{"id":"https://openalex.org/W2734402169","doi":"https://doi.org/10.1137/17m1116271","title":"The Asymptotic Behavior of Solutions to the Repulsive $n$-Body Problem","display_name":"The Asymptotic Behavior of Solutions to the Repulsive $n$-Body Problem","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2734402169","doi":"https://doi.org/10.1137/17m1116271","mag":"2734402169"},"language":"en","primary_location":{"id":"doi:10.1137/17m1116271","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1116271","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.03626","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gerhard Rein","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056733786"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01966189,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"1","first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9991999864578247,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/coulomb","display_name":"Coulomb","score":0.7074988484382629},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5830786228179932},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5585910677909851},{"id":"https://openalex.org/keywords/three-body-problem","display_name":"Three-body problem","score":0.5582950115203857},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5376485586166382},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.5241822600364685},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4562552869319916},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3942430913448334},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3483491539955139},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3220808506011963},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21466344594955444},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18306148052215576}],"concepts":[{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.7074988484382629},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5830786228179932},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5585910677909851},{"id":"https://openalex.org/C34725247","wikidata":"https://www.wikidata.org/wiki/Q607699","display_name":"Three-body problem","level":2,"score":0.5582950115203857},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5376485586166382},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.5241822600364685},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4562552869319916},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3942430913448334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3483491539955139},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3220808506011963},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21466344594955444},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18306148052215576},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1116271","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1116271","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1707.03626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.03626","pdf_url":"https://arxiv.org/pdf/1707.03626","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":"","raw_type":"text"},{"id":"mag:2734402169","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1707.03626.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1707.03626","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1707.03626","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.03626","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.03626","pdf_url":"https://arxiv.org/pdf/1707.03626","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2734402169.pdf","grobid_xml":"https://content.openalex.org/works/W2734402169.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1994761506","https://openalex.org/W2012340283","https://openalex.org/W2029166690","https://openalex.org/W2036106014"],"related_works":["https://openalex.org/W2963351489","https://openalex.org/W2950980913","https://openalex.org/W1998532422","https://openalex.org/W2059897668","https://openalex.org/W2963184134","https://openalex.org/W2015088995","https://openalex.org/W3099862326","https://openalex.org/W3140183570","https://openalex.org/W3105210319","https://openalex.org/W3102701049","https://openalex.org/W2015623482","https://openalex.org/W2768053293","https://openalex.org/W2072685048","https://openalex.org/W2044954352","https://openalex.org/W2989010865","https://openalex.org/W2058992555","https://openalex.org/W2158424793","https://openalex.org/W3037904633","https://openalex.org/W1998844169","https://openalex.org/W2950587390"],"abstract_inverted_index":{"The":[0,29],"$n$-body":[1],"problem":[2],"with":[3,39],"a":[4,36,40],"purely":[5],"repulsive":[6],"Coulomb":[7],"interaction":[8],"is":[9,12,34,44],"considered.":[10],"It":[11],"shown":[13],"that":[14],"for":[15,46],"large":[16],"times":[17],"$t$":[18],"the":[19],"distance":[20],"between":[21],"any":[22],"two":[23],"particles":[24],"grows":[25],"linearly":[26],"in":[27],"$t$.":[28],"trajectory":[30],"of":[31],"each":[32],"particle":[33],"asymptotically":[35],"straight":[37],"line":[38],"fixed":[41],"velocity":[42],"which":[43],"different":[45,47],"particles.":[48]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
