{"id":115,"date":"2024-10-28T22:35:29","date_gmt":"2024-10-29T01:35:29","guid":{"rendered":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/?p=115"},"modified":"2024-11-04T15:06:55","modified_gmt":"2024-11-04T18:06:55","slug":"tbd","status":"publish","type":"post","link":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/2024\/10\/tbd\/","title":{"rendered":"Reconstructing elastic strain fields from its Longitudinal Ray Transform"},"content":{"rendered":"<div class=\"\"><b class=\"\"><span class=\"\">D\u00cdA \/ HORA:<\/span><\/b><span class=\"\"> Viernes 8 de noviembre 2024 \/ 15:00 &#8211; 16:00<\/span><\/div>\n<div><strong>EXPOSITOR: Mat\u00edas Courdurier<\/strong>,\u00a0 Facultad de Matem\u00e1ticas, Universidad Cat\u00f3lica de Chile.<\/div>\n<div class=\"\"><\/div>\n<div class=\"\">\n<div class=\"\">\n<p><b class=\"\"><span class=\"\">RESUMEN<\/span><\/b><span class=\"\"><span class=\"\">: <\/span><\/span>In the problem of Bragg-edge elastic strain tomography, measurements are obtained from energy resolved neutron transmission imaging, which provides information about the Longitudinal Ray Transform (LRT) of the elastic strain field. The goal is to recover the elastic strain field by inverting its LRT.<\/p>\n<p>The inversion of the ray transform for tensor fields is a well studied problem [1]. It is known that only the solenoidal part of symmetric tensor fields can be recovered from their LRT, there are inversion formulas available that reconstruct such solenoidal component and there are stability estimates for such reconstruction.<\/p>\n<p>Nonetheless, by taking into account that elastic strain fields additionally satisfy an equilibrium equation, it is possible to also recover the potential part of the elastic strain, for simply connected object [3], or under some extra requirements [2].<\/p>\n<p>In this talk I will present the problem of inverting the LRT for elastic strain tomography that arises from energy resolved neutron transmission imaging,\u00a0 I will recall the classic results about the inversion of the ray transform for tensor fields, and I will present the contributions of [2,3] dealing with the reconstruction of the potential part of the elastic strain field using the equilibrium equation that is satisfied.<\/p>\n<p>[1] V. A. Sharafutdinov, Integral geometry of tensor fields, Vol. 1, Walter de Gruyter, 2012.<\/p>\n<p>[2] C M Wensrich, S Holman, M Courdurier, W R B Lionheart, A P Polyakova and I E Svetov, Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields, Inverse Problems, Volume 40, Number 7, 2024.<\/p>\n<p>[3] C M Wensrich, S Holman, W R B Lionheart, M Courdurier, A P Polyakova, I E Svetov, T Doubikin, General reconstruction of elastic strain fields from their Longitudinal Ray Transform, arXiv:2408.10250, 2024.<\/p>\n<\/div>\n<div><\/div>\n<p><span class=\"\"><b class=\"\">IDIOMA: <\/b>Espa\u00f1ol<\/span><\/p>\n<\/div>\n<div class=\"\"><b class=\"\"><span class=\"\">LUGAR<\/span><\/b><span class=\"\">: <\/span><span class=\"\">Auditorio del Departamento de Matem\u00e1tica y Ciencia de la Computaci\u00f3n, Universidad de Santiago de Chile<br \/>\n<\/span><\/div>\n<div><\/div>\n<div class=\"\"><span class=\"\"><strong>DIRECCI\u00d3N:<\/strong> Av. Libertador Bernardo O&#8217;Higgins 3363, Estaci\u00f3n Central. <a href=\"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/lugar\/\">C\u00f3mo llegar<\/a>.<\/span><\/div>\n<div><\/div>\n<div class=\"\"><strong>MODALIDAD:<\/strong> Presencial y transmisi\u00f3n online por Microsoft Teams.<\/div>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Mat\u00edas Courdurier,\u00a0 Facultad de Matem\u00e1ticas, Universidad Cat\u00f3lica de Chile.<\/p>\n","protected":false},"author":116,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-115","post","type-post","status-publish","format-standard","hentry","category-seminarios"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/comments?post=115"}],"version-history":[{"count":5,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/115\/revisions"}],"predecessor-version":[{"id":132,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/posts\/115\/revisions\/132"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/media?parent=115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/categories?post=115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/seminarioipct\/wp-json\/wp\/v2\/tags?post=115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}