shoji Hashimoto ◽  
Takashi Kaneko ◽  
Hiroshi Ohki
Keyword(s):  
Lattice Qcd ◽  
Cross Sections ◽  
Scattering Cross ◽  
Scattering Cross Sections

scholarly journals Combining ADF-EDX scattering cross-sections for elemental quantification of nanostructures

2021 ◽  
Vol 27 (S1) ◽  
pp. 600-602
Author(s):  
Zezhong Zhang ◽  
Annick De Backer ◽  
Ivan Lobato ◽  
Sandra Van Aert ◽  
Peter Nellist
Keyword(s):  
Cross Sections ◽  
Scattering Cross ◽  
Scattering Cross Sections

Neutron diffraction, inelastic scattering and the structure of amphiphiles and macromolecules in solution

1975 ◽  
Vol 345 (1640) ◽  
pp. 119-144 ◽  
Keyword(s):  
Neutron Diffraction ◽  
Inelastic Scattering ◽  
Cross Sections ◽  
Biological Molecules ◽  
Variation Method ◽  
Contrast Variation ◽  
Structure And Dynamics ◽  
Spin Resonance ◽  
Scattering Lengths ◽  
Scattering Cross Sections

The methods by which neutron diffraction and inelastic scattering may be used to study the structure and dynamics of solutions are reviewed, with particular reference to solutions of amphiphile and biological molecules in water. Neutron methods have particular power because the scattering lengths for protons and deuterons are of opposite sign, and hence there exists the possibility of obtaining variable contrast between the scattering of the aqueous medium and the molecules in it. In addition, the contrast variation method is also applicable to inelastic scattering studies whereby the dynamics of one component of the solution can be preferentially studied due to large and variable differences in the scattering cross sections. Both applications of contrast variation are illustrated with examples of amphiphile-water lamellar mesophases, diffraction from collagen, viruses, and polymer solutions. Inelastic scattering observations and the dynamics of water between the lamellar sheets allow microscopic measurements of the water diffusion along and perpendicular to the layers. The information obtained is complementary to that from nuclear magnetic resonance and electron spin resonance studies of diffusion.

Sign in / Sign up

Export Citation Format

Share Document