In 1939, Frenkel and Kontorova proposed a model for the motion of a dislocation (an imperfection in a crystal). The\u00a0model is simple, a chain of atoms following Newton’s equation of motion. The atoms interact with their nearest\u00a0neighbours via a harmonic spring and are exposed to a periodic (non-convex) on-site potential. Despite the simplicity,\u00a0the model has proved to be a mathematical challenge. Iooss and Kirchg\\”assner made a fundamental contribution\u00a0regarding the existence of small solutions. This talk will disucss the model and the method used by Iooss and\u00a0Kirchg\\”assner, and then present results for the coherent motion of dislocations. The latter results are joint work\u00a0with Boris Buffoni (Lausanne) and Hartmut Schwetlick (Bath).<\/p>\n","protected":false},"excerpt":{"rendered":"
In 1939, Frenkel and Kontorova proposed a model for the motion of a dislocation (an imperfection in a crystal). The\u00a0model is simple, a chain of atoms following Newton’s equation of motion. The atoms interact with their nearest\u00a0neighbours via a harmonic spring and are exposed to a periodic (non-convex) on-site potential. Despite the simplicity,\u00a0the model has\u2026 Read More »<\/a><\/span><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-127","post","type-post","status-publish","format-standard","hentry","category-abstracts"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/comments?post=127"}],"version-history":[{"count":0,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/posts\/127\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/media?parent=127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/categories?post=127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/swngsn\/wp-json\/wp\/v2\/tags?post=127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}