{"id":"https://openalex.org/W2140494519","doi":"https://doi.org/10.1007/s10915-008-9207-7","title":"Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in\u00a0Solids","display_name":"Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in\u00a0Solids","publication_year":2008,"publication_date":"2008-06-19","ids":{"openalex":"https://openalex.org/W2140494519","doi":"https://doi.org/10.1007/s10915-008-9207-7","mag":"2140494519"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-008-9207-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-008-9207-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","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/A5100699231","display_name":"Lei Zhang","orcid":"https://orcid.org/0000-0002-2917-9652"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lei Zhang","raw_affiliation_strings":["Department of Mathematics, Penn State University, PA, 16802, Centre County, USA","Department of Mathematics, Penn State University, Centre County, USA 16802#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Penn State University, PA, 16802, Centre County, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mathematics, Penn State University, Centre County, USA 16802#TAB#","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100333572","display_name":"Long\u2010Qing Chen","orcid":"https://orcid.org/0000-0003-3359-3781"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Long-Qing Chen","raw_affiliation_strings":["Department of Materials Science and Engineering, Penn State University, PA, 16802, Centre County, USA","Department of Materials Science and Engineering, Penn State University, Centre County, USA 16802"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Materials Science and Engineering, Penn State University, PA, 16802, Centre County, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Materials Science and Engineering, Penn State University, Centre County, USA 16802","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056115552","display_name":"Qiang Du","orcid":"https://orcid.org/0000-0002-1067-8937"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qiang Du","raw_affiliation_strings":["Department of Mathematics and Department of Materials Science and Engineering, Penn State University, PA, 16802, Centre County, USA","Department of Mathematics and Department of Materials Science and Engineering, Penn State University, Centre County, USA 16802#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Department of Materials Science and Engineering, Penn State University, PA, 16802, Centre County, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Mathematics and Department of Materials Science and Engineering, Penn State University, Centre County, USA 16802#TAB#","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056115552"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.7866,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.71107352,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"37","issue":"1","first_page":"89","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9987000226974487,"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/T10670","display_name":"Aluminum Alloy Microstructure Properties","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nucleation","display_name":"Nucleation","score":0.638572096824646},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.5830885767936707},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5303068161010742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5238195061683655},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.515782356262207},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.49517717957496643},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.48560160398483276},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.48557087779045105},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.46355903148651123},{"id":"https://openalex.org/keywords/phase-field-models","display_name":"Phase field models","score":0.4550623893737793},{"id":"https://openalex.org/keywords/morphology","display_name":"Morphology (biology)","score":0.43856796622276306},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.4126422703266144},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.37600088119506836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2816939949989319},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2590346336364746},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2259942889213562},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1025693416595459},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.10137966275215149},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0968489944934845},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08609703183174133}],"concepts":[{"id":"https://openalex.org/C61048295","wikidata":"https://www.wikidata.org/wiki/Q909022","display_name":"Nucleation","level":2,"score":0.638572096824646},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.5830885767936707},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5303068161010742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5238195061683655},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.515782356262207},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.49517717957496643},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.48560160398483276},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48557087779045105},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.46355903148651123},{"id":"https://openalex.org/C2780568864","wikidata":"https://www.wikidata.org/wiki/Q1640482","display_name":"Phase field models","level":3,"score":0.4550623893737793},{"id":"https://openalex.org/C499950583","wikidata":"https://www.wikidata.org/wiki/Q183252","display_name":"Morphology (biology)","level":2,"score":0.43856796622276306},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.4126422703266144},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.37600088119506836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2816939949989319},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2590346336364746},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2259942889213562},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1025693416595459},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.10137966275215149},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0968489944934845},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08609703183174133},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-008-9207-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-008-9207-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"},{"id":"https://openalex.org/F4320337396","display_name":"Division of Industrial Innovation and Partnerships","ror":"https://ror.org/03xyg3m20"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W11459100","https://openalex.org/W97270569","https://openalex.org/W137296298","https://openalex.org/W1582930900","https://openalex.org/W1595065160","https://openalex.org/W1967676806","https://openalex.org/W1968435982","https://openalex.org/W1970269511","https://openalex.org/W1977069262","https://openalex.org/W1984966193","https://openalex.org/W1986614779","https://openalex.org/W2004751437","https://openalex.org/W2006290293","https://openalex.org/W2015894407","https://openalex.org/W2019658175","https://openalex.org/W2023724667","https://openalex.org/W2035391644","https://openalex.org/W2039552609","https://openalex.org/W2039585221","https://openalex.org/W2042842088","https://openalex.org/W2045823559","https://openalex.org/W2046046478","https://openalex.org/W2055481609","https://openalex.org/W2058270372","https://openalex.org/W2058585715","https://openalex.org/W2062788197","https://openalex.org/W2068914374","https://openalex.org/W2075050641","https://openalex.org/W2091344193","https://openalex.org/W2096997237","https://openalex.org/W2097973750","https://openalex.org/W2106449638","https://openalex.org/W2110043143","https://openalex.org/W2120626377","https://openalex.org/W2121413806","https://openalex.org/W2122427541","https://openalex.org/W2130457461","https://openalex.org/W2135579713","https://openalex.org/W2150388881","https://openalex.org/W2151239679","https://openalex.org/W2166999972","https://openalex.org/W2274629352","https://openalex.org/W2323573981","https://openalex.org/W2884403958","https://openalex.org/W3021722416"],"related_works":["https://openalex.org/W4313886759","https://openalex.org/W2014598323","https://openalex.org/W2067018196","https://openalex.org/W3196590631","https://openalex.org/W2612434493","https://openalex.org/W2095069391","https://openalex.org/W4313420253","https://openalex.org/W2129835731","https://openalex.org/W2091640184","https://openalex.org/W2356146795"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
