{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:28:23Z","timestamp":1787228903560,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>N\u00e9el walls and cross-tie walls are two structures commonly seen in ferromagnetic thin films. They are interesting because their internal length scales are not determined by dimensional analysis alone. This paper studies (a) the repulsive interaction of one-dimensional N\u00e9el walls and (b) the internal length scale of the cross-tie wall. Our analysis of (a) is mathematically rigorous; it provides, roughly speaking, the first two terms of an asymptotic expansion for the energy of a pair of interacting walls. Our analysis of (b) is heuristic, since it rests on an analogy between the cross-tie wall and an ensemble of N\u00e9el walls. This analogy, combined with our results on N\u00e9el walls and a judicious choice of parameter regime, yields a specific prediction for the internal length scale of a cross-tie wall. This prediction is consistent with the experimentally observed trends.<\/jats:p>","DOI":"10.1137\/s1540345902402734","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"57-104","source":"Crossref","is-referenced-by-count":24,"title":["Repulsive Interaction of N\u00e9el Walls, and the Internal Length Scale of the Cross-Tie Wall"],"prefix":"10.1137","volume":"1","author":[{"given":"Antonio","family":"DeSimone","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert V.","family":"Kohn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"M\u00fcller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felix","family":"Otto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2002017"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Antonio DeSimone, Robert Kohn, Stefan M\u00fcller, Felix Otto, Magnetic microstructures\u2014a paradigm of multiscale problems, Oxford Univ. Press, Oxford, 2000, 175\u20131901824443","DOI":"10.1093\/oso\/9780198505143.003.0016"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-8853(01)01356-7"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3028"},{"key":"R5","unstructured":"C. Garcia\u2013Cervera,\n                      Magnetic Domains and Magnetic Domain Walls\n                      , Ph.D. thesis, New York University, New York, NY, 1999."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01691548"},{"key":"R7","first-page":"145","volume":"26","author":"Holz A.","year":"1969","journal-title":"Z. Angew. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0044-2283","issn-type":"print"},{"key":"R8","unstructured":"A. Hubert and R. Sch\u00e4fer,\n                      Magnetic Domains\n                      , Springer, Berlin, 1998."},{"key":"R9","unstructured":"C. Melcher,\n                      The logarithmic tail of N\u00e9el walls in thin films\n                      , Arch. Ration. Mech. Anal., to appear."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1063\/1.1729367"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1002\/pssb.2220460136"}],"container-title":["Multiscale Modeling &amp; Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1540345902402734","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:01:08Z","timestamp":1787227268000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1540345902402734"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S1540345902402734"],"URL":"https:\/\/doi.org\/10.1137\/s1540345902402734","relation":{},"ISSN":["1540-3459","1540-3467"],"issn-type":[{"value":"1540-3459","type":"print"},{"value":"1540-3467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}