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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.
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.