Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 12
250
Views
3
CrossRef citations to date
0
Altmetric
Articles

Foldy–Lax approximation on multiple scattering by many small scatterers

Pages 2547-2560 | Received 23 Mar 2012, Accepted 29 Oct 2012, Published online: 29 Nov 2012
 

Abstract

The multiple scattering of time harmonic wave emitted by a localized source through a medium with many scatterers can be approximated by an Foldy–Lax self-consistent system when the relative radius of each scatterer is small and the distribution of scatterers is sparse. The scattering amplitude in the Foldy–Lax self-consistent system will be specified in terms of scatterer volume and scattering strength. By neglecting the self-interaction effect, the difference from the exciting field in the Foldy–Lax formula to the analytic wave field given implicitly by the Lippmann–Schwinger integral equation is compared. An upper bound of the difference is obtained in terms of scaled radius and sparsity of the distribution of the scatterers.

AMS Subject Classifications::

View correction statement:
Erratum

Acknowledgements

This work was suggested by Professor George Papanicolaou, who devoted much time and energy on this research. The author is grateful to his hospitality and generous help during his visit to Stanford University. He thanks Professor P. A. Martin for many valuable suggestions. Many helpful comments from anonymous referee are gracefully acknowledged. The research is partially supported by the National Natural Science Foundation of China (Nos. 11126082, 11171211 and 11171212).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.