{"id":"https://openalex.org/W3214583801","doi":"https://doi.org/10.1137/21m1463288","title":"Tilt Grain Boundaries of Hexagonal Structures: A Spectral Viewpoint","display_name":"Tilt Grain Boundaries of Hexagonal Structures: A Spectral Viewpoint","publication_year":2022,"publication_date":"2022-07-21","ids":{"openalex":"https://openalex.org/W3214583801","doi":"https://doi.org/10.1137/21m1463288","mag":"3214583801"},"language":"en","primary_location":{"id":"doi:10.1137/21m1463288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1463288","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101621260","display_name":"Kai Jiang","orcid":"https://orcid.org/0000-0001-5566-3942"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Jiang","raw_affiliation_strings":["School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, China, 411105"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, China, 411105","institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101965191","display_name":"Wei Si","orcid":"https://orcid.org/0000-0001-5002-7488"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Si","raw_affiliation_strings":["School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, China, 411105"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, China, 411105","institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101439697","display_name":"Jie Xu","orcid":"https://orcid.org/0000-0002-5096-2342"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210095018","display_name":"National Center for Mathematics and Interdisciplinary Sciences","ror":"https://ror.org/00s97k668","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210095018"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Xu","raw_affiliation_strings":["LSEC & NCMIS, Institute of Computational Mathematics and Scientific/Engineering Com-puting (ICMSEC), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LSEC & NCMIS, Institute of Computational Mathematics and Scientific/Engineering Com-puting (ICMSEC), Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210095018","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5475,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.54235988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"82","issue":"4","first_page":"1267","last_page":"1286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.996399998664856,"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/T13531","display_name":"Surface and Thin Film Phenomena","score":0.9890000224113464,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quasiperiodic-function","display_name":"Quasiperiodic function","score":0.8978618383407593},{"id":"https://openalex.org/keywords/grain-boundary","display_name":"Grain boundary","score":0.7834078073501587},{"id":"https://openalex.org/keywords/tilt","display_name":"Tilt (camera)","score":0.7490181922912598},{"id":"https://openalex.org/keywords/spectral-line","display_name":"Spectral line","score":0.6062448620796204},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5553808212280273},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4659028947353363},{"id":"https://openalex.org/keywords/hexagonal-crystal-system","display_name":"Hexagonal crystal system","score":0.46230781078338623},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.44849351048469543},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4341030418872833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37217801809310913},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.35623428225517273},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3503226339817047},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.32974404096603394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2933337092399597},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2645963728427887},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.24193057417869568},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.160262793302536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.158464252948761},{"id":"https://openalex.org/keywords/microstructure","display_name":"Microstructure","score":0.11164867877960205},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10833597183227539},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07642489671707153}],"concepts":[{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.8978618383407593},{"id":"https://openalex.org/C47908070","wikidata":"https://www.wikidata.org/wiki/Q900515","display_name":"Grain boundary","level":3,"score":0.7834078073501587},{"id":"https://openalex.org/C2779844322","wikidata":"https://www.wikidata.org/wiki/Q2919140","display_name":"Tilt (camera)","level":2,"score":0.7490181922912598},{"id":"https://openalex.org/C4839761","wikidata":"https://www.wikidata.org/wiki/Q212111","display_name":"Spectral line","level":2,"score":0.6062448620796204},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5553808212280273},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4659028947353363},{"id":"https://openalex.org/C128765274","wikidata":"https://www.wikidata.org/wiki/Q663314","display_name":"Hexagonal crystal system","level":2,"score":0.46230781078338623},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.44849351048469543},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4341030418872833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37217801809310913},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.35623428225517273},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3503226339817047},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.32974404096603394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2933337092399597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2645963728427887},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.24193057417869568},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.160262793302536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.158464252948761},{"id":"https://openalex.org/C87976508","wikidata":"https://www.wikidata.org/wiki/Q1498213","display_name":"Microstructure","level":2,"score":0.11164867877960205},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10833597183227539},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07642489671707153},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1463288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1463288","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2877107312","display_name":null,"funder_award_id":"12001524","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5112625999","display_name":null,"funder_award_id":"CX20200612","funder_id":"https://openalex.org/F4320326217","funder_display_name":"Hunan Provincial Innovation Foundation for Postgraduate"},{"id":"https://openalex.org/G6960247750","display_name":null,"funder_award_id":"2021JJ10037","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G7329969484","display_name":null,"funder_award_id":"12171412","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320326217","display_name":"Hunan Provincial Innovation Foundation for Postgraduate","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W240688302","https://openalex.org/W1581623368","https://openalex.org/W1966366359","https://openalex.org/W1978005036","https://openalex.org/W1988619801","https://openalex.org/W1992244966","https://openalex.org/W1999099759","https://openalex.org/W2007120406","https://openalex.org/W2009658756","https://openalex.org/W2052683749","https://openalex.org/W2064320065","https://openalex.org/W2067606286","https://openalex.org/W2075173505","https://openalex.org/W2094106520","https://openalex.org/W2281061730","https://openalex.org/W2613383371","https://openalex.org/W2933141219","https://openalex.org/W2969292053","https://openalex.org/W2973089289","https://openalex.org/W2990111512","https://openalex.org/W2992036760","https://openalex.org/W3005412638","https://openalex.org/W3088999759","https://openalex.org/W3089187830","https://openalex.org/W3099429082","https://openalex.org/W3099616761","https://openalex.org/W3104284044","https://openalex.org/W3136856760","https://openalex.org/W3183470127","https://openalex.org/W4255612844"],"related_works":["https://openalex.org/W4309428383","https://openalex.org/W2041444941","https://openalex.org/W2040831198","https://openalex.org/W2146522850","https://openalex.org/W785957202","https://openalex.org/W2146156922","https://openalex.org/W2020423209","https://openalex.org/W2808406012","https://openalex.org/W2064348882","https://openalex.org/W2013638723"],"abstract_inverted_index":{"We":[0,65],"propose":[1,107],"a":[2,69,108],"spectral":[3,38,104],"viewpoint":[4,39],"for":[5,26],"grain":[6,43,52,78],"boundaries":[7,44,53],"that":[8,67],"are":[9,54,57,120],"generally":[10],"quasiperiodic.":[11],"To":[12],"accurately":[13],"capture":[14],"the":[15,23,31,37,46,75,84,88,95,100,103,111],"spectra":[16,71,86],"computationally,":[17],"it":[18],"is":[19,92],"crucial":[20],"to":[21,40,60,74,83],"adopt":[22],"projection":[24],"method":[25],"quasiperiodic":[27],"functions.":[28],"Armed":[29],"with":[30,122],"Lifshitz--Petrich":[32],"free":[33],"energy,":[34],"we":[35,106],"take":[36],"examine":[41],"tilt":[42,96],"of":[45,51,77,87,94,102,110],"hexagonal":[47,90],"phase.":[48],"Several":[49],"ingredients":[50],"extracted,":[55],"which":[56],"not":[58],"easy":[59],"obtain":[61],"from":[62,117],"real-space":[63],"profiles.":[64],"find":[66],"only":[68],"few":[70],"substantially":[72],"contribute":[73],"formation":[76],"boundaries.":[79],"Their":[80],"linear":[81],"relation":[82],"intrinsic":[85],"bulk":[89],"phase":[91],"independent":[93],"angle.":[97],"By":[98],"examining":[99],"feature":[101],"intensities,":[105],"definition":[109,119],"interface":[112],"width.":[113],"The":[114],"widths":[115],"calculated":[116],"this":[118],"consistent":[121],"visual":[123],"estimation.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
