Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2089966270', 'doi': 'https://doi.org/10.1103/physreve.60.1724', 'title': 'Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach', 'display_name': 'Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach', 'publication_year': 1999, 'publication_date': '1999-08-01', 'ids': {'openalex': 'https://openalex.org/W2089966270', 'doi': 'https://doi.org/10.1103/physreve.60.1724', 'mag': '2089966270', 'pmid': 'https://pubmed.ncbi.nlm.nih.gov/11969954'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physreve.60.1724', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210224030', 'display_name': 'Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics', 'issn_l': '1063-651X', 'issn': ['1063-651X', '1095-3787', '1538-4519'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320261', 'host_organization_name': 'American Physical Society', 'host_organization_lineage': ['https://openalex.org/P4310320261'], 'host_organization_lineage_names': ['American Physical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite', 'pubmed'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/pdf/cond-mat/9903171', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5046597946', 'display_name': 'R. Folch', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I71999127', 'display_name': 'Universitat de Barcelona', 'ror': 'https://ror.org/021018s57', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I71999127']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'R. Folch', 'raw_affiliation_strings': ['Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain'], 'affiliations': [{'raw_affiliation_string': 'Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain', 'institution_ids': ['https://openalex.org/I71999127']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5026108546', 'display_name': 'Jaume Casademunt', 'orcid': 'https://orcid.org/0000-0002-6154-439X'}, 'institutions': [{'id': 'https://openalex.org/I71999127', 'display_name': 'Universitat de Barcelona', 'ror': 'https://ror.org/021018s57', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I71999127']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'J. Casademunt', 'raw_affiliation_strings': ['Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain'], 'affiliations': [{'raw_affiliation_string': 'Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain', 'institution_ids': ['https://openalex.org/I71999127']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5002954708', 'display_name': 'A. Hernández–Machado', 'orcid': 'https://orcid.org/0000-0002-0397-5255'}, 'institutions': [{'id': 'https://openalex.org/I71999127', 'display_name': 'Universitat de Barcelona', 'ror': 'https://ror.org/021018s57', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I71999127']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'A. Hernández-Machado', 'raw_affiliation_strings': ['Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain'], 'affiliations': [{'raw_affiliation_string': 'Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, E-08028 Barcelona, Spain', 'institution_ids': ['https://openalex.org/I71999127']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5066356709', 'display_name': 'L. Ramírez–Piscina', 'orcid': 'https://orcid.org/0000-0003-4019-245X'}, 'institutions': [{'id': 'https://openalex.org/I9617848', 'display_name': 'Universitat Politècnica de Catalunya', 'ror': 'https://ror.org/03mb6wj31', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I9617848']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'L. Ramírez-Piscina', 'raw_affiliation_strings': ['Departament de Física Aplicada, Universitat Politècnica de Catalunya, Avinguda Dr. Marañón, 50, E-08028 Barcelona, Spain'], 'affiliations': [{'raw_affiliation_string': 'Departament de Física Aplicada, Universitat Politècnica de Catalunya, Avinguda Dr. Marañón, 50, E-08028 Barcelona, Spain', 'institution_ids': ['https://openalex.org/I9617848']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 2.408, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 148, 'citation_normalized_percentile': {'value': 0.99983, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 97, 'max': 98}, 'biblio': {'volume': '60', 'issue': '2', 'first_page': '1724', 'last_page': '1733'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10591', 'display_name': 'Theoretical and Computational Physics', 'score': 0.9992, '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'}}, 'topics': [{'id': 'https://openalex.org/T10591', 'display_name': 'Theoretical and Computational Physics', 'score': 0.9992, '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': 0.9984, '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/T11187', 'display_name': 'Nonlinear Dynamics and Pattern Formation', 'score': 0.9944, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/hele-shaw-flow', 'display_name': 'Hele-Shaw flow', 'score': 0.6830548}, {'id': 'https://openalex.org/keywords/asymptotic-analysis', 'display_name': 'Asymptotic Analysis', 'score': 0.47833347}, {'id': 'https://openalex.org/keywords/viscous-fingering', 'display_name': 'Viscous fingering', 'score': 0.46114096}, {'id': 'https://openalex.org/keywords/interface', 'display_name': 'Interface (matter)', 'score': 0.4402662}], 'concepts': [{'id': 'https://openalex.org/C45502583', 'wikidata': 'https://www.wikidata.org/wiki/Q5701708', 'display_name': 'Hele-Shaw flow', 'level': 4, 'score': 0.6830548}, {'id': 'https://openalex.org/C127172972', 'wikidata': 'https://www.wikidata.org/wiki/Q128709', 'display_name': 'Viscosity', 'level': 2, 'score': 0.5951355}, {'id': 'https://openalex.org/C2777303404', 'wikidata': 'https://www.wikidata.org/wiki/Q759757', 'display_name': 'Convergence (economics)', 'level': 2, 'score': 0.51335734}, {'id': 'https://openalex.org/C205147927', 'wikidata': 'https://www.wikidata.org/wiki/Q752718', 'display_name': 'Asymptotic analysis', 'level': 2, 'score': 0.47833347}, {'id': 'https://openalex.org/C151201525', 'wikidata': 'https://www.wikidata.org/wiki/Q177239', 'display_name': 'Limit (mathematics)', 'level': 2, 'score': 0.46724322}, {'id': 'https://openalex.org/C44280652', 'wikidata': 'https://www.wikidata.org/wiki/Q104837', 'display_name': 'Phase (matter)', 'level': 2, 'score': 0.46260628}, {'id': 'https://openalex.org/C2778737968', 'wikidata': 'https://www.wikidata.org/wiki/Q3027832', 'display_name': 'Viscous fingering', 'level': 4, 'score': 0.46114096}, {'id': 'https://openalex.org/C134786449', 'wikidata': 'https://www.wikidata.org/wiki/Q3391255', 'display_name': 'Planar', 'level': 2, 'score': 0.45557255}, {'id': 'https://openalex.org/C113843644', 'wikidata': 'https://www.wikidata.org/wiki/Q901882', 'display_name': 'Interface (matter)', 'level': 4, 'score': 0.4402662}, {'id': 'https://openalex.org/C38349280', 'wikidata': 'https://www.wikidata.org/wiki/Q1434290', 'display_name': 'Flow (mathematics)', 'level': 2, 'score': 0.385489}, {'id': 'https://openalex.org/C57879066', 'wikidata': 'https://www.wikidata.org/wiki/Q41217', 'display_name': 'Mechanics', 'level': 1, 'score': 0.3835883}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.3623855}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.35885102}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.35278887}, {'id': 'https://openalex.org/C105569014', 'wikidata': 'https://www.wikidata.org/wiki/Q3271208', 'display_name': 'Porous medium', 'level': 3, 'score': 0.26669937}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.21663237}, {'id': 'https://openalex.org/C192562407', 'wikidata': 'https://www.wikidata.org/wiki/Q228736', 'display_name': 'Materials science', 'level': 0, 'score': 0.15840736}, {'id': 'https://openalex.org/C180925781', 'wikidata': 'https://www.wikidata.org/wiki/Q514096', 'display_name': 'Open-channel flow', 'level': 3, 'score': 0.13920778}, {'id': 'https://openalex.org/C97355855', 'wikidata': 'https://www.wikidata.org/wiki/Q11473', 'display_name': 'Thermodynamics', 'level': 1, 'score': 0.1121397}, {'id': 'https://openalex.org/C6648577', 'wikidata': 'https://www.wikidata.org/wiki/Q622669', 'display_name': 'Porosity', 'level': 2, 'score': 0.07926658}, {'id': 'https://openalex.org/C121684516', 'wikidata': 'https://www.wikidata.org/wiki/Q7600677', 'display_name': 'Computer graphics (images)', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C157915830', 'wikidata': 'https://www.wikidata.org/wiki/Q2928001', 'display_name': 'Bubble', 'level': 2, '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/C129307140', 'wikidata': 'https://www.wikidata.org/wiki/Q6795880', 'display_name': 'Maximum bubble pressure method', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C162324750', 'wikidata': 'https://www.wikidata.org/wiki/Q8134', 'display_name': 'Economics', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C50522688', 'wikidata': 'https://www.wikidata.org/wiki/Q189833', 'display_name': 'Economic growth', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C159985019', 'wikidata': 'https://www.wikidata.org/wiki/Q181790', 'display_name': 'Composite material', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physreve.60.1724', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210224030', 'display_name': 'Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics', 'issn_l': '1063-651X', 'issn': ['1063-651X', '1095-3787', '1538-4519'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320261', 'host_organization_name': 'American Physical Society', 'host_organization_lineage': ['https://openalex.org/P4310320261'], 'host_organization_lineage_names': ['American Physical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/cond-mat/9903171', 'pdf_url': 'https://arxiv.org/pdf/cond-mat/9903171', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://hdl.handle.net/2445/18762', 'pdf_url': 'https://diposit.ub.edu/dspace/bitstream/2445/18762/1/145941.pdf', 'source': {'id': 'https://openalex.org/S4377196108', 'display_name': 'Hispana', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': None, 'host_organization_name': None, 'host_organization_lineage': [], 'host_organization_lineage_names': [], 'type': 'repository'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': False, 'landing_page_url': 'https://pubmed.ncbi.nlm.nih.gov/11969954', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306525036', 'display_name': 'PubMed', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1299303238', 'host_organization_name': 'National Institutes of Health', 'host_organization_lineage': ['https://openalex.org/I1299303238'], 'host_organization_lineage_names': ['National Institutes of Health'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.cond-mat/9903171', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/cond-mat/9903171', 'pdf_url': 'https://arxiv.org/pdf/cond-mat/9903171', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W2089966270'], 'referenced_works_count': 39, 'referenced_works': ['https://openalex.org/W1965624194', 'https://openalex.org/W1967550227', 'https://openalex.org/W1969323823', 'https://openalex.org/W1973146039', 'https://openalex.org/W1977032047', 'https://openalex.org/W1981478237', 'https://openalex.org/W1985396160', 'https://openalex.org/W1989117272', 'https://openalex.org/W1998833803', 'https://openalex.org/W2004716724', 'https://openalex.org/W2009181446', 'https://openalex.org/W2010014688', 'https://openalex.org/W2010684197', 'https://openalex.org/W2012312088', 'https://openalex.org/W2020227380', 'https://openalex.org/W2020299774', 'https://openalex.org/W2021203048', 'https://openalex.org/W2028487377', 'https://openalex.org/W2034595601', 'https://openalex.org/W2037065221', 'https://openalex.org/W2041170998', 'https://openalex.org/W2049090408', 'https://openalex.org/W2066359652', 'https://openalex.org/W2068272626', 'https://openalex.org/W2070227701', 'https://openalex.org/W2080477605', 'https://openalex.org/W2090913143', 'https://openalex.org/W2091081344', 'https://openalex.org/W2091112632', 'https://openalex.org/W2124457264', 'https://openalex.org/W2130207930', 'https://openalex.org/W2135243606', 'https://openalex.org/W2146993344', 'https://openalex.org/W2151838369', 'https://openalex.org/W2153230371', 'https://openalex.org/W3098353281', 'https://openalex.org/W4229878554', 'https://openalex.org/W4420592', 'https://openalex.org/W584821784'], 'related_works': ['https://openalex.org/W4322763587', 'https://openalex.org/W4322744399', 'https://openalex.org/W4308572070', 'https://openalex.org/W2753224743', 'https://openalex.org/W2619841764', 'https://openalex.org/W2613929631', 'https://openalex.org/W2593135060', 'https://openalex.org/W2052559186', 'https://openalex.org/W2039699594', 'https://openalex.org/W1967091491'], 'abstract_inverted_index': {'We': [0, 56, 73], 'present': [1], 'a': [2, 20], 'phase-field': [3, 91], 'model': [4, 31, 92], 'for': [5, 106], 'the': [6, 9, 30, 34, 39, 44, 53, 59, 65, 70, 77, 80, 85, 90, 94, 100], 'dynamics': [7], 'of': [8, 61, 69, 89], 'interface': [10, 54, 81], 'between': [11], 'two': [12], 'inmiscible': [13], 'fluids': [14], 'with': [15], 'arbitrary': [16], 'viscosity': [17, 108], 'contrast': [18], 'in': [19, 38, 52, 75], 'rectangular': [21], 'Hele-Shaw': [22, 36, 96], 'cell.': [23], 'With': [24], 'asymptotic': [25], 'matching': [26], 'techniques': [27], 'we': [28], 'check': [29], 'to': [32, 46, 49, 83, 93, 103], 'yield': [33], 'right': [35], 'equations': [37, 48], 'sharp-interface': [40], 'limit,': [41], 'and': [42, 87], 'compute': [43, 58], 'corrections': [45, 63], 'these': [47], 'first': [50], 'order': [51], 'thickness.': [55], 'also': [57], 'effect': [60], 'such': [62], 'on': [64, 79], 'linear': [66], 'dispersion': [67], 'relation': [68], 'planar': [71], 'interface.': [72], 'discuss': [74], 'detail': [76], 'conditions': [78], 'thickness': [82], 'control': [84], 'accuracy': [86], 'convergence': [88, 101], 'limiting': [95], 'dynamics.': [97], 'In': [98], 'particular,': [99], 'appears': [102], 'be': [104], 'slower': [105], 'high': [107], 'contrasts.': [109]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2089966270', 'counts_by_year': [{'year': 2024, 'cited_by_count': 8}, {'year': 2023, 'cited_by_count': 8}, {'year': 2022, 'cited_by_count': 4}, {'year': 2021, 'cited_by_count': 6}, {'year': 2020, 'cited_by_count': 12}, {'year': 2019, 'cited_by_count': 4}, {'year': 2018, 'cited_by_count': 8}, {'year': 2017, 'cited_by_count': 11}, {'year': 2016, 'cited_by_count': 4}, {'year': 2015, 'cited_by_count': 5}, {'year': 2014, 'cited_by_count': 4}, {'year': 2013, 'cited_by_count': 6}, {'year': 2012, 'cited_by_count': 4}], 'updated_date': '2024-12-24T14:31:37.545962', 'created_date': '2016-06-24'}