Authors : Joly, Patrick (Author of the conference)
CIRM (Publisher )
Abstract :
In collaboration with Maxence Cassier (Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel) and Luis Alejandro Rosas Martinez (POEMS, CNRS, INRIA, ENSTA Paris).
It is well-known that electromagnetic dispersive structures such as metamaterials obey mathematical models whose construction, based on fundamental physical such as causality and passivity, emphasizes the role of Herglotz functions. Among these models an important class is provided by generalized Drude-Lorentz models, see e.g. [1]. In this work, we are interested in dissipative Drude-Lorentz open structures and we wish to quantify the loss in such media in terms of the long time decay rate of the electromagnetic energy for the corresponding Cauchy problem. By using two different approaches, one based on (frequency dependent) Lyapounov estimates and the other on modal analysis, we show that this decay is polynomial in time. These results generalize a part the ones obtained for bounded media in [2] via a quite different method based on the notion of cumulated past history and semi-group theory. A great advantage of the approaches developed here is to be directly connected to the physics of the system via energy balances or modes behavior.
MSC Codes :
Film maker : Hennenfent, Guillaume
Language : English
Available date : 20/06/2022
Conference Date : 25/05/2022
Subseries : Research talks
arXiv category : Analysis of PDEs ; Numerical Analysis
Mathematical Area(s) : Numerical Analysis & Scientific Computing ; Mathematical Physics
Format : MP4 (.mp4) - HD
Video Time : 00:58:04
Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
Download : https://videos.cirm-math.fr/2022-05-25_Joly.mp4
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Event Title : Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials / Fonctions de Herglotz-Nevanlinna et leurs applications aux systèmes dispersifs et aux matériaux composites Event Organizers : Bonnet-Ben Dhia, Anne-Sophie ; Cassier, Maxence ; Gralak, Boris ; Luger, Annemarie ; Milton, Graeme Dates : 23/05/2022 - 27/05/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2225.html
DOI : 10.24350/CIRM.V.19919903
Cite this video as:
Joly, Patrick (2022). Long time behaviour of the solution of Maxwell's equations in dissipative Lorentz media. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19919903
URI : http://dx.doi.org/10.24350/CIRM.V.19919903
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See Also
Bibliography
- CASSIER, Maxence, JOLY, Patrick, et KACHANOVSKA, Maryna. Mathematical models for dispersive electromagnetic waves: an overview. Computers & Mathematics with Applications, 2017, vol. 74, no 11, p. 2792-2830. - https://doi.org/10.1016/j.camwa.2017.07.025
- NICAISE, Serge et PIGNOTTI, Cristina. Asymptotic behavior of dispersive electromagnetic waves in bounded domains. Zeitschrift für angewandte Mathematik und Physik, 2020, vol. 71, no 3, p. 1-26. - http://dx.doi.org/10.1007/s00033-020-01297-6