The APDE seminar on Monday, 08\/26 will be given by Thilo Simon in Evans 939 from 4:10 to 5pm. <\/p>\n\n\n\n
Title:
Skyrmions and stability of degree \u00b11 harmonic maps from the plane to the two-dimensional sphere.<\/p>\n\n\n\n
Abstract: Skyrmions are topologically nontrivial patterns in the magnetization of extremely thin ferromagnets. Typically thought of as stabilized by the so-called Dzyaloshinskii-Moriya interaction (DMI), or antisymmetric exchange interaction, arising in such materials, they are of great interest in the physics community due to possible applications in memory devices. <\/p>\n\n\n\n
In this talk, I will characterize skyrmions as local minimizers of a
two-dimensional limit of the full micromagnetic energy, augmented by DMI and retaining the nonlocal character of the stray field energy. In the regime of dominating Dirichlet energy, I will provide rigorous predictions for their size and “wall angles”. The main tool is a quantitative stability result for harmonic maps of degree \u00b1 1 from the plane to the two-dimensional sphere, relating the energy excess of any competitor to the homogeneous H\u00b9-distance to the closest harmonic map. This is joint work with Anne Bernand-Mantel and Cyrill B. Muratov.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"
The APDE seminar on Monday, 08\/26 will be given by Thilo Simon in Evans 939 from 4:10 to 5pm. Title: Skyrmions and stability of degree \u00b11 harmonic maps from the plane to the two-dimensional sphere. Abstract: Skyrmions are topologically nontrivial patterns in the magnetization of extremely thin ferromagnets. Typically thought of as stabilized by the […]<\/p>\n","protected":false},"author":104,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-724","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/724","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/104"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=724"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/724\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=724"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=724"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}