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Title	On the Helmholtz equations with sign changing coefficients
Creator	Nguyen, Hoai-Minh
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2015-09-02T09:52
Description	This talk is devoted to various properties and applica- tions of the Helmholtz equations with sign changing coefficients. These equations are used to model negative index materials which are artifi- cial structures whose refractive index are negative over some frequency range. These materials were first investigated theoretically by Veselago in 1964 and their existence was confirmed experimentally by Shelby et al. in 2001. The study of these equations faces two difficulties. First the ellipticity and the compactness are lost in general due to the changing sign coefficients. Second, the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others as the loss (the viscosity) goes to 0, might occur. In this talk, I will present several remarkable properties of these equations and their applications such as cloaking and superlensing using complementary media and cloaking an object via anomalous localized resonance. Various conditions under which the equations are stable are also presented. Some useful tech- niques dealing with these equations such as reflecting and removing localized singularity techniques are mentioned.
Extent	51 minutes
Subject	Mathematics Partial differential equations Calculus of variations and optimal control; optimization
Geographic Location	Banff (Alta.)
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Ecole Polytechnique Federale de Lausanne, EPFL
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2016-03-11
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0228166
URI	http://hdl.handle.net/2429/57142
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Postdoctoral
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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