Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1968524769', 'doi': 'https://doi.org/10.1103/physrevd.58.044007', 'title': 'Critical collapse of collisionless matter: A numerical investigation', 'display_name': 'Critical collapse of collisionless matter: A numerical investigation', 'publication_year': 1998, 'publication_date': '1998-07-10', 'ids': {'openalex': 'https://openalex.org/W1968524769', 'doi': 'https://doi.org/10.1103/physrevd.58.044007', 'mag': '1968524769'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physrevd.58.044007', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210190737', 'display_name': 'Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields', 'issn_l': '0556-2821', 'issn': ['0556-2821', '1089-4918', '1538-4500'], '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'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/pdf/gr-qc/9804040', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5056733786', 'display_name': 'Gerhard Rein', 'orcid': 'https://orcid.org/0000-0003-0028-3963'}, 'institutions': [{'id': 'https://openalex.org/I8204097', 'display_name': 'Ludwig-Maximilians-Universität München', 'ror': 'https://ror.org/05591te55', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I8204097']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Gerhard Rein', 'raw_affiliation_strings': ['Mathematisches Institut der Universität München, Theresienstrasse 39, 80333 München, Germany'], 'affiliations': [{'raw_affiliation_string': 'Mathematisches Institut der Universität München, Theresienstrasse 39, 80333 München, Germany', 'institution_ids': ['https://openalex.org/I8204097']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5013576177', 'display_name': 'Alan D. Rendall', 'orcid': 'https://orcid.org/0000-0003-3666-6632'}, 'institutions': [{'id': 'https://openalex.org/I149899117', 'display_name': 'Max Planck Society', 'ror': 'https://ror.org/01hhn8329', 'country_code': 'DE', 'type': 'nonprofit', 'lineage': ['https://openalex.org/I149899117']}, {'id': 'https://openalex.org/I4210127646', 'display_name': 'Max Planck Institute for Gravitational Physics', 'ror': 'https://ror.org/03sry2h30', 'country_code': 'DE', 'type': 'facility', 'lineage': ['https://openalex.org/I149899117', 'https://openalex.org/I4210127646']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Alan D. Rendall', 'raw_affiliation_strings': ['Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society'], 'affiliations': [{'raw_affiliation_string': 'Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society', 'institution_ids': ['https://openalex.org/I149899117', 'https://openalex.org/I4210127646']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5063102789', 'display_name': 'Jack Schaeffer', 'orcid': 'https://orcid.org/0000-0002-3534-5290'}, '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': 'Jack Schaeffer', 'raw_affiliation_strings': ['Department of Mathematics Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213', 'institution_ids': ['https://openalex.org/I74973139']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 4, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 2.962, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 57, 'citation_normalized_percentile': {'value': 0.938228, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 92, 'max': 93}, 'biblio': {'volume': '58', 'issue': '4', 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10095', 'display_name': 'Cosmology and Gravitation Theories', 'score': 0.9996, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, '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/T10095', 'display_name': 'Cosmology and Gravitation Theories', 'score': 0.9996, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, '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/T11012', 'display_name': 'Gas Dynamics and Kinetic Theory', 'score': 0.9975, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10025', 'display_name': 'Black Holes and Theoretical Physics', 'score': 0.9973, 'subfield': {'id': 'https://openalex.org/subfields/3106', 'display_name': 'Nuclear and High Energy Physics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/black-hole', 'display_name': 'Black hole (networking)', 'score': 0.70401806}, {'id': 'https://openalex.org/keywords/discontinuity', 'display_name': 'Discontinuity (linguistics)', 'score': 0.49315065}, {'id': 'https://openalex.org/keywords/primordial-black-hole', 'display_name': 'Primordial black hole', 'score': 0.47754893}], 'concepts': [{'id': 'https://openalex.org/C118396296', 'wikidata': 'https://www.wikidata.org/wiki/Q329273', 'display_name': 'Gravitational collapse', 'level': 2, 'score': 0.8168143}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.8099451}, {'id': 'https://openalex.org/C50341732', 'wikidata': 'https://www.wikidata.org/wiki/Q880302', 'display_name': 'Black hole (networking)', 'level': 5, 'score': 0.70401806}, {'id': 'https://openalex.org/C2779343474', 'wikidata': 'https://www.wikidata.org/wiki/Q3109175', 'display_name': 'Context (archaeology)', 'level': 2, 'score': 0.58936906}, {'id': 'https://openalex.org/C2777042112', 'wikidata': 'https://www.wikidata.org/wiki/Q5281658', 'display_name': 'Discontinuity (linguistics)', 'level': 2, 'score': 0.49315065}, {'id': 'https://openalex.org/C182877743', 'wikidata': 'https://www.wikidata.org/wiki/Q1155939', 'display_name': 'Primordial black hole', 'level': 4, 'score': 0.47754893}, {'id': 'https://openalex.org/C44870925', 'wikidata': 'https://www.wikidata.org/wiki/Q37547', 'display_name': 'Astrophysics', 'level': 1, 'score': 0.32583869}, {'id': 'https://openalex.org/C190330329', 'wikidata': 'https://www.wikidata.org/wiki/Q190035', 'display_name': 'Gravitational wave', 'level': 2, 'score': 0.32496446}, {'id': 'https://openalex.org/C32602459', 'wikidata': 'https://www.wikidata.org/wiki/Q4913879', 'display_name': 'Binary black hole', 'level': 3, 'score': 0.19178033}, {'id': 'https://openalex.org/C127313418', 'wikidata': 'https://www.wikidata.org/wiki/Q1069', 'display_name': 'Geology', 'level': 0, 'score': 0.05610454}, {'id': 'https://openalex.org/C31258907', 'wikidata': 'https://www.wikidata.org/wiki/Q1301371', 'display_name': 'Computer network', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C151730666', 'wikidata': 'https://www.wikidata.org/wiki/Q7205', 'display_name': 'Paleontology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C104954878', 'wikidata': 'https://www.wikidata.org/wiki/Q1648707', 'display_name': 'Routing protocol', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C74172769', 'wikidata': 'https://www.wikidata.org/wiki/Q1446839', 'display_name': 'Routing (electronic design automation)', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, '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/C89305328', 'wikidata': 'https://www.wikidata.org/wiki/Q1755411', 'display_name': 'Link-state routing protocol', 'level': 4, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1103/physrevd.58.044007', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210190737', 'display_name': 'Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields', 'issn_l': '0556-2821', 'issn': ['0556-2821', '1089-4918', '1538-4500'], '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/gr-qc/9804040', 'pdf_url': 'https://arxiv.org/pdf/gr-qc/9804040', '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': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.gr-qc/9804040', '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/gr-qc/9804040', 'pdf_url': 'https://arxiv.org/pdf/gr-qc/9804040', '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/W1968524769'], 'referenced_works_count': 29, 'referenced_works': ['https://openalex.org/W119119258', 'https://openalex.org/W1559947614', 'https://openalex.org/W1675922226', 'https://openalex.org/W1963704011', 'https://openalex.org/W1974428826', 'https://openalex.org/W1974747498', 'https://openalex.org/W1987529853', 'https://openalex.org/W1999339270', 'https://openalex.org/W2008766677', 'https://openalex.org/W2020184849', 'https://openalex.org/W2034172803', 'https://openalex.org/W2038980259', 'https://openalex.org/W2040215514', 'https://openalex.org/W2047211625', 'https://openalex.org/W2062182342', 'https://openalex.org/W2074298472', 'https://openalex.org/W2076997505', 'https://openalex.org/W2093767736', 'https://openalex.org/W2169377271', 'https://openalex.org/W2489369796', 'https://openalex.org/W2561725998', 'https://openalex.org/W2796323095', 'https://openalex.org/W3034991593', 'https://openalex.org/W3037966406', 'https://openalex.org/W3103122522', 'https://openalex.org/W3104785168', 'https://openalex.org/W4246652625', 'https://openalex.org/W4285719527', 'https://openalex.org/W4299601108'], 'related_works': ['https://openalex.org/W4387253538', 'https://openalex.org/W4366549493', 'https://openalex.org/W4285026773', 'https://openalex.org/W4226193981', 'https://openalex.org/W3196387258', 'https://openalex.org/W3123167463', 'https://openalex.org/W3122961569', 'https://openalex.org/W2974544503', 'https://openalex.org/W2788955161', 'https://openalex.org/W2506531441'], 'abstract_inverted_index': {'In': [0, 23], 'recent': [1], 'years': [2], 'the': [3, 26, 47, 56, 62, 89, 94, 100, 104, 119, 122, 126], 'threshold': [4], 'of': [5, 20, 58, 72, 99, 121, 128], 'black': [6, 52, 105, 109, 123, 129], 'hole': [7, 53, 106, 110, 124, 130], 'formation': [8, 54], 'in': [9, 42, 55, 81, 115, 118], 'spherically': [10], 'symmetric': [11], 'gravitational': [12], 'collapse': [13, 57], 'has': [14], 'been': [15], 'studied': [16], 'for': [17, 31, 88, 92], 'a': [18, 32, 73, 108, 116], 'variety': [19], 'matter': [21, 33, 60, 101], 'models.': [22], 'this': [24, 43], 'paper': [25], 'corresponding': [27], 'issue': [28], 'is': [29, 65, 68, 86, 111], 'investigated': [30], 'model': [34], 'significantly': [35], 'different': [36], 'from': [37, 49], 'those': [38, 78], 'considered': [39], 'so': [40], 'far': [41], 'context.': [44], 'We': [45], 'study': [46], 'transition': [48], 'dispersion': [50], 'to': [51, 77], 'collisionless': [59], 'when': [61], 'initial': [63, 90], 'data': [64, 91], 'scaled.': [66], 'This': [67, 113], 'done': [69], 'by': [70], 'means': [71], 'numerical': [74], 'code': [75], 'similar': [76], 'commonly': [79], 'used': [80], 'plasma': [82], 'physics.': [83], 'The': [84], 'result': [85], 'that,': [87], 'which': [93], 'solutions': [95], 'were': [96], 'computed,': [97], 'most': [98], 'falls': [102], 'into': [103], 'whenever': [107], 'formed.': [112], 'results': [114], 'discontinuity': [117], 'mass': [120], 'at': [125], 'onset': [127], 'formation.': [131]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1968524769', 'counts_by_year': [{'year': 2024, 'cited_by_count': 2}, {'year': 2023, 'cited_by_count': 2}, {'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 2}, {'year': 2020, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 2}, {'year': 2014, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2025-01-06T13:41:29.685106', 'created_date': '2016-06-24'}