{"id":"https://openalex.org/W1974108099","doi":"https://doi.org/10.1007/s003329910010","title":"The Geometry of the Phase Diffusion Equation","display_name":"The Geometry of the Phase Diffusion Equation","publication_year":2000,"publication_date":"2000-02-01","ids":{"openalex":"https://openalex.org/W1974108099","doi":"https://doi.org/10.1007/s003329910010","mag":"1974108099"},"language":"en","primary_location":{"id":"doi:10.1007/s003329910010","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s003329910010","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":["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/A5004936939","display_name":"Nicholas M. Ercolani","orcid":null},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"N. M. Ercolani","raw_affiliation_strings":["Department of Mathematics, University of Arizona, Tucson, AZ 85719, USA, US","Department of Mathematics, University of Arizona, Tucson, AZ 85719 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Arizona, Tucson, AZ 85719, USA, US","institution_ids":["https://openalex.org/I138006243"]},{"raw_affiliation_string":"Department of Mathematics, University of Arizona, Tucson, AZ 85719 USA","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016964442","display_name":"R. Indik","orcid":null},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Indik","raw_affiliation_strings":["Department of Mathematics, University of Arizona, Tucson, AZ 85719, USA, US","Department of Mathematics, University of Arizona, Tucson, AZ 85719 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Arizona, Tucson, AZ 85719, USA, US","institution_ids":["https://openalex.org/I138006243"]},{"raw_affiliation_string":"Department of Mathematics, University of Arizona, Tucson, AZ 85719 USA","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032713818","display_name":"A. C. Newell","orcid":null},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A. C. Newell","raw_affiliation_strings":["Mathematical Institute, University of Warwick, Coventry CV4 7AL, UK, GB","Mathematical Institute, University of Warwick, Coventry CV4\u00a07AL, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Warwick, Coventry CV4 7AL, UK, GB","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Mathematical Institute, University of Warwick, Coventry CV4\u00a07AL, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014092499","display_name":"T. Passot","orcid":"https://orcid.org/0000-0002-6845-9729"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"T. Passot","raw_affiliation_strings":["Mathematical Institute, University of Warwick, Coventry CV4 7AL, UK, GB","Mathematical Institute, University of Warwick, Coventry CV4\u00a07AL, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Warwick, Coventry CV4 7AL, UK, GB","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Mathematical Institute, University of Warwick, Coventry CV4\u00a07AL, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004936939"],"corresponding_institution_ids":["https://openalex.org/I138006243"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":3.8601,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.93566073,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"2","first_page":"223","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9951000213623047,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6784569621086121},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6181147694587708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5762737393379211},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5599579811096191},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.45856013894081116}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6784569621086121},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6181147694587708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5762737393379211},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5599579811096191},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.45856013894081116},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s003329910010","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s003329910010","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8299999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W1499787021","https://openalex.org/W1532111732","https://openalex.org/W1532515344","https://openalex.org/W1577768379","https://openalex.org/W1644094888","https://openalex.org/W1965224293","https://openalex.org/W1986788497","https://openalex.org/W1988270146","https://openalex.org/W1993553692","https://openalex.org/W1993817015","https://openalex.org/W1994209621","https://openalex.org/W1998678324","https://openalex.org/W2001155644","https://openalex.org/W2005306494","https://openalex.org/W2006240454","https://openalex.org/W2007123411","https://openalex.org/W2007356002","https://openalex.org/W2010816452","https://openalex.org/W2017962183","https://openalex.org/W2039876742","https://openalex.org/W2040734864","https://openalex.org/W2048290375","https://openalex.org/W2055931342","https://openalex.org/W2057096097","https://openalex.org/W2059327787","https://openalex.org/W2065357863","https://openalex.org/W2067614613","https://openalex.org/W2070305919","https://openalex.org/W2083024456","https://openalex.org/W2083515198","https://openalex.org/W2084390456","https://openalex.org/W2086126894","https://openalex.org/W2086829188","https://openalex.org/W2092101903","https://openalex.org/W2092369655","https://openalex.org/W2095528560","https://openalex.org/W2098399303","https://openalex.org/W2103588786","https://openalex.org/W2110990313","https://openalex.org/W2120062331","https://openalex.org/W2125092472","https://openalex.org/W2138607334","https://openalex.org/W2145553955","https://openalex.org/W2147266641","https://openalex.org/W2169925500","https://openalex.org/W2325300816","https://openalex.org/W3002379364","https://openalex.org/W3021722416","https://openalex.org/W3025452706","https://openalex.org/W3111685920","https://openalex.org/W3135116447","https://openalex.org/W4243904728"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}