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Ph. D. thesis

Analysis of two wave propagation phenomena : 1) Space–time focusing in acoustics ; 2) Transmission between a dielectric and a metamaterial.,
Maxence Cassier, Ecole Polytechnique, 2014.

Published or accepted papers

Imaging small polarizable scatterers with polarization data,
Patrick Bardsley, Maxence Cassier and Fernando Guevara Vasquez, 39 pages (on Arxiv), accepted for publication in Inverse Problems.

Spectral theory for Maxwell's equations at the interface of a metamaterial. Part I: Generalized Fourier transform.,
Maxence Cassier, Christophe Hazard and Patrick Joly, Communications in Partial Differential Equations, vol 42 No 11, Pages 1707-1748, 2017.

Mathematical models for dispersive electromagnetic waves: an overview,
Maxence Cassier, Patrick Joly and Maryna Kachanovska, Computers and Mathematics with Applications, vol 74 No 11, Pages 2792-2830, 2107.

Imaging polarizable dipoles,
Maxence Cassier and Fernando Guevara Vasquez, SIAM J. Imaging Sci., vol 10 No. 3, pp. 1381-1415, 2017.

Bounds on Herglotz functions and fundamental limits of broadband passive quasi-static cloaking,
Maxence Cassier and Graeme W. Milton, Journal of Mathematical Physics 58 (7) 071504 (27 pages), 2017.

Space-time focusing on unknown scatterers,
Maxence Cassier and Christophe Hazard, Wave Motion,vol. 51(8) pp. 1254-1272, 2014.

Multiple scattering of acoustic waves by small sound-soft obstacles in two dimensions: mathematical justification of the Foldy--Lax model,
Maxence Cassier and Christophe Hazard, Wave Motion, vol. 50 (1), pp. 18-28, 2013.

Papers in preparation

Spectral theory for Maxwell's equations at the interface of a metamaterial. Part II: Limiting absorption and limiting amplitude principles,
Maxence Cassier, Christoph Hazard and Patrick Joly.

Bounds on the DtN map and fundamental limits of broadband passive near-cloaking for the conductivity problem,
Maxence Cassier, Graeme W. Milton and Aaron Welter.

Book chapters

Electromagnetic waves in photonic crystals: laws of dispersion, causality and analytical properties,
Boris Gralak, Maxence Cassier, Guillaume Demésy and Sébastien Guenneau, 31 pages, to appear in a book on electromagnetism edited by Vadim Merkel et Igor Tsuckerman dans WS Reference Set.

Analyticity of the Dirichlet-to-Neumann map for the time-harmonic Maxwell's equations,
Maxence Cassier, Aaron Welters and Graeme W. Milton, chapter in Extending the theory of composites to other areas of science edited by Graeme W. Milton and reviewed by the Journal of Applied Mechanics and SIAM Review, pp 95-122, 2016.

A rigorous approach to the field recursion method for a two-component composites with isotropic phases,
Maxence Cassier, Aaron Welters and Graeme W. Milton, chapter in Extending the theory of composites to other areas of science edited b Graeme W. Milton and reviewed by the Journal of Applied Mechanics and SIAM Review, pp. 287-307, 2016.

Reports

Imaging small scatterers with electromagnetic waves,
Maxence Cassier and Fernando Guevara Vasquez 3 pages, to appear in Oberwolfach reports 2017.

Selective focusing for time-dependent waves,
Maxence Cassier, Christophe Hazard and Patrick Joly, Oberwolfach report No. 03 2013 , pp. 150-153.

Conference proceedings

Imaging polarizable dipoles,
Maxence Cassier and Fernando Guevara Vasquez, Waves 2017 (Minneapolis) conference proceedings, 2 pages.

Limiting amplitude principle for a two-layered medium composed of a dielectric material and a metamaterial,
Maxence Cassier,Christophe Hazard and Patrick Joly, Waves 2015 (Karlsruhe) conference proceedings, 2 pages.

Selective focusing on unknown scatterers,
Maxence Cassier,Christophe Hazard and Patrick Joly, Waves 2013 (Tunis) conference proceedings, pp. 129-130.

Multiple acoustic scattering by small obstacles in two dimensions,
Maxence Cassier and Christophe Hazard, Waves 2011 (Vancouver) conference proceedings, pp. 631-634.

Using time reversal for space-time focusing of acoustic waves,
Maxence Cassier and Christophe Hazard, 5ème Colloque sur les Tendances des Applications Mathématiques en Tunisie, Algérie, Maroc (TAMTAM) proceedings, 2011, 6 pages.