{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T15:19:27Z","timestamp":1785424767422,"version":"3.56.0"},"reference-count":29,"publisher":"National Academy of Sciences","issue":"28","license":[{"start":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T00:00:00Z","timestamp":1783555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"MEC | Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2024-156067NB-I00"],"award-info":[{"award-number":["PID2024-156067NB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMR-2003659"],"award-info":[{"award-number":["DMR-2003659"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100023561","name":"Ministerio de Universidades","doi-asserted-by":"publisher","award":["FPU20\/03682"],"award-info":[{"award-number":["FPU20\/03682"]}],"id":[{"id":"10.13039\/501100023561","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,7,14]]},"abstract":"<jats:p>We observe the formation of stable, magnetic field induced, alignment inversion walls, also called Helfrich walls, in nematic liquid crystals (NLCs) confined to a toroidal droplet with tangential anchoring at the boundaries. Walls are rare in NLCs due to their high energy compared to lower-dimensional defect structures. However, we find that Helfrich walls naturally form, transform, and migrate in this unconventional toroidal setting, generating intricate director-field configurations due to the interplay of confining geometry and external fields. Interestingly, the presence and number of point defects in the zero field nematic configuration of the toroid influences the types of walls that arise. In the absence of point defects, splay-bend walls emerge. By contrast, when a point defect pair exists on the toroidal surface, a wall not previously classified by Helfrich, and that involves both twist and splay-bend distortions, forms, and transforms. Our experiments and numerical simulations enable the quantification and elucidation of the physics behind the formation and transformation of these wall structures, extending the class of walls that were believed to occur in NLCs.<\/jats:p>","DOI":"10.1073\/pnas.2603043123","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T17:57:37Z","timestamp":1783619857000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Helfrich walls in nematic toroidal droplets in the presence of magnetic fields"],"prefix":"10.1073","volume":"123","author":[{"given":"Javier","family":"Rojo-Gonzalez","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/021018s57","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Condensed Matter Physics, University of Barcelona","place":["Barcelona, Spain"]},{"id":[{"id":"https:\/\/ror.org\/021018s57","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute of Complex Systems (UBICS), University of Barcelona","place":["Barcelona, Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1950-9556","authenticated-orcid":false,"given":"Charlotte G.","family":"Slaughter","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00b30xv10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, University of Pennsylvania","place":["Philadelphia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4009-0974","authenticated-orcid":false,"given":"Peter J.","family":"Collings","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00b30xv10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, University of Pennsylvania","place":["Philadelphia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jay","family":"Kikkawa","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00b30xv10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, University of Pennsylvania","place":["Philadelphia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4744-2706","authenticated-orcid":false,"given":"Arjun G.","family":"Yodh","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00b30xv10","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics and Astronomy, University of Pennsylvania","place":["Philadelphia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1286-9809","authenticated-orcid":false,"given":"Alberto","family":"Fernandez-Nieves","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/021018s57","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Condensed Matter Physics, University of Barcelona","place":["Barcelona, Spain"]},{"id":[{"id":"https:\/\/ror.org\/021018s57","id-type":"ROR","asserted-by":"publisher"}],"name":"Institute of Complex Systems (UBICS), University of Barcelona","place":["Barcelona, Spain"]},{"id":[{"id":"https:\/\/ror.org\/0371hy230","id-type":"ROR","asserted-by":"publisher"}],"name":"Institucio Catalana de Recerca i Estudis Avancats","place":["Barcelona, Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,7,9]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.51.591"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0217751X9400090X"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-021-04105-x"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.120406"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/14786430600593016"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-020-0235-z"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.201904784"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-023-00602-2"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature21718"},{"key":"e_1_3_4_10_2","doi-asserted-by":"crossref","unstructured":"PGd Gennes J Prost The physics of Liquid Crystals (Oxford University Press 1995).","DOI":"10.1063\/1.2808028"},{"key":"e_1_3_4_11_2","volume-title":"Chapter 1- Liquid Crystals for Electro-Optic Applications, page 1\u201366","author":"Kelly S. M.","year":"2001","unstructured":"S. M. Kelly, M. O\u2019Neill, Chapter 1- Liquid Crystals for Electro-Optic Applications, page 1\u201366 (Academic Press, 2001)."},{"key":"e_1_3_4_12_2","doi-asserted-by":"crossref","unstructured":"G. P. Alexander B. G. G. Chen E. A. Matsumoto R. D. Kamien Colloquium: Disclination loops point defects and all that in nematic liquid crystals. Rev. Mod. Phys. 84 497\u2013514 (2012).","DOI":"10.1103\/RevModPhys.84.497"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1039\/f29726800001"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017-00548-x"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphys1920"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.21.1518"},{"key":"e_1_3_4_17_2","volume-title":"Magnetostatic Principles in Ferromagnetism, Selected Topics in Solid State Physics","author":"Brown W.","year":"1962","unstructured":"W. Brown, Magnetostatic Principles in Ferromagnetism, Selected Topics in Solid State Physics (North-Holland Publishing Company, 1962)."},{"key":"e_1_3_4_18_2","volume-title":"Magnetism in Condensed Matter, Oxford Master Series in Condensed Matter Physics 4","author":"Blundell S.","year":"2001","unstructured":"S. Blundell, Magnetism in Condensed Matter, Oxford Master Series in Condensed Matter Physics 4 (OUP Oxford, 2001)."},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1039\/D0SM00340A"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/0038-1098(72)90588-1"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0009-2614(72)80249-5"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.023261"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1080\/026782997207894"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1051\/jphyscol:1975135"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms9067"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1221380110"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1039\/C4SM00076E"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.6.L012065"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.108.024704"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2603043123","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2603043123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T17:57:46Z","timestamp":1783619866000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2603043123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,9]]},"references-count":29,"journal-issue":{"issue":"28","published-print":{"date-parts":[[2026,7,14]]}},"alternative-id":["10.1073\/pnas.2603043123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2603043123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,9]]},"assertion":[{"value":"2026-01-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-05-19","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-09","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2603043123"}}