Shape reconstruction methods with incomplete data

Nakahata, K.; Kitahara, M.
May 2000
AIP Conference Proceedings;2000, Vol. 509 Issue 1, p919
Academic Journal
Linearized inverse scattering methods are applied to the shape reconstruction of defects in elastic solids. The linearized methods are based on the Born approximation in the low frequency range and the Kirchhoff approximation in the high frequency range. The experimental measurement is performed to collect the scattering data from defects. The processed data from the measurement are fed into the linearized methods and the shape of the defect is reconstructed by two linearized methods. The importance of scattering data in the low frequency range is pointed out not only for Born inversion but also for Kirchhoff inversion. In the ultrasonic measurement for the real structure, the access points of the sensor may be limited to one side of the structural surfaces and a part of the surface. From the viewpoint of application, the incomplete scattering data are used as inputs for the shape reconstruction methods and the effect of the sensing points are discussed. © 2000 American Institute of Physics.


Related Articles

  • Static and stationary multiple soliton solutions to the Einstein equations. Letelier, Patricio S. // Journal of Mathematical Physics;Mar1985, Vol. 26 Issue 3, p467 

    The application of the Belinsky–Zakharov solution-generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having...

  • Geometric approach to inverse scattering for hydrogen-like systems in a homogeneous magnetic field.  // Journal of Mathematical Physics;Apr98, Vol. 39 Issue 4, p1730 

    Focuses on the geometric approach to inverse scattering for hydrogen-like systems in a homogeneous magnetic field. Use of a method developed by V. Enss and R. Weder to prove the theorems; Discussion on the determination of scalar potential; Evaluation of quantum particles with opposite charges...

  • Gain-maximized GaAs/AlGaAs quantum-cascade laser with digitally graded active region. Indjin, D.; Tomic, S.; Ikonic, Z.; Harrison, P.; Kelsall, R. W.; Milanovic, V.; Kocˇinac, S. // Applied Physics Letters;9/16/2002, Vol. 81 Issue 12, p2163 

    An advanced strategy for the optimal design and realization of a GaAs/AlGaAs quantum-cascade laser is presented. It relies on recently established inverse scattering techniques to design an optimal smooth active region profile, followed by a conversion to an almost equivalent digitally graded...

  • The inverse scattering problem for the soft ellipsoid. Dassios, George // Journal of Mathematical Physics;Dec87, Vol. 28 Issue 12, p2858 

    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...

  • On nontrivial interactions and complete integrability of soliton equations. Beals, Richard; Konopelchenko, Boris // Journal of Mathematical Physics;Oct91, Vol. 32 Issue 10, p2695 

    Interacting multisoliton solutions of soliton equations are constructed using the inverse spectral transform and their asymptotics are analyzed. The Hamiltonian structure is obtained in terms of scattering data and the complete integrability of solutions of the N-wave equations with nontrivial...

  • Three-dimensional electromagnetic inverse scattering for blisotrophic dispersive media. He, Sailing; Weston, Vaughan H. // Journal of Mathematical Physics;Jan1997, Vol. 38 Issue 1, p182 

    Examines the three-dimensional electromagnetic inverse scattering for bilosotropic dispersive media. Rewriting of the Maxwell's equations in terms of the tangential fields; Application of the time domain wave-splitting of Maxwell's equations to the total field generated by a dipole exterior to...

  • Inverse scattering for inhomogeneous viscoelastic media. Cheng, Chang-jun; Chen, Xian-yao // Journal of Mathematical Physics;May2000, Vol. 41 Issue 5 

    In this paper, the inverse scattering problems for the full inhomogeneous viscoelastic medium are studied via the invariant imbedding technique. Special attention is paid to the propagation operators of the viscoelastic medium and the imbedding equations for these operators are derived. For the...

  • Regularized long wave equation and inverse scattering transform. Yan, Chuntao // Journal of Mathematical Physics;Jun93, Vol. 34 Issue 6, p2618 

    The sech2 solitary wave solution of the regularized long wave equation is reobtained via the inverse scattering transform. The wave function of the eigenvalue problem of the relevant Schrodinger equation is proved reflectionless with sech2 potential of arbitrary amplitude. Moreover, the...

  • On an old article of Tzitzeica and the inverse scattering method. Boldin, A. Yu.; Safin, S. S.; Sharipov, R. A. // Journal of Mathematical Physics;Dec93, Vol. 34 Issue 12, p5801 

    Tzitzeica’s class of surfaces in R3 is considered in connection with the inverse scattering method for the associated equation uxy=eu-e-2u. The Bäcklund transformation for this equation is derived from Tzitzeica’s Darboux transformation for it.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics