{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,4]],"date-time":"2026-11-04T23:50:26Z","timestamp":1793836226101,"version":"4.6.1"},"reference-count":73,"publisher":"American Physical Society (APS)","issue":"3","license":[{"start":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T00:00:00Z","timestamp":1789430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/link.aps.org\/licenses\/aps-default-license"}],"funder":[{"DOI":"10.13039\/501100000844","name":"European Space Agency","doi-asserted-by":"publisher","award":["1000012348"],"award-info":[{"award-number":["1000012348"]}],"id":[{"id":"10.13039\/501100000844","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,6,17]]},"DOI":"10.1103\/7y6z-4bwy","type":"journal-article","created":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T15:49:50Z","timestamp":1781711390000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Polar chiral active matter as a motile, disordered Josephson array: Information supercurrents and Goldstone spin waves"],"prefix":"10.1103","volume":"114","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3116-6209","authenticated-orcid":true,"given":"Magnus F","family":"Ivarsen","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/010x8gc63","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Saskatchewan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,9,15]]},"reference":[{"key":"7y6z-4bwyCc1R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1202032109","type":"journal-article"},{"key":"7y6z-4bwyCc2R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6633\/ac723d","type":"journal-article"},{"key":"7y6z-4bwyCc3R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-conmatphys-082321-035957","type":"journal-article"},{"key":"7y6z-4bwyCc4R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.10.021065","type":"journal-article"},{"key":"7y6z-4bwyCc5R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-022-00820-7","type":"journal-article"},{"key":"7y6z-4bwyCc6R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.crhy.2013.04.001","type":"journal-article"},{"key":"7y6z-4bwyCc7R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevFluids.7.034602","type":"journal-article"},{"key":"7y6z-4bwyCc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.048001","type":"journal-article"},{"key":"7y6z-4bwyCc9R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-014-1119-3","type":"journal-article"},{"key":"7y6z-4bwyCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.258101","type":"journal-article"},{"key":"7y6z-4bwyCc11R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-023-01442-3","type":"journal-article"},{"key":"7y6z-4bwyCc12R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-024-01817-0","type":"journal-article"},{"key":"7y6z-4bwyCc13R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-024-07074-z","type":"journal-article"},{"key":"7y6z-4bwyCc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.132.246503","type":"journal-article"},{"key":"7y6z-4bwyCc15R1","doi-asserted-by":"publisher","DOI":"10.1103\/hc9d-fpmj","type":"journal-article"},{"key":"7y6z-4bwyCc16R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.58.4828","type":"journal-article"},{"key":"7y6z-4bwyCc17R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.77.137","type":"journal-article"},{"key":"7y6z-4bwyCc18R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2007.06.025","type":"journal-article"},{"key":"7y6z-4bwyCc19R1","doi-asserted-by":"publisher","DOI":"10.1038\/nrmicro3491","type":"journal-article"},{"key":"7y6z-4bwyCc20R1","doi-asserted-by":"publisher","DOI":"10.1016\/0031-9163(62)91369-0","type":"journal-article"},{"key":"7y6z-4bwyCc21R1","volume-title":"Introduction to Superconductivity","author":"M. Tinkham","year":"2004","type":"book"},{"key":"7y6z-4bwyCc22R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.76.404","type":"journal-article"},{"key":"7y6z-4bwyCc23R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.22.1364","type":"journal-article"},{"key":"7y6z-4bwyCc24R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1651991","type":"journal-article"},{"key":"7y6z-4bwyCc25R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1656743","type":"journal-article"},{"key":"7y6z-4bwyCc26R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.104.054517","type":"journal-article"},{"key":"7y6z-4bwyCc27R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.115114","type":"journal-article"},{"key":"7y6z-4bwyCc28R1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-5155-6","type":"book","volume-title":"Turbulence and Self-Organization: Modeling Astrophysical Objects","author":"M.\u00a0Y. Marov","year":"2013"},{"key":"7y6z-4bwyCc29R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.104993","type":"journal-article"},{"key":"7y6z-4bwyCc30R1","doi-asserted-by":"publisher","DOI":"10.1103\/kynj-l87s","type":"journal-article"},{"key":"7y6z-4bwyCc31R1","doi-asserted-by":"crossref","unstructured":"P. Bhansali and J. Roychowdhury, Gen-Adler: The generalized Adler's equation for injection locking analysis in oscillators, in Proceedings of the Asia and South Pacific Design Automation Conference (IEEE, Piscataway, NJ, 2009), pp. 522\u2013527.","DOI":"10.1109\/ASPDAC.2009.4796533","type":"conference-proceedings"},{"key":"7y6z-4bwyCc32R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.92.062914","type":"journal-article"},{"key":"7y6z-4bwyCc33R1","volume-title":"Dynamics of Josephson Junctions and Circuits","author":"K.\u00a0K. Likharev","year":"1986","type":"book"},{"key":"7y6z-4bwyCc34R1","volume-title":"Solid State Physics","author":"R.\u00a0S. Newrock","year":"2000","type":"book"},{"key":"7y6z-4bwyCc35R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1706024","type":"journal-article"},{"key":"7y6z-4bwyCc36R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.68.2730","type":"journal-article"},{"key":"7y6z-4bwyCc37R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.66.2735","type":"journal-article"},{"key":"7y6z-4bwyCc38R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.857970","type":"journal-article"},{"key":"7y6z-4bwyCc39R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/7y6z-4bwy for a video of the simulation run described in the caption of Fig.   3.","type":"other"},{"key":"7y6z-4bwyCc40R1","unstructured":"J. D'Errico, SLM-shape language modeling, SLMShape Language Modeling, http:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/24443-slm-shapelanguage-modeling: Mathworks (2009).","type":"other"},{"key":"7y6z-4bwyCc41R1","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2010.0319","type":"journal-article"},{"key":"7y6z-4bwyCc42R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.55.1790","type":"journal-article"},{"key":"7y6z-4bwyCc43R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.50.395","type":"journal-article"},{"key":"7y6z-4bwyCc44R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.101.052601","type":"journal-article"},{"key":"7y6z-4bwyCc45R1","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2012.2484","type":"journal-article"},{"key":"7y6z-4bwyCc46R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.89.042806","type":"journal-article"},{"key":"7y6z-4bwyCc47R1","doi-asserted-by":"publisher","DOI":"10.1038\/nphys3035","type":"journal-article"},{"key":"7y6z-4bwyCc48R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1005766107","type":"journal-article"},{"key":"7y6z-4bwyCc49R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ad7ca0","type":"journal-article"},{"key":"7y6z-4bwyCc50R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.218001","type":"journal-article"},{"key":"7y6z-4bwyCc51R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-024-01637-2","type":"journal-article"},{"key":"7y6z-4bwyCc52R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41567-024-02651-5","type":"journal-article"},{"key":"7y6z-4bwyCc53R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42005-024-01720-8","type":"journal-article"},{"key":"7y6z-4bwyCc54R1","doi-asserted-by":"publisher","DOI":"10.1360\/nso\/20230086","type":"journal-article"},{"key":"7y6z-4bwyCc55R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aa8ed7","type":"journal-article"},{"key":"7y6z-4bwyCc56R1","doi-asserted-by":"publisher","DOI":"10.1038\/s42254-022-00445-3","type":"journal-article"},{"key":"7y6z-4bwyCc57R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.5.031003","type":"journal-article"},{"key":"7y6z-4bwyCc58R1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms10557","type":"journal-article"},{"key":"7y6z-4bwyCc60R1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms9396","type":"journal-article"},{"key":"7y6z-4bwyCc61R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.1226","type":"journal-article"},{"key":"7y6z-4bwyCc62R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.85.1143","type":"journal-article"},{"key":"7y6z-4bwyCc63R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.106.067202","type":"journal-article"},{"key":"7y6z-4bwyCc64R1","author":"M. Ivarsen","year":"2026","journal-title":"Zenodo","type":"dataset"},{"key":"7y6z-4bwyCc65R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017-01190-3","type":"journal-article"},{"key":"7y6z-4bwyCc66R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5039564","type":"journal-article"},{"key":"7y6z-4bwyCc67R1","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2026018","type":"journal-article"},{"key":"7y6z-4bwyCc68R1","volume-title":"Numerical Methods for Scientists and Engineers","author":"R.\u00a0W. Hamming","year":"1986","type":"book"},{"key":"7y6z-4bwyCc69R1","volume-title":"Turbulent Flows","author":"S.\u00a0B. Pope","year":"2000","type":"book"},{"key":"7y6z-4bwyCc70R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.028103","type":"journal-article"},{"key":"7y6z-4bwyCc71R1","volume-title":"Shallow Water Hydrodynamics: Mathematical Theory and Numerical Solution for a Two-Dimensional System of Shallow-Water Equations","author":"W.\u00a0Y. Tan","year":"1992","type":"book"},{"key":"7y6z-4bwyCc72R1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195108088.001.0001","type":"book","volume-title":"Lectures on Geophysical Fluid Dynamics","author":"R. Salmon","year":"1998"},{"key":"7y6z-4bwyCc73R1","volume-title":"Course of Theoretical Physics","author":"L.\u00a0D. Landau","year":"2013","type":"book"},{"key":"7y6z-4bwyCc74R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00159-009-0024-2","type":"journal-article"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/7y6z-4bwy","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/7y6z-4bwy\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T18:27:41Z","timestamp":1790879261000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/7y6z-4bwy"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,15]]},"references-count":73,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9]]}},"URL":"https:\/\/doi.org\/10.1103\/7y6z-4bwy","relation":{},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,15]]},"assertion":[{"value":"2025-12-21","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a92026 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"035417"}}