Quarterly of Applied Mathematics

Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity

Author(s): C. Athanasiadis; V. Sevroglou; I. G. Stratis
Journal: Quart. Appl. Math. 64 (2006), 695-710.
MSC (2000): Primary 74J20; Secondary 74B05
Posted: October 31, 2006
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Abstract: The problem of scattering of elastic waves by a bounded obstacle in two-dimensional linear elasticity is considered. The scattering problems are presented in a dyadic form. An incident dyadic field generated by a point source is disturbed by a rigid body, a cavity, or a penetrable obstacle. General scattering theorems are proved, relating the far-field patterns due to scattering of waves from a point source set up in either of two different locations. The most general reciprocity theorem is established, and mixed scattering relations are also proved. Finally, a relation between the incident and the scattered wave which refers to the mechanism of energy transfer of the scatterer, the so-called optical theorem, is established.

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C. Athanasiadis
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis, GR 157 84 Athens, Greece
Email: cathan@math.uoa.gr

V. Sevroglou
Affiliation: Department of Mathematics, University of Ioannina, GR 45110 Ioannina, Greece
Email: bsevro@cc.uoi.gr

I. G. Stratis
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis, GR 157 84 Athens, Greece
Email: istratis@math.uoa.gr

PII: S0033-569X-06-01041-0
Keywords: Dyadic scattering, point sources, scattering relations
Received by editor(s): January 19, 2006
Posted: October 31, 2006
Additional Notes: The authors acknowledge partial financial support from EPEAEK II (``Pythagoras II'' research fellowships, project title ``Mathematical Analysis of Wave Propagation in Chiral Electromagnetic and Elastic Media'', University of Athens).
Copyright of article: Copyright 2006, Brown University
The copyright for this article reverts to public domain after 28 years from publication.

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