scholarly journals Anisotropic Scattering Characteristics of a Radially Multilayered Gyrotropic Sphere

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lei Cao ◽  
Yongpin Chen ◽  
Kai Kang
Keyword(s):  
Plane Wave ◽  
Spherical Wave ◽  
Fem Simulation ◽  
Closed Form Solution ◽  
Anisotropic Scattering ◽  
Form Solution ◽  
Scattering Coefficients ◽  
Full Wave ◽  
Spherical Scatterer ◽  
Analytical Expressions

We present a new closed-form solution to the scattering of a monochromatic plane wave by a radially multilayered gyrotropic sphere using the T-matrix method. This approach can be utilized to investigate the interactions of a plane wave and a gyrotropic spherical scatterer of multiple layers with each layer characterized by both permittivity and permeability tensors. Based on the completeness and noncoplanar properties of vector spherical wave functions (VSWFs), analytical expressions of the electromagnetic fields in each gyrotropic layer are first derived. The boundary conditions are then applied on each discontinuous interface to obtain the scattering coefficients. Validations are made by first comparing the radar cross section (RCS) values of a 2-layered gyrotropic sphere with that computed from the full-wave finite element method (FEM) simulation and then reducing the general case to uniaxial case to compare the RCS values with the published results computed by Fourier transform combined with VSWFs method; in both cases good agreements are observed. Several specific cases are fully explored to investigate how the RCS are influenced by the parameters of the multilayered spherical structure. The results show that when both electric and magnetic gyrotropy tensors are considered, the RCS of the multilayered spherical scatterer can be suppressed or enhanced, depending on proper configurations of the material parameters.

scholarly journals Sound Radiation due to Modal Vibrations of a Spherical Source in an Acoustic Quarterspace

2004 ◽  
Vol 11 (5-6) ◽  
pp. 625-635 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Mahdi Azarpeyvand
Keyword(s):  
Acoustic Radiation ◽  
Classical Method ◽  
Spherical Wave ◽  
Closed Form Solution ◽  
Addition Theorem ◽  
Form Solution ◽  
Surface Velocity ◽  
Rigid Boundary ◽  
Radiation Impedance ◽  
Spherical Source

Radiation of sound from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity, while positioned within an acoustic quarterspace is analyzed in an exact manner. The formulation utilizes the appropriate wave field expansions along with the translational addition theorem for spherical wave functions in combination with the classical method of images to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the spherical source, vibrating in the pulsating (n= 0) and translational oscillating (n= 1) modes, is positioned near the rigid boundary of a water-filled quarterspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.

Scattering by hard and soft parallel half-planes

1981 ◽  
Vol 59 (12) ◽  
pp. 1879-1885 ◽  
Author(s):  
R. A. Hurd ◽  
E. Lüneburg
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Half Plane ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Normal Derivative ◽  
Form Solution ◽  
The Other ◽  
Total Field

We consider the diffraction of a scalar plane wave by two parallel half-planes. On one half-plane the total field vanishes whilst on the other its normal derivative is zero. This is a new canonical diffraction problem and we give an exact closed-form solution to it. The problem has applications to the design of acoustic barriers.

Determination of the Electrical Radius ka of a Spherical Scatterer from the Scattered Field

1971 ◽  
Vol 49 (11) ◽  
pp. 1507-1535 ◽  
Author(s):  
W. M. Boerner ◽  
F. H. Vandenberghe
Keyword(s):  
Inverse Problem ◽  
Closed Form ◽  
Scattered Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vector Wave ◽  
Wave Expansion ◽  
Spherical Scatterer ◽  
Expansion Coefficients ◽  
Spherical Vector

The inverse problem of scattering for a spherical vector scattering geometry is considered. The transverse scattered field components are related to the expansion coefficients of Hansen's vector wave expansion in terms of the scattered field matrix. This matrix needs to be inverted to obtain the unknown expansion coefficients which are required to recover the shape of the target in question. Since the particular properties of the spherical vector wave expansion may cause highly instable matrix inversion, an analytical, closed form solution of the determinant associated with the scattered field matrix was sought. For vector scattering geometries representing the mth degree multipole cases such closed form solutions for the associated determinant of truncated order 2N are derived, using a novel complementary series expansion for the employed forms of the associated Legendre's functions of the first kind. A novel determinate optimization procedure is presented which enables the specification of the optimal distribution of measurement aspect angles within any given finite measurement cone of the unit sphere of directions. The closed form solution for nonsymmetrical vector scattering geometries is presented in Appendix III only for the value N = 3 (m = 0 and 1) employing properties of quadratic forms as derived in Appendix II. It is then shown that the electrical radius ka of a perfectly conducting spherical scatterer can be directly recovered from a finite number of contiguous expansion coefficients similar to the cylindrical case presented in Boerner, Vandenberghe, and Hamid. Furthermore, relationships between contiguous expansion coefficients of both electric and magnetic type result, which are relevant to the general inverse problem since the scattered field can be uniquely expressed in terms of only one set of expansion coefficients associated with either the electric or magnetic vector wave functions.

On the response of steered vertical line arrays to anisotropic noise

1979 ◽  
Vol 367 (1731) ◽  
pp. 539-547
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Approximate Method ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vertical Line ◽  
Acoustic Sensors ◽  
Gain Function ◽  
Line Array ◽  
Arbitrary Anisotropy

An approximate method is presented for evaluating, through the noise gain function, the response of a steered vertical line array of acoustic sensors to anisotrophic, plane-wave noise fields. On the basis of the high- N approximation a closed form solution is obtained for the noise gain function, even for the general case of arbitrary anisotropy. The main features on the noise gain curves are discussed and interpreted in terms of conventional beamforming concepts.

scholarly journals Experimental verification of spherical-wave effect on the AVO response and implications for three-term inversion

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. C7-C12 ◽  
Author(s):  
Mohammed Alhussain ◽  
Boris Gurevich ◽  
Milovan Urosevic
Keyword(s):  
Plane Wave ◽  
Spherical Wave ◽  
Least Square ◽  
Elastic Parameters ◽  
Least Square Fitting ◽  
Full Wave ◽  
Alternative Approach ◽  
Class 1 ◽  
Elastic Inversion ◽  
Two Parameter

Spherical-wave offset-dependent reflectivity is investigated by measuring ultrasonic reflection amplitudes from a water/Plexiglas interface. The experimental results show substantial deviation of the measured amplitudes from the plane-wave reflection coefficients at large angles. However, full-wave numerical simulations of the point source reflection response using the reflectivity algorithm show excellent agreement with the measurements, demonstrating that the deviation from the plane-wave response is caused by the wavefront curvature. To analyze the effect of wavefront curvature on elastic inversion, we simulate the spherical-wave reflectivity at different frequencies and invert for elastic parameters by least-square fitting of the plane-wave (Zoeppritz) solution. The results show that the two-parameter inversion based on the intercept and gradient is robust, although estimation of three parameters ([Formula: see text], [Formula: see text], and density) that use the curvature of the offset variation with angle (AVA) response is prone to substantial frequency-dependent errors. We propose an alternative approach to parameter estimation, one that uses critical angles estimated from AVA curves (instead of the AVA curvature). This approach shows a significant improvement in the estimation of elastic parameters, and it could be applied to class 1 AVO responses.

scholarly journals Solutions for Downslope Pipeline Walking on a Seabed With a Peaky Trilinear Soil Resistance Model

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Adriano Castelo ◽  
David White ◽  
Yinghui Tian
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Soil Resistance ◽  
Finite Element Analyses ◽  
Soil Behavior ◽  
Rigid Plastic ◽  
Offshore Pipelines ◽  
Soil Response ◽  
Resistance Model ◽  
Analytical Expressions

Abstract Offshore pipelines used for transporting hydrocarbons are cyclically loaded by great variations of pressure and temperature. These variations can induce axial instability in such pipelines. This instability may cause the pipelines to migrate globally along their length; an effect known as pipeline walking. Traditional models of pipeline walking have considered the axial soil response as rigid-plastic (RP); however, such behavior does not match observations from physical soil tests. It leads to inaccurate estimates of walking rate (WR) per cycle and over design. In this paper, a trilinear (3L) soil resistance model is used to represent seabed resistance to investigate the behavior of pipeline walking. Different parameters, i.e., shapes and properties of trilinearity (within the peaky soil model type), have been considered leading to a closed-form solution. This solution improves the understanding of the main properties involved in the peaky trilinear soil behavior by providing a set of analytical expressions for pipe walking, which were benchmarked and validated against a set of finite element analyses.

View Factors in Radiation Between Two Parallel Oriented Cylinders of Finite Lengths

1982 ◽  
Vol 104 (2) ◽  
pp. 384-388 ◽  
Author(s):  
N. H. Juul
Keyword(s):  
Line Source ◽  
Closed Form Solution ◽  
Diffuse Radiation ◽  
Form Solution ◽  
View Factor ◽  
Double Integral ◽  
Integral Expression ◽  
View Factors ◽  
Limiting Case ◽  
Analytical Expressions

A simple double-integral expression for the diffuse radiation view factor, F12, between two parallel cylinders of finite lengths is derived. No closed-form solution appears possible except for the limiting case of infinite long cylinders for which an analytical expression for the view factor F12∞ is derived by applying the crossed string method. The accuracies of the line source approximations are evaluated, and the regions for which they are accurate to one percentage or better are identified. The view factor F12 between two opposing cylinders of equal length is computed by numerical integration and normalized by F12∞. The results are presented. Analytical expressions, which approximate the view factors between two opposite cylinders of finite length, are derived and their accuracy is evaluated over a useful parameter range. The range of their applications corresponds approximately to that for the line source approximation. This result is expected, because the errors are caused in part by blockage of radiation which is similar.

Diffraction by an infinite set of hard and soft parallel half planes

1982 ◽  
Vol 60 (1) ◽  
pp. 1-9 ◽  
Author(s):  
E. Lüneburg ◽  
R. A. Hurd
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Normal Derivative ◽  
Form Solution ◽  
Total Field ◽  
Bifurcation Problems ◽  
Infinite Set

We consider the diffraction of a plane wave by an infinite set of parallel half planes. On alternate half planes the total field or its normal derivative vanishes. An exact closed-form solution to this new canonical diffraction problem is presented. The problem also contains the solution to ten intrinsically different waveguide "bifurcation" problems.

Diffraction by an anisotropic impedance half plane

1985 ◽  
Vol 63 (9) ◽  
pp. 1135-1140 ◽  
Author(s):  
R. A. Hurd ◽  
E. Lüneburg
Keyword(s):  
Plane Wave ◽  
Closed Form ◽  
Half Plane ◽  
Matrix Factorization ◽  
Closed Form Solution ◽  
Form Solution ◽  
Obliquely Incident

We solve a new canonical problem: that of a plane wave obliquely incident on an anisotropic imperfectly conducting half plane. An exact closed-form solution is obtained by factorizing a 2 × 2 Wiener–Hopf matrix. The problem had earlier been considered insoluble, but yields to a combination of new and old matrix-factorization techniques.

Motion of a Bored Sphere in a Spinning Spherical Cavity

1981 ◽  
Vol 103 (4) ◽  
pp. 389-394 ◽  
Author(s):  
R. H. Nunn ◽  
J. W. Bloomer
Keyword(s):  
Numerical Methods ◽  
Closed Form ◽  
Predictive Model ◽  
Spherical Cavity ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Analytical Expressions ◽  
Theory And Experiment

Theory and experiment are combined to develop a predictive model for the motion of a bored sphere within a spinning spherical cavity. The motion is gyroscopic in nature with the sphere eventually aligning its hole with the axis of spin of the cavity. Analytical expressions are derived for the applied moments on the sphere due to its motion relative to that of the cavity, and the resulting equations of motion are solved by numerical methods. An approximate closed-form solution is also obtained. Experiments are described in which the measured nutation of the sphere substantiates the analytical predictions.

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