Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Sub-wavelength focusing of acoustic waves in bubbly media

by H. Ammari and B. Fitzpatrick and D. Gontier and H. Lee and H. Zhang

(Report number 2017-28)

Abstract
The purpose of this paper is to investigate acoustic wave scattering by a large number of bubbles in a liquid at frequencies near the Minnaert resonance frequency. This bubbly media has been exploited in practice to obtain super-focusing of acoustic waves. Using layer potential techniques we derive the scattering function for a single spherical bubble excited by an incident wave in the low frequency regime. We then derive the point scatter approximation for multiple scattering by $N$ bubbles. We describe several numerical experiments based on the point scatterer approximation that demonstrate the possibility of achieving super-focusing using bubbly media.

Keywords: Minnaert resonance, system of bubbles, sub-wavelength focusing.

@Techreport{AFGLZ17_724,
  author = {H. Ammari and B. Fitzpatrick and D. Gontier and H. Lee and H. Zhang},
  title = {Sub-wavelength focusing of acoustic waves in bubbly media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-28},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-28.pdf },
  year = {2017}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).