{"id":"https://openalex.org/W2014154331","doi":"https://doi.org/10.1007/bf01014395","title":"Uniform expansion of the transition rate in Kramers' problem","display_name":"Uniform expansion of the transition rate in Kramers' problem","publication_year":1984,"publication_date":"1984-05-01","ids":{"openalex":"https://openalex.org/W2014154331","doi":"https://doi.org/10.1007/bf01014395","mag":"2014154331"},"language":"en","primary_location":{"id":"doi:10.1007/bf01014395","doi":"https://doi.org/10.1007/bf01014395","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01014395","pdf_url":null,"source":{"id":"https://openalex.org/S185067381","display_name":"Journal of Statistical Physics","issn_l":"0022-4715","issn":["0022-4715","1572-9613"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"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 Statistical Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5000956173","display_name":"Bernard J. Matkowsky","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. J. Matkowsky","raw_affiliation_strings":["Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois","Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston,","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072194007","display_name":"Z. Schuss","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Z. Schuss","raw_affiliation_strings":["Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois","Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston,","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042966516","display_name":"Charles Tier","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Tier","raw_affiliation_strings":["Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois","Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, 60201, Evanston, Illinois","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Engineering Sciences and Applied Mathematics, The Technological Institute, Northwestern University, Evanston,","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":5.937,"has_fulltext":false,"cited_by_count":104,"citation_normalized_percentile":{"value":0.96785557,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"35","issue":"3-4","first_page":"443","last_page":"456"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.8349999785423279,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.8349999785423279,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.07400000095367432,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.031599998474121094,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kramers-problem","display_name":"Kramers problem","score":0.703000009059906},{"id":"https://openalex.org/keywords/escape-rate","display_name":"escape rate","score":0.8240000009536743},{"id":"https://openalex.org/keywords/transition-rates","display_name":"transition rates","score":0.6779999732971191},{"id":"https://openalex.org/keywords/potential-barrier","display_name":"potential barrier","score":0.6349999904632568},{"id":"https://openalex.org/keywords/transition-state-theory","display_name":"transition state theory","score":0.7639999985694885},{"id":"https://openalex.org/keywords/uniform-asymptotic-expansions","display_name":"uniform asymptotic expansions","score":0.8100000023841858},{"id":"https://openalex.org/keywords/chemical-reactions","display_name":"chemical reactions","score":0.628000020980835}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6624442338943481},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6020261645317078},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5822656154632568},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5665675401687622},{"id":"https://openalex.org/C70557757","wikidata":"https://www.wikidata.org/wiki/Q7834432","display_name":"Transition rate matrix","level":2,"score":0.5031422972679138},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.45763707160949707},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.4464520514011383},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3229841887950897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28621798753738403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2562072277069092},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.23078429698944092},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1248491108417511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0713837742805481},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01014395","doi":"https://doi.org/10.1007/bf01014395","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01014395","pdf_url":null,"source":{"id":"https://openalex.org/S185067381","display_name":"Journal of Statistical Physics","issn_l":"0022-4715","issn":["0022-4715","1572-9613"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"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 Statistical Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1979120800","https://openalex.org/W1999486339","https://openalex.org/W2035564683","https://openalex.org/W2063917008","https://openalex.org/W2083438625","https://openalex.org/W2085266415","https://openalex.org/W2321762697","https://openalex.org/W2493432345"],"related_works":["https://openalex.org/W2027516596","https://openalex.org/W2991604236","https://openalex.org/W2092144432","https://openalex.org/W7099690832","https://openalex.org/W2064881896","https://openalex.org/W4310881664","https://openalex.org/W2078198134","https://openalex.org/W2035564683","https://openalex.org/W2092556171","https://openalex.org/W2000777310"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}