{"id":"https://openalex.org/W2007386207","doi":"https://doi.org/10.1103/physreve.67.061105","title":"Power law diffusion coefficient and anomalous diffusion: Analysis of solutions and first passage time","display_name":"Power law diffusion coefficient and anomalous diffusion: Analysis of solutions and first passage time","publication_year":2003,"publication_date":"2003-06-10","ids":{"openalex":"https://openalex.org/W2007386207","doi":"https://doi.org/10.1103/physreve.67.061105","mag":"2007386207","pmid":"https://pubmed.ncbi.nlm.nih.gov/16241197"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.67.061105","doi":"https://doi.org/10.1103/physreve.67.061105","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.67.061105","pdf_url":null,"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,"listed_in":["anvur-scientific","cwts-core"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5022941544","display_name":"Kwok Sau Fa","orcid":"https://orcid.org/0000-0002-2327-9919","observed_orcids":["https://orcid.org/0000-0002-2327-9919"]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Kwok Sau Fa","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maring\u00e1-PR, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maring\u00e1-PR, Brazil","institution_ids":["https://openalex.org/I123443094"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060481487","display_name":"Ervin Kaminski Lenzi","orcid":"https://orcid.org/0000-0003-3853-1790","observed_orcids":["https://orcid.org/0000-0003-3853-1790"]},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"E. K. Lenzi","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo 5790, 87020-900 Maring\u00e1-PR, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Avenida Colombo 5790, 87020-900 Maring\u00e1-PR, Brazil","institution_ids":["https://openalex.org/I123443094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I123443094"],"apc_list":null,"apc_paid":null,"fwci":4.6915,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.93890866,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"67","issue":"6","first_page":"061105","last_page":"061105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9204000234603882,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9204000234603882,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.0674000009894371,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.0019000000320374966,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"anomalous diffusion","score":0.9779999852180481},{"id":"https://openalex.org/keywords/mean-first-passage-time","display_name":"mean first passage time","score":0.8650000095367432},{"id":"https://openalex.org/keywords/quartic-potential","display_name":"quartic potential","score":0.7620000243186951},{"id":"https://openalex.org/keywords/one-dimensional-diffusion-equation","display_name":"one-dimensional diffusion equation","score":0.8399999737739563},{"id":"https://openalex.org/keywords/fractional-derivatives","display_name":"fractional derivatives","score":0.4699999988079071},{"id":"https://openalex.org/keywords/subdiffusion","display_name":"subdiffusion","score":0.37299999594688416}],"concepts":[{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.8524247407913208},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.7795780897140503},{"id":"https://openalex.org/C70816921","wikidata":"https://www.wikidata.org/wiki/Q258852","display_name":"Effective diffusion coefficient","level":3,"score":0.7237499356269836},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.6418414115905762},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5373050570487976},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.49223461747169495},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4360354244709015},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4269360601902008},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.38098520040512085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2807817757129669},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11390447616577148},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.06978374719619751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05789989233016968},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0},{"id":"https://openalex.org/C143409427","wikidata":"https://www.wikidata.org/wiki/Q161238","display_name":"Magnetic resonance imaging","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1103/physreve.67.061105","doi":"https://doi.org/10.1103/physreve.67.061105","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.67.061105","pdf_url":null,"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,"listed_in":["anvur-scientific","cwts-core"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review E","raw_type":"journal-article"},{"id":"pmid:16241197","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/16241197","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter 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":47,"referenced_works":["https://openalex.org/W1602153432","https://openalex.org/W1621611876","https://openalex.org/W1966410390","https://openalex.org/W1968094130","https://openalex.org/W1968848806","https://openalex.org/W1970316683","https://openalex.org/W1972763260","https://openalex.org/W1975665006","https://openalex.org/W1981401935","https://openalex.org/W1982297412","https://openalex.org/W1983386853","https://openalex.org/W1986060769","https://openalex.org/W1990433225","https://openalex.org/W1995449037","https://openalex.org/W2001851383","https://openalex.org/W2008506646","https://openalex.org/W2013838424","https://openalex.org/W2017349124","https://openalex.org/W2025843255","https://openalex.org/W2028551431","https://openalex.org/W2028977664","https://openalex.org/W2032364313","https://openalex.org/W2039246606","https://openalex.org/W2041571443","https://openalex.org/W2042211449","https://openalex.org/W2044034224","https://openalex.org/W2051108643","https://openalex.org/W2054095018","https://openalex.org/W2056213417","https://openalex.org/W2059255837","https://openalex.org/W2062517214","https://openalex.org/W2064368705","https://openalex.org/W2070078286","https://openalex.org/W2073485865","https://openalex.org/W2079483931","https://openalex.org/W2081142490","https://openalex.org/W2092144432","https://openalex.org/W2111271983","https://openalex.org/W2141496833","https://openalex.org/W2143415309","https://openalex.org/W2157123559","https://openalex.org/W2158060535","https://openalex.org/W2167500235","https://openalex.org/W2417961396","https://openalex.org/W3101940648","https://openalex.org/W4211019631","https://openalex.org/W4254241916"],"related_works":["https://openalex.org/W2040633180","https://openalex.org/W1985614716","https://openalex.org/W2054095018","https://openalex.org/W2017083733","https://openalex.org/W4388626301","https://openalex.org/W2349345604","https://openalex.org/W1967694075","https://openalex.org/W2038375813","https://openalex.org/W4252893594","https://openalex.org/W1979863594"],"abstract_inverted_index":{"We":[0,58,69],"investigate":[1,60],"one-dimensional":[2],"equations":[3,39],"for":[4,85],"the":[5,13,18,24,61,72,75,79,86,97,100,103],"diffusion":[6,10,25,38],"with":[7,47,74,93,99],"a":[8,34,41],"nonconstant":[9],"coefficient":[11,26,76,101],"inside":[12,102],"second":[14],"derivative":[15],"and":[16,33,56],"between":[17,78],"derivatives.":[19,104],"In":[20],"particular,":[21],"we":[22],"employ":[23],"D(x)":[27,77],"proportional":[28],"to":[29],"/x/(-theta)(theta":[30],"in":[31,91],"R)":[32],"quartic":[35],"potential.":[36],"These":[37],"present":[40],"rich":[42],"variety":[43],"of":[44,51,66],"behaviors":[45,84],"associated":[46],"different":[48,83],"regimes.":[49],"Results":[50],"two":[52],"approaches":[53],"are":[54],"analyzed":[55],"compared.":[57],"also":[59],"mean":[62,87],"first":[63,88],"passage":[64,89],"time":[65,90],"these":[67],"systems.":[68],"show":[70],"that":[71],"system":[73,98],"derivatives":[80],"can":[81],"produce":[82],"comparison":[92],"those":[94],"obtained":[95],"by":[96]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
