{"id":"https://openalex.org/W2056909920","doi":"https://doi.org/10.1137/s0036139997330027","title":"Second-Order Phase Field Asymptotics for Unequal Conductivities","display_name":"Second-Order Phase Field Asymptotics for Unequal Conductivities","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2056909920","doi":"https://doi.org/10.1137/s0036139997330027","mag":"2056909920"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139997330027","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997330027","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/A5013048210","display_name":"Robert Almgren","orcid":"https://orcid.org/0000-0003-2038-354X"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert F. Almgren","raw_affiliation_strings":["The University of Chicago, Chicago IL"],"affiliations":[{"raw_affiliation_string":"The University of Chicago, Chicago IL","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013048210"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":4.9477,"has_fulltext":false,"cited_by_count":182,"citation_normalized_percentile":{"value":0.96064219,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"59","issue":"6","first_page":"2086","last_page":"2107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9995999932289124,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6275417804718018},{"id":"https://openalex.org/keywords/isothermal-process","display_name":"Isothermal process","score":0.6067635416984558},{"id":"https://openalex.org/keywords/phase-field-models","display_name":"Phase field models","score":0.5240155458450317},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.4817340672016144},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4425972104072571},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4363269507884979},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43402552604675293},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.41722139716148376},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.41558220982551575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4130333960056305},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25795379281044006},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10692355036735535},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07633709907531738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6275417804718018},{"id":"https://openalex.org/C133347239","wikidata":"https://www.wikidata.org/wiki/Q486921","display_name":"Isothermal process","level":2,"score":0.6067635416984558},{"id":"https://openalex.org/C2780568864","wikidata":"https://www.wikidata.org/wiki/Q1640482","display_name":"Phase field models","level":3,"score":0.5240155458450317},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.4817340672016144},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4425972104072571},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4363269507884979},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43402552604675293},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.41722139716148376},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.41558220982551575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4130333960056305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25795379281044006},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10692355036735535},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07633709907531738},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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":3,"locations":[{"id":"doi:10.1137/s0036139997330027","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997330027","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.421.6916","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.421.6916","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cims.nyu.edu/~almgren/papers/Almgren99.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.9984","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.9984","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uchicago.edu/camp/preprints/Almgren97.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W74483410","https://openalex.org/W1970009482","https://openalex.org/W1981478237","https://openalex.org/W1985396160","https://openalex.org/W1987139950","https://openalex.org/W2009181446","https://openalex.org/W2009785047","https://openalex.org/W2010014688","https://openalex.org/W2020227380","https://openalex.org/W2037913112","https://openalex.org/W2041041421","https://openalex.org/W2043055773","https://openalex.org/W2049090408","https://openalex.org/W2059827887","https://openalex.org/W2080149290","https://openalex.org/W2080477605","https://openalex.org/W2083440017","https://openalex.org/W2727498417"],"related_works":["https://openalex.org/W2028866325","https://openalex.org/W2031402404","https://openalex.org/W2888120784","https://openalex.org/W3005179320","https://openalex.org/W4200198618","https://openalex.org/W2365698943","https://openalex.org/W2366722091","https://openalex.org/W2525229663","https://openalex.org/W1970293971","https://openalex.org/W2625602263"],"abstract_inverted_index":{"We":[0,20],"extend":[1],"Karma":[2],"and":[3,18,39,112],"Rappel's":[4],"improved":[5],"asymptotic":[6],"analysis":[7],"of":[8],"the":[9,28,36,40,46,53,57,101,118],"phase":[10,58,81,123],"field":[11,59],"model":[12,60],"to":[13,63,78,91,109,116],"different":[14],"diffusivities":[15,74],"in":[16,26,44],"solid":[17],"liquid.":[19],"consider":[21],"both":[22],"second-order":[23,89],"\"classical\"":[24],"asymptotics,":[25,43],"which":[27,45,86],"interface":[29],"thickness":[30],"is":[31,61,76,114],"taken":[32],"much":[33],"smaller":[34],"than":[35],"capillary":[37],"length,":[38],"new":[41],"\"isothermal\"":[42],"two":[47],"lengths":[48],"are":[49,107],"considered":[50],"comparable.":[51],"In":[52,100],"first":[54],"case,":[55,103],"if":[56],"required":[62],"be":[64],"gradient":[65],"flow":[66],"for":[67,72],"an":[68],"entropy":[69],"functional,":[70],"then":[71],"unequal":[73],"it":[75,113],"impossible":[77],"construct":[79],"a":[80,92],"equation":[82],"with":[83,88,96,121],"finite":[84,122],"kinetics":[85],"converges":[87],"accuracy":[90],"Gibbs--Thomson":[93],"equilibrium":[94],"condition":[95],"infinitely":[97],"fast":[98],"kinetics.":[99,124],"second":[102],"some":[104],"error":[105],"terms":[106],"pushed":[108],"higher":[110],"orders,":[111],"easy":[115],"eliminate":[117],"remaining":[119],"errors":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
