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Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Mathematical modeling of the Photoacoustic effect generated by the heating of metallic nanoparticles


Authors: Faouzi Triki and Margaux Vauthrin
Journal: Quart. Appl. Math.
MSC (2010): Primary 35B30, 35R30
DOI: https://doi.org/10.1090/qam/1502
Published electronically: February 22, 2018
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Abstract: This paper is devoted to the modeling of the photoacoustic effect generated by the electromagnetic heating of metallic nanoparticles embedded in a biological tissue. We first derive an asymptotic model for the plasmonic resonances and the electromagnetic fields. We then describe the acoustic generation created by the electromagnetic heating of the nanoparticle. Precisely, we derive the model equations that describe the coupling between the temperature rise in the medium and the acoustic wave generation. We obtain a direct relation between the acoustic waves and the electromagnetic external sources. Finally, we solve the multiwave inverse problem that consists in the recovery of the electric permittivity of the biological tissue from the measurements of the generated acoustic waves on the boundary of the sample.


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Additional Information

Faouzi Triki
Affiliation: Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin-d’Hères, France
Email: Faouzi.Triki@univ-grenoble-alpes.fr

Margaux Vauthrin
Affiliation: Laboratoire Jean Kuntzmann, UMR CNRS 5224, Université Grenoble-Alpes, 700 Avenue Centrale, 38401 Saint-Martin-d’Hères, France
Email: Margaux.Vauthrin@univ-grenoble-alpes.fr

DOI: https://doi.org/10.1090/qam/1502
Keywords: Inverse problem, photoacoustic, nanoparticle, plasmonic
Received by editor(s): January 23, 2017
Received by editor(s) in revised form: December 23, 2017
Published electronically: February 22, 2018
Additional Notes: The work of the first author was partially supported by Labex PERSYVAL-Lab (ANR-11-LABX-0025-01)
Article copyright: © Copyright 2018 Brown University

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