Page UMA de Lucas Chesnel
Activités de recherche
J'ai réalisé ma thèse sous la direction d' Anne-Sophie Bonnet-BenDhia et Patrick Ciarlet. Je me suis intéressé à des problèmes de transmission présentant des changements de signe. Ces problèmes apparaissent dans divers contextes. On les rencontre notamment dans le cadre de
- la modélisation des phénomènes électromagnétiques en régime harmonique dans les milieux diélectrique/métamatériau;
- la modélisation des plasmons de surface, des ondes qui se propagent, à fréquences optiques, à l'interface entre un diélectrique et un métal;
- l'étude du problème de transmission intérieur, un problème spectral qui apparaît en théorie du scattering.
Activités d'enseignement
Chargé de TD (2009-2012) pour le cours MA201 de l'Ensta : Introduction à la méthode des éléments finis.
Chargé de TD (2009-2011) pour le cours MA205 de l'Ensta : Fonctions de variable complexe.
Chargé de TD (2010-2012) pour le cours MA261 de l'Ensta : Introduction au Calcul Scientifique.
Chargé de TD (2011-2012) pour le cours C7-1 de l'Ensta : Les équations de Maxwell et leur approximation.
Chargé de TD (2009-2011) pour le cours MA205 de l'Ensta : Fonctions de variable complexe.
Chargé de TD (2010-2012) pour le cours MA261 de l'Ensta : Introduction au Calcul Scientifique.
Chargé de TD (2011-2012) pour le cours C7-1 de l'Ensta : Les équations de Maxwell et leur approximation.
Publications
Articles (revues avec comité de lecture)
2022
- Maxwell's equations with hypersingularities at a conical plasmonic tip
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Journal de mathématiques pures et appliquées, vol. 161, pp. 70-110, feb, 2022
2021
- A continuation method for building invisible obstacles in waveguides
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Quarterly Journal of Mechanics and Applied Mathematics, 2021
2020
- Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides
and
Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, may, 2020 - Homogenization of Maxwell's equations and related scalar problems with sign-changing coefficients
, , and
Annales de la Faculté des Sciences de Toulouse, dec, 2020 
- On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates
and
M2AN, vol. 54-2, pp. 493-529, feb, 2020 [
] - Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
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Asymptotic Analysis, IOS Press, 2020
2019
- On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
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Communications in Mathematical Sciences, vol. 17/6, pp. 1487 – 1529, dec, 2019 [ ] 
2018
- On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
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sep, 2018 [ ] - Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem
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Proceedings of the Royal Society A, 2018 [ ]
2017
- Eigenvalue problems with sign-changing coefficients
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C. R. Acad. Sci. Paris, Ser. I, vol. 355, pp. 671-675, 2017 - Perfect transmission invisibility for waveguides with sound hard walls
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Journal de Mathématiques Pures et Appliquées, 2017
2016
- On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients
, , and
J. Comput. Phys., vol. 322, pp. 224-247, 2016
2015
- Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions
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Inverse Problems, vol. 31, 2015 [ ]
2014
- T-coercivity for the Maxwell problem with sign-changing coefficients
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Communications in Partial Differential Equations, vol. 39, pp. 1007-1031, 2014 - Two-dimensional Maxwell's equations with sign-changing coefficients
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Applied Numerical Mathematics, vol. 79, pp. 29-41, 2014 [ ]
2013
- Radiation condition for a non-smooth interface between a dielectric and a metamaterial
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Math. Models Meth. App. Sci., vol. 3, aug, 2013 [ ] - Strongly oscillating singularities for the interior transmission eigenvalue problem
and
Inverse Problems, vol. 19(10), pp. 104004, 2013 - T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients
and
Numer. Math., vol. 124, pp. 1-19, 2013 [ ]
2012
- Interior transmission eigenvalue problem for Maxwell's equations: the T-coercivity as an alternative approach
Inverse problems, vol. 28, pp. 065005, 2012 [ ] - T-coercivity for scalar interface problems between dielectrics and metamaterials
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Math. Mod. Num. Anal., vol. 46, pp. 1363-1387, 2012 [ ]
2011
- Compact imbeddings in electromagnetism with interfaces between classical materials and meta-materials
and
SIAM J. Math. Anal., vol. 43(5), pp. 2150-2169, 2011 [ ] - On the use of T-coercivity to study the Interior Transmission Eigenvalue Problem.
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C. R. Acad. Sci., Ser. I, vol. 340, 2011 [ ]
Conférences internationales avec actes
2013
- Negative materials and corners in electromagnetism
, , , and
Report No.3/2013 of Mathematisches Forschungsinstitut Oberwolfach "Computational Electromagnetism and Acoustics", Oberwolfach., Allemagne, 2013 [ ] - Plasmonic cavity modes: black-hole phenomena captured by Perfectly Matched Layers
, , and
PIERS, Stockholm, aug, 2013 [ ]
Conférences sans actes
2014
- Leaky modes in a non dissipative plasmonic waveguide with a bounded cross section
, , and
OWTNM, Nice, France, jun, 2014 - Revealing guides modes in a plasmonic waveguide using Perfectly Matched Layers at the corners
, , and
KOZWaves, Newcastle, Australia, feb, 2014 [ ]
2013
- Negative materials and corners in electromagnetism
, , , and
Conference on Computational Electromagnetism and Acoustics, Oberwolfach, Allemagne, 2013 [ ] - Plasmonic cavity modes with sign changing permittivity
, , , and
WAVES, Tunisia, jun, 2013 [ ]
2012
- Black holes in metamaterials
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MATHmONDES 2012, Reading, jul, 2012 - Interior Transmission Eigenvalue Problem and T-coercivity
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Picof conference, Palaiseau, 2012 [ ] - Mathematical analysis of time harmonic Maxwell equations with sign changing coefficients
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Journées de Metz 2012, 2012 - On the use of Perfectly Matched Layers to capture strongly confined plasmonic edge waves
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ETOPIM (Electrical, Transport and Optical Properties of Inhomogeneous Media), Marseille, sep, 2012 - PhD defense. Investigation of some transmission problems with sign changing coefficients. Application to metamaterials.
Ensta Paris, Palaiseau, oct 2012 [ ] - Time harmonic Maxwell equations with sign changing coefficients
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Workshop: around scattering by obstacles and billiards, Aveiro, 2012 [ ] - Transmission eigenvalue problems with sign-changing coefficients
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Picof conference, Palaiseau, 2012 [ ] - Transmission problems with sign-changing coefficients
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Congrès de MÉthodes numériques et MOdélisation, Tunis, dec, 2012
2011
- Les problèmes mathématiques et numériques posés par la simulation des interfaces entre diélectriques et métamatériaux
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Colloque National Métamatériaux 2011, Orsay, 2011 [ ] - Problèmes de propagation d'ondes dans un milieu diélectrique métamatériau
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Congrès d'inauguration de la Fondation Mathématique Jacques Hadamard, Ecole Polytechnique, Palaiseau, 2011 [ ] - Radiation condition for a non-smooth interface between a dielectric and a metamaterial
, and
10th International Conference on Mathematical and Numerical Aspects of Waves, Waves 2011, Vancouver, 2011 [ ] - Radiation condition for a non-smooth interface between a dielectric and a metamaterial
, , and
Numerical Electromagnetics & Industrial Applications (NELIA 2011), Santiago de Compostela, 2011 [ ] - Radiation condition for a non-smooth interface between a dielectric and a metamaterial
, and
10th International Conference on Mathematical and Numerical Aspects of Waves, Waves 2011, Vancouver, 2011 [ ] - Scalar waves transmission problems with sign-changing coefficients
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ICIAM conference, Vancouver, 2011 [ ]
2010
- Electromagnetic wave propagation at classical/metamaterial interfaces - Mathematical aspects
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Workshop : Metamaterials: Applications, Analysis and Modeling, IPAM (Los Angeles), 2010 [ ]
Thèse
2012
- Étude de quelques problèmes de transmission avec changement de signe. Application aux métamatériaux.
Ecole doctorale de l'Ecole Polytechnique (EDX) - ED 447, oct 2012 [ ]
Multimédia
2017
- A new complex spectrum associated to invisibility in waveguides
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Mathematical aspects of physics with non-self-adjoint operators, CIRM, Marseille, 2017