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  • 1
    Electronic Resource
    Electronic Resource
    Low-frequency moments in inverse scattering theory (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1691-1692 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The low-frequency moments of the scattering amplitude are utilized in order to identify the capacity, the center, and the orientation of an acoustically soft scatterer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528716
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  • 2
    Electronic Resource
    Electronic Resource
    Equipartition of energy in magnetohydrodynamics (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 3845-3846 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The time evolution of the energy for wave propagation in an infinite ideal magnetofluid is studied analytically. It is found that equipartition between the kinetic and potential energies is achieved. Equipartition occurs either in finite time or asymptotically as t→∞ depending upon whether the initial data are compactly supported or have finite energy, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866426
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  • 3
    Electronic Resource
    Electronic Resource
    On the harmonic radius and the capacity of an inverse ellipsoid (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 835-836 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the capacity of a body, obtained by Kelvin inversion, is equal to the inverse of the harmonic radius of the image domain with respect to the center of inversion. Using the monotonicity of the harmonic radius and an appropriate isoperimetric inequality, lower and upper estimates for the capacity of an inverse ellipsoid are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527979
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  • 4
    Electronic Resource
    Electronic Resource
    Inverse scattering via low-frequency moments (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 4206-4216 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An acoustically soft scatterer defined by a closed and star shape polynomial surface of any degree disturbs the propagation of a time harmonic plane incident wave. It is demonstrated that, under the hypotheses of Schiffer's uniqueness theorem, all the generalized low-frequency moments corresponding to the capacity potential can be obtained from the scattering amplitude. An analytic algorithm is proposed that recovers the geometry of the body whenever a finite number of generalized moments generated by the leading low-frequency approximation are given. What is striking here is the fact that a surface measure generated by a potential problem is enough to recover the geometry of the scatterer. The idea here is to relate the given moments to a set of particular combined spherical moments that appear as coefficients of an algebraic linear system, whose solution provides the coefficients of the scattering surface in spherical harmonics. This is done with the help of an inner product defined over the surface of the unit sphere with respect to an unknown positive surface measure. In contrast to other existing techniques of shape reconstruction, the one proposed here does not involve the solution of any optimization problem. Instead, only some finite expansions in spherical harmonics and the solution of a linear algebraic system is involved. Tikhonov regularization is used to treat the case of inexact data. The proposed method is illustrated in the case of second degree surfaces where exact analytical data are available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529819
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  • 5
    Electronic Resource
    Electronic Resource
    The inverse scattering problem for the soft ellipsoid (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2858-2862 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A soft triaxial ellipsoid, of unknown semiaxes and orientation, is excited into secondary radiation by a plane acoustic wave of a fixed low frequency. It is proved that one measurement of the leading low-frequency coefficient and exactly six measurements of the second low-frequency coefficient of the real part of the forward or the backward scattering amplitude are enough to specify completely both the semiaxes, as well as the orientation of the ellipsoid. Therefore, only the first two low-frequency coefficients of the real part of the scattering amplitude are needed in order to solve the inverse scattering problem for the soft ellipsoid. For the case of spheroids, the number of measurements is restricted to one for the first and three for the second coefficient. Finally, the sphere is specified by a single measurement of the leading coefficient. The special cases where the orientation or the semiaxes are known are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527684
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  • 6
    Electronic Resource
    Electronic Resource
    On the scattering amplitudes for elastic waves (1987)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 38 (1987), S. 856-873 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Reciprocity and scattering theorems for the normalized spherical scattering amplitude for elastic waves are obtained for the case of a rigid scatterer, a cavity and a penetrable scattering region. Depending on the polarization of the two incident waves reciprocity relations of the radial-radial, radial-angular, and angular-angular type are established. Radial and angular scattering theorems, expressing the corresponding scattering amplitudes via integrals of the amplitudes over all directions of observation, as well as their special forms for scatterers with inversion symmetry are also provided. As a consequence of the stated scattering theorems the scattering cross-section for either a longitudinal, or a transverse incident wave is expressed through the forward value of the radial, or the angular amplitude, correspondingly. All the known relative theorems for acoustic scattering are trivially recovered from their elastic counterparts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945822
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  • 7
    Electronic Resource
    Electronic Resource
    Dissipation rates and partition of energy in thermoelasticity (1984)
    Springer
    Archive for rational mechanics and analysis 87 (1984), S. 49-91 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00251002
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  • 8
    Electronic Resource
    Electronic Resource
    Estimates for low-frequency elastic scattering by a rigid body (1988)
    Springer
    Journal of elasticity 20 (1988), S. 161-180 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract When a plane elastic wave is scattered by a rigid body the surface integral of the traction, projected along the direction of polarization of the incident wave, provides the leading low-frequency approximation for the scattering amplitudes. Two kinds of lower and upper bounds for the surface traction integral are given. One is based on the geometrical characteristics of the scatterer and is expressed in terms of corresponding values of the best fitting interior and exterior confocal triaxial ellipsoids. The case of best fitting interior and exterior spheres is examined as a special case. These bounds are sharp in the sense that they both become equalities when the scatterer degenerates to an ellipsoid. The other kind of lower and upper bounds involve the capacity of the scatterer. All estimates were obtained by using the generalized Dirichlet and Thomson Principles of Potential Theory in Elastostatics. Furthermore, all constants appearing in the bounds are given in terms of the ratio of the phase velocities for the transverse and the longitudinal wave. An upper bound for scattering by a cube at normal incidence is also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00043199
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  • 9
    Electronic Resource
    Electronic Resource
    High-frequency asymptotics in inverse scattering by ellipsoids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 1-12 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High-frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high-frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non-zero-measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160102
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  • 10
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    Convergent low‐frequency expansions for penetrable scatterers (1977)
    American Institute of Physics
    Details
    Publication Date: 1977-01-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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