{"id":4,"date":"2011-12-08T11:55:34","date_gmt":"2011-12-08T11:55:34","guid":{"rendered":"http:\/\/project.inria.fr\/template1\/?page_id=4"},"modified":"2016-11-14T15:20:26","modified_gmt":"2016-11-14T14:20:26","slug":"home","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/mokabajour\/","title":{"rendered":"Home"},"content":{"rendered":"<h1 style=\"text-align: center;\"><span><strong>Welcome on MOKABAJOUR project website.<\/strong><\/span><\/h1>\n<h2>Who we are<\/h2>\n<p>The MOKABAJOUR team gathers researchers\/engineer from INRIA, CNRS and LJK:<\/p>\n<p><span style=\"text-decoration: underline;\">Researchers:<\/span><\/p>\n<ul>\n<li><a title=\"Page personnelle de Jean-David Benamou\" href=\"https:\/\/who.rocq.inria.fr\/Jean-David.Benamou\/\" target=\"_blank\">Jean-David Benamou<\/a> (INRIA DR)<\/li>\n<li><a title=\"Page personnelle de Quentin M\u00e9rigot\" href=\"http:\/\/quentin.mrgt.fr\/\" target=\"_blank\">Quentin M\u00e9rigot<\/a> (CNRS,Ceremade)<\/li>\n<li><a title=\"Page personnelle de Boris Thibert\" href=\"http:\/\/ljk.imag.fr\/membres\/Boris.Thibert\/\" target=\"_blank\">Boris Thibert<\/a> (LJK, U. Grenoble)<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline;\">Engineer:<\/span><\/p>\n<ul>\n<li>Simon Legrand (INRIA)<\/li>\n<\/ul>\n<h2>What we do<\/h2>\n<p>We design a software resolving the following inverse problem: define the shape of a mirror which reflects the light from a source to a defined target, distribution and support of densities being prescribed. Classical applications include the conception of solar oven, public lightning, car headlights&#8230;\u00a0Mathematical modeling of this problem, related to the optimal transport theory, takes the form of a nonlinear Monge-Ampere type PDE.\u00a0The high definition numerical resolution of these models remained until recently a largely open problem. MOKABAJOUR project aims to develop, using algorithms invented especially at INRIA and LJK, a reflector design software more efficient than geometrical methods used so far. The next step would be to realize and physically test prototype reflectors.<\/p>\n<p>Since a good picture is better than a long speech, here is a graphical representation of the problem. X and Y are two ensembles with prescribed densities and we look for u, which describes the shape of the reflector.<\/p>\n<p><a href=\"https:\/\/project.inria.fr\/mokabajour\/files\/2011\/12\/reflector_problem.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-88\" alt=\"reflector_problem\" src=\"https:\/\/project.inria.fr\/mokabajour\/files\/2011\/12\/reflector_problem-300x229.png\" width=\"300\" height=\"229\" srcset=\"https:\/\/project.inria.fr\/mokabajour\/files\/2011\/12\/reflector_problem-300x229.png 300w, https:\/\/project.inria.fr\/mokabajour\/files\/2011\/12\/reflector_problem.png 773w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<h2>Download page and wikis<\/h2>\n<p>You can find further information and download our application <a \" href=\"https:\/\/github.com\/simonlegrand\/reflector\" title=\"here\" target=\"_blank\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Welcome on MOKABAJOUR project website. Who we are The MOKABAJOUR team gathers researchers\/engineer from INRIA, CNRS and LJK: Researchers: Jean-David Benamou (INRIA DR) Quentin M\u00e9rigot (CNRS,Ceremade) Boris Thibert (LJK, U. Grenoble) Engineer: Simon Legrand (INRIA) What we do We design a software resolving the following inverse problem: define the shape of a mirror which reflects &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/project.inria.fr\/mokabajour\/\">Continue reading<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-4","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/pages\/4","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/comments?post=4"}],"version-history":[{"count":21,"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/pages\/4\/revisions"}],"predecessor-version":[{"id":459,"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/pages\/4\/revisions\/459"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/mokabajour\/wp-json\/wp\/v2\/media?parent=4"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}