{ "items" : [ { "id" : "http://www.idref.fr/213407353/id" "properties" : { "http://www.w3.org/1999/02/22-rdf-syntax-ns#type" : [ "http://purl.org/vocab/frbr/core#Work", "http://rdaregistry.info/Elements/c/C10001" ] , "http://id.loc.gov/vocabulary/relators/ths" : [ "http://www.idref.fr/08757201X/id", "http://www.idref.fr/154306878/id", "http://www.idref.fr/032076134/id" ] , "http://id.loc.gov/vocabulary/relators/aut" : [ "http://www.idref.fr/154307998/id" ] , "http://www.w3.org/2004/02/skos/core#altLabel" : [ "Mathematical and numerical study of highly contrasted photonic cristals" ] , "http://purl.org/dc/elements/1.1/subject" : [ "Homog\u00E9n\u00E9isation (\u00E9quations diff\u00E9rentielles)", "Cristaux photoniques", "M\u00E9tamat\u00E9riaux", "\u00C9quations aux d\u00E9riv\u00E9es partielles", "Maxwell, \u00C9quations de", "Th\u00E8ses et \u00E9crits acad\u00E9miques" ] , "http://www.w3.org/2004/02/skos/core#prefLabel" : [ "Etude math\u00E9matique et num\u00E9rique de cristaux photoniques fortement contrast\u00E9s" ] , "http://purl.org/dc/terms/language" : [ "http://lexvo.org/id/iso639-3/fra" ] , "http://purl.org/dc/terms/subject" : [ "http://www.idref.fr/027225402/id", "http://www.idref.fr/052653757/id", "http://www.idref.fr/028637739/id", "http://www.idref.fr/027253139/id", "http://www.idref.fr/132896826/id", "http://www.idref.fr/033088470/id" ] , "http://purl.org/dc/elements/1.1/title" : [ "Etude math\u00E9matique et num\u00E9rique de cristaux photoniques fortement contrast\u00E9s" ] , "http://id.loc.gov/vocabulary/relators/dgg" : [ "http://www.idref.fr/031122337/id" ] , "http://www.w3.org/2004/02/skos/core#note" : [ "Dans cette th\u00E8se, on se propose d\u2019\u00E9tudier rigoureusement le comportement macroscopique de mat\u00E9riaux composites fortement contrast\u00E9s dans le cadre de l\u2019\u00E9lectromagn\u00E9tisme. Nous consid\u00E9rons des structures constitu\u00E9es de micro-inclusions r\u00E9parties p\u00E9riodiquement (ou al\u00E9atoirement), au sein desquelles un mat\u00E9riau de tr\u00E8s grande permittivit\u00E9, ou de tr\u00E8s grande conductivit\u00E9, sera dispos\u00E9. En pratique, une telle structure occupe un domaine born\u00E9 3D et est \u00E9clair\u00E9e par une onde incidente monochromatique (de fr\u00E9quence fix\u00E9e) venant de l\u2019infini. Notre approche math\u00E9matique consiste \u00E0 passer \u00E0 la limite dans le syst\u00E8me de Maxwell d\u00E9crivant le probl\u00E8me de diffraction lorsque la distance s\u00E9parant les inclusions tend vers z\u00E9ro, et que l\u2019indice \u00E9lectromagn\u00E9tique des inclusions tend vers l\u2019infini (\u00AB fort contraste \u00BB). Nous \u00E9tudions deux types de structures diffractantes 3D qui permettent de r\u00E9aliser des mat\u00E9riaux de permittivit\u00E9 ou perm\u00E9abilit\u00E9 n\u00E9gatives. L\u2019\u00E9tude asymptotique et bas\u00E9e sur la m\u00E9thode de convergence double-\u00E9chelle (parfois dans une variante stochastique), et les probl\u00E8mes sur la cellule de p\u00E9riodicit\u00E9 qui en r\u00E9sultent sont r\u00E9solus par m\u00E9thode spectrale. Ceci permet d\u2019obtenir explicitement les tenseurs effectifs en fonction de la fr\u00E9quence, mettant ainsi en \u00E9vidence leurs grandes variations autour de fr\u00E9quences de r\u00E9sonances.", "This thesis is to develop the macroscopic behaviour of highly contrasted composite materials in an electromagnetic framework. We consider structures made of periodically (or randomly) distributed micro-inclusions made of high conductivity or high permittivity medium. Actually, such a structure is to be found in a three-dimensional bounded domain which is illuminated by an infinity-coming monochromatic incident wave. Our mathematical approach consists in passing to the limit in the Maxwell system describing the diffraction problem when the distance between inclusions goes to zero while the electromagnetic constant of inclusions goes to infinity (\u201Chigh contrast\u201D) We are studying two 3D diffracting structures which lead to negative permittivity or permeability materials. The asymptotic study is based on the two-scale convergence method (sometimes in a stochastic way), and the resulting unit cell problems are solved by spectral method. This leads to an explicit formulation of the effective tensor according to the frequency, which highlights their huge variations around the so-called resonant frequencies." ] , "http://purl.org/dc/elements/1.1/type" : [ "Text" ] , "http://iflastandards.info/ns/isbd/elements/P1001" : [ "http://iflastandards.info/ns/isbd/terms/contentform/T1009" ] , "http://rdaregistry.info/Elements/w/P10219" : [ "2010" ] , "http://rdaregistry.info/Elements/u/P60049" : [ "http://rdaregistry.info/termList/RDAContentType/1020"] } } }