{"id":"https://openalex.org/W2996828316","doi":"https://doi.org/10.1007/s00332-020-09637-6","title":"Phase Separation in the Advective Cahn\u2013Hilliard Equation","display_name":"Phase Separation in the Advective Cahn\u2013Hilliard Equation","publication_year":2020,"publication_date":"2020-06-18","ids":{"openalex":"https://openalex.org/W2996828316","doi":"https://doi.org/10.1007/s00332-020-09637-6","mag":"2996828316"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-020-09637-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-020-09637-6","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1912.12714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yu Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yu Feng","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","Department of Mathematics, University of Wisconsin \u2013 Madison, Madison, WI, 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin \u2013 Madison, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yuanyuan Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuanyuan Feng","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","Department of Mathematics, University of Wisconsin \u2013 Madison, Madison, WI, 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin \u2013 Madison, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Gautam Iyer","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gautam Iyer","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jean-Luc Thiffeault","orcid":"https://orcid.org/0000-0001-7724-7966"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean-Luc Thiffeault","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin \u2013 Madison, Madison, WI, 53706, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin \u2013 Madison, Madison, WI, 53706, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135310074","https://openalex.org/I74973139"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.8137,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.66911951,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"30","issue":"6","first_page":"2821","last_page":"2845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9706000089645386,"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":0.9706000089645386,"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/T11471","display_name":"Block Copolymer Self-Assembly","score":0.017400000244379044,"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":0.0010999999940395355,"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/dissipation","display_name":"Dissipation","score":0.8429999947547913},{"id":"https://openalex.org/keywords/advection","display_name":"Advection","score":0.7373999953269958},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.6863999962806702},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5515000224113464},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.46709999442100525},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4586000144481659},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.4426000118255615},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.3847000002861023}],"concepts":[{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.8429999947547913},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.7373999953269958},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6863999962806702},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5813999772071838},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5515000224113464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47119998931884766},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4586000144481659},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.3847000002861023},{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.352400004863739},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.33880001306533813},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33660000562667847},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C159722891","wikidata":"https://www.wikidata.org/wiki/Q913323","display_name":"Separation of variables","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2542000114917755}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00332-020-09637-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-020-09637-6","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1912.12714","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.12714","pdf_url":"https://arxiv.org/pdf/1912.12714","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1912.12714","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.12714","pdf_url":"https://arxiv.org/pdf/1912.12714","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8652786474","display_name":null,"funder_award_id":"DMS-1814147","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"}],"funders":[{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1521182415","https://openalex.org/W1595630901","https://openalex.org/W1965337938","https://openalex.org/W1974311804","https://openalex.org/W1982646491","https://openalex.org/W1988655316","https://openalex.org/W1992261133","https://openalex.org/W1996232406","https://openalex.org/W1999275765","https://openalex.org/W2003331624","https://openalex.org/W2004512206","https://openalex.org/W2005928884","https://openalex.org/W2027312025","https://openalex.org/W2032257836","https://openalex.org/W2034879619","https://openalex.org/W2035449125","https://openalex.org/W2046528357","https://openalex.org/W2054083100","https://openalex.org/W2058986816","https://openalex.org/W2080023131","https://openalex.org/W2106967316","https://openalex.org/W2112250505","https://openalex.org/W2153003691","https://openalex.org/W2160970016","https://openalex.org/W2271999072","https://openalex.org/W2326825004","https://openalex.org/W2569713119","https://openalex.org/W2781067205","https://openalex.org/W2806151361","https://openalex.org/W2962999217","https://openalex.org/W2963485210","https://openalex.org/W2963709756","https://openalex.org/W2964314376","https://openalex.org/W2974106327","https://openalex.org/W6600983401","https://openalex.org/W6636723609","https://openalex.org/W6827907110"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2020-01-10T00:00:00"}