Menu:
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
Active exterior cloaking for the 2D Helmholtz equation with complex wavenumbers and application to thermal cloaking,
Maxence Cassier, Trent DeGiovanni, Sébastien Guenneau and Fernando Guevara Vasquez, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380 (2237) (29 pages), 2022.
Spectral theory for Maxwell's equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance,
Maxence Cassier, Christophe Hazard and Patrick Joly, 79 pages, Communications in
Partial Differential Equations, 47 (6) (2022), pages 1217-1295, 2022.
High contrast elliptic operators in honeycomb structures,
Maxence Cassier and Michael I. Weinstein, SIAM journal Multiscale Modeling and Simulation, Vol. 19, No. 4 :
pp. 1784-1856, 2021.
Active thermal cloaking and mimicking,
Maxence Cassier, Trent DeGiovanni, Sébastien Guenneau and Fernando Guevara Vasquez, Proceedings of the Royal Society A, 477(2249), 20200941 (27 pages), 2021.
Imaging small polarizable scatterers with polarization data,
Patrick Bardsley, Maxence Cassier and Fernando Guevara Vasquez, Inverse Problems 34.10: 104002 (40 pages), 2018.
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, 2017.
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.
Paper submitted
Long time behaviour of the solution of Maxwell's equations in dissipative generalized Lorentz materials (I) A frequency dependent Lyapunov function approach,
Maxence Cassier, Patrick Joly and Luis Alejandro Rosas Martínez, 33 pages on arxiv format.
Paper in preparation
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, in Compendium on Electromagnetic Analysis: From Electrostatics to Photonics: Fundamentals and Applications for Physicists and Engineers Volume 4 Optics and Photonics I, pp. 205-241, edited by World Scientific, 2020
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
Bounds on Herglotz functions and physical limits to broadband
passive cloaking in the quasitatic regime,
Maxence Cassier and Graeme W. Milton in
Oberwolfach report No. 39 2020, pp 1913--1916.
Imaging small scatterers with electromagnetic waves,
Maxence Cassier and Fernando Guevara Vasquez in
Oberwolfach report No. 24, pp 1516--1519,
2017.
Selective focusing for time-dependent waves,
Maxence Cassier,
Christophe Hazard and Patrick Joly, Oberwolfach report No. 03
2013 , pp. 150-153.
Conference proceedings
Active exterior cloaking and mimicking for the heat equation,Maxence Cassier, Trent DeGiovanni, Sébastien Guenneau and Fernando Guevara Vasquez, 2022 Sixteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), IEEE, pp. 178-180, 2022. TE band structure for honeycomb media in a high contrast regime
Maxence Cassier and Michael I. Weisntein,Waves 2022 (Palaiseau) conference proceedings, 2 pages. Long time behaviour for electromagnetic waves in dissipative Lorentz media.
Maxence Cassier, Patrick Joly and Luis Alejandro Rosas Martínez, Waves 2022 (Palaiseau) conference proceedings, 2 pages.
TE Band Structure for High Contrast Honeycomb Media.
Maxence Cassier and Michael I. Weinstein, 2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), IEEE, pp. 479-481, 2020.
Imaging small dielectric inclusions with polarization data,
Patrick Bardsley, Maxence Cassier and Fernando Guevara Vasquez Waves 2019 (Vienna)
conference proceedings, 2 pages.
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.