{"id":"https://openalex.org/W2999462745","doi":"https://doi.org/10.1007/s00332-019-09606-8","title":"Homogenization of Chiral Magnetic Materials: A Mathematical Evidence of Dzyaloshinskii\u2019s Predictions on Helical Structures","display_name":"Homogenization of Chiral Magnetic Materials: A Mathematical Evidence of Dzyaloshinskii\u2019s Predictions on Helical Structures","publication_year":2020,"publication_date":"2020-01-08","ids":{"openalex":"https://openalex.org/W2999462745","doi":"https://doi.org/10.1007/s00332-019-09606-8","mag":"2999462745"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-019-09606-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-019-09606-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-019-09606-8.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-019-09606-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006393097","display_name":"Elisa Davoli","orcid":"https://orcid.org/0000-0002-1715-5004"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"E. Davoli","raw_affiliation_strings":["Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-1715-5004","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058948920","display_name":"Giovanni Di Fratta","orcid":"https://orcid.org/0000-0003-0254-2957"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"G. Di Fratta","raw_affiliation_strings":["Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, TU Wien, Wiedner Hauptstra\u00dfe 8-10, 1040, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006393097"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":1996,"currency":"EUR","value_usd":2152},"fwci":1.3188,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.79363201,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"30","issue":"3","first_page":"1229","last_page":"1262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10049","display_name":"Magnetic properties of thin films","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10049","display_name":"Magnetic properties of thin films","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8371732831001282},{"id":"https://openalex.org/keywords/ferromagnetism","display_name":"Ferromagnetism","score":0.7545424699783325},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.5850057601928711},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5427009463310242},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5215599536895752},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.49721792340278625},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41208741068840027},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37424561381340027}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8371732831001282},{"id":"https://openalex.org/C82217956","wikidata":"https://www.wikidata.org/wiki/Q184207","display_name":"Ferromagnetism","level":2,"score":0.7545424699783325},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.5850057601928711},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5427009463310242},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5215599536895752},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.49721792340278625},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41208741068840027},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37424561381340027},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-019-09606-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-019-09606-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-019-09606-8.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00332-019-09606-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-019-09606-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-019-09606-8.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5699999928474426,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1535315551","display_name":null,"funder_award_id":"MA14-44","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G2556411738","display_name":null,"funder_award_id":"Grant SFB F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3534629015","display_name":null,"funder_award_id":"Grant MA14-44","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G3958550971","display_name":null,"funder_award_id":"V 662","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6669124832","display_name":null,"funder_award_id":"I 4052","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7830124546","display_name":null,"funder_award_id":"SFB F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320313284","display_name":"Isaac Newton Institute for Mathematical Sciences","ror":null},{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999462745.pdf","grobid_xml":"https://content.openalex.org/works/W2999462745.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W225012726","https://openalex.org/W1547249381","https://openalex.org/W1550742503","https://openalex.org/W1565212980","https://openalex.org/W1581406479","https://openalex.org/W1594665187","https://openalex.org/W1641896143","https://openalex.org/W1846798839","https://openalex.org/W1965401456","https://openalex.org/W1971359990","https://openalex.org/W1982223847","https://openalex.org/W1988077190","https://openalex.org/W1991395163","https://openalex.org/W1994047255","https://openalex.org/W2013306662","https://openalex.org/W2027239222","https://openalex.org/W2031783283","https://openalex.org/W2034258734","https://openalex.org/W2038561289","https://openalex.org/W2041064634","https://openalex.org/W2042153946","https://openalex.org/W2059755416","https://openalex.org/W2066202614","https://openalex.org/W2068046064","https://openalex.org/W2088081187","https://openalex.org/W2116801612","https://openalex.org/W2141824261","https://openalex.org/W2142903973","https://openalex.org/W2154419092","https://openalex.org/W2168406111","https://openalex.org/W2268743548","https://openalex.org/W2341275299","https://openalex.org/W2504943536","https://openalex.org/W2507447962","https://openalex.org/W2513682997","https://openalex.org/W2553339351","https://openalex.org/W2590880597","https://openalex.org/W2625683381","https://openalex.org/W2735806552","https://openalex.org/W2737756950","https://openalex.org/W2747653033","https://openalex.org/W2774446992","https://openalex.org/W2781570618","https://openalex.org/W2883699056","https://openalex.org/W2897725581","https://openalex.org/W2939965333","https://openalex.org/W2963621661","https://openalex.org/W2963674667","https://openalex.org/W3099787693","https://openalex.org/W3100076761","https://openalex.org/W3101033209","https://openalex.org/W3101124449","https://openalex.org/W3102098294","https://openalex.org/W3103699933","https://openalex.org/W3192328293","https://openalex.org/W4210453612","https://openalex.org/W4233371490","https://openalex.org/W6609199809"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W140119233","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W2025913943","https://openalex.org/W1492688905","https://openalex.org/W2524071042","https://openalex.org/W166351930","https://openalex.org/W2312674383"],"abstract_inverted_index":{"Abstract":[0],"In":[1,99],"this":[2],"paper,":[3],"we":[4,101],"investigate":[5],"the":[6,9,14,26,52,66,72,78,103],"influence":[7],"of":[8,17,28,49,51,55,75,80,86,89],"bulk":[10],"Dzyaloshinskii\u2013Moriya":[11],"interaction":[12],"on":[13,71,77,110],"magnetic":[15,53],"properties":[16],"composite":[18],"ferromagnetic":[19,90],"materials":[20],"with":[21],"highly":[22],"oscillating":[23],"heterogeneities,":[24],"in":[25],"framework":[27],"$$\\Gamma":[29],"$$":[30],"<mml:math":[31],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u0393</mml:mi></mml:math>":[32],"-convergence":[33],"and":[34],"2-scale":[35],"convergence.":[36],"The":[37],"homogeneous":[38],"energy":[39],"functional":[40],"resulting":[41],"from":[42],"our":[43,59],"analysis":[44],"provides":[45],"an":[46],"effective":[47],"description":[48],"most":[50],"composites":[54],"interest":[56],"nowadays.":[57],"Although":[58],"study":[60],"covers":[61],"more":[62],"general":[63],"scenarios":[64],"than":[65],"micromagnetic":[67],"one,":[68],"it":[69],"builds":[70],"phenomenological":[73],"considerations":[74],"Dzyaloshinskii":[76],"existence":[79],"helicoidal":[81],"textures,":[82],"as":[83],"a":[84],"result":[85],"possible":[87],"instabilities":[88],"structures":[91],"under":[92],"small":[93],"relativistic":[94],"spin\u2013lattice":[95],"or":[96],"spin\u2013spin":[97],"interactions.":[98],"particular,":[100],"provide":[102],"first":[104],"quantitative":[105],"counterpart":[106],"to":[107],"Dzyaloshinskii\u2019s":[108],"predictions":[109],"helical":[111],"structures.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}