Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-29T16:10:58.129Z Has data issue: false hasContentIssue false
  • English
  • Français

On the acoustic scattering amplitude for a multi-layered Scatterer

Published online by Cambridge University Press:  17 February 2009

Christodoulos Athanasiadis
Christodoulos Athanasiadis
Affiliation:
Department of Mathematics, University of Athens, Panepistemiopolis, GR 157 84 Athens, Greece
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the boundary-value problems corresponding to the scattering of a time-harmonic acoustic plane wave by a multi-layered obstacle with a sound-soft, hard or penetrable core. Firstly, we construct in closed forms the normalized scattering amplitudes and prove the classical reciprocity and scattering theorems for these problems. These results are then used to study the spectrum of the scattering amplitude operator. The scattering cross-section is expressed in terms of the forward value of the corresponding normalized scattering amplitude. Finally, we develop a more general theory for scattering relations.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 4 , April 1998 , pp. 431 - 448
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Angell, T. S., Kleinman, R. E. and Hettlich, F., “The resistive and conductive problems for the exterior Helmholtz equation”, SIAM J. Appl. Math. 50 (1990) 1607–1623.CrossRefGoogle Scholar
[2]Athanasiadis, C., “Low-frequency electromagnetic scattering theory for a multi-layered scatterer”, Q. J. Mech. Appl. Math. 44 (1991) 55–67.Google Scholar
[3]Athanasiadis, C., “The hard-core multi-layered ellipsoid in a low-frequency acoustic field”, Int. J. Eng. 32 (1994) 1352–1359.Google Scholar
[4]Athanasiadis, C., “The multi-layered ellipsoid with a soft core in the presence of a low-frequency acoustic wave”, Q. J. Mech. Appl. Math. 47 (1994) 441–159.CrossRefGoogle Scholar
[5]Athanasiadis, C. and Stratis, I. G., “Low-frequency acoustic scattering by a infinitely stratified scatterer”, Rend. Mat. 15 (1995) 133–152.Google Scholar
[6]Colton, D. and Kress, R., Integral equation methods in Scattering theory, (John Wiley, New York, 1983).Google Scholar
[7]Colton, D. and Kress, R., Inverse acoustic and electromagnetic scattering theory (Springer, New York, 1992).Google Scholar
[8]Colton, D. and Kress, R., “Eigenvalues of the far field operator and inverse scattering theory”, SIAM J. Appl. Math. 26 (1995) 601–615.CrossRefGoogle Scholar
[9]Dassios, G., “Second order low-frequency scattering by the soft ellipsoid”, SIAM J. Appl. Math. 38 (1980) 373–381.Google Scholar
[10]Dassios, G., “Low-frequency scattering theory for a penetrable body with an impenetrable core”, SIAM J. Appl. Math. 42 (1982) 272–280.Google Scholar
[11]Dassios, G., Kiriaki, K. and Polysos, D., “On the scattering amplitudes for ealstic waves” J. Appl. Math. Phys. 38 (1987) 856–873.Google Scholar
[12]DeFacio, B., “Classical, linear, electromagnetic impedance theory with infinite integrable discon- tinuites”, J. Math. Phys. 31 (1990) 2155–2164.CrossRefGoogle Scholar
[13]Jones, D. S., Acoustic and electromagnetic scattering (Clarendon Press, Oxford, 1986).Google Scholar
[14]Kleinman, R. E. and Martin, P. A., “On single integral euqations for the transmission problem of acoustics”, SIAM J. Appl. Math. 44 (1988) 307–325.CrossRefGoogle Scholar
[15]Kleinman, R. E. and Senior, T. B. A., In low and high frequency asymptotics. Volume 2 (eds. Varadan, V. K. and Varadan, V. V., Elsevier, Amsterdam, 1986) 1–70.Google Scholar
[16]Kress, R. and Roach, G. F., “Transmission problems for the Helmholtz equation”, J. Math. Phys. 19 (1975) 1433–1437.CrossRefGoogle Scholar
[17]Miranda, C., Partial differential equations of elliptic type (Springer, New York, 1970).Google Scholar
[18]Sabatier, P. C., “On modelling discontinuous media. Three dimensional scattering”, J. Math. Phys. 30 (1989) 2585–2598.Google Scholar
[19]Twersky, V., “Certain transmissions and reflection theorems”, J. Appl. Phys. 25 (1954) 859–862.Google Scholar
[20]Twersky, V., “Multiple scattering of electromagnetic waves by arbitrary configurations”, J. Math. Phys. 8 (1966) 589–598.Google Scholar