{"id":"https://openalex.org/W2075057438","doi":"https://doi.org/10.1016/j.cnsns.2013.09.031","title":"Drawdown in prolate spheroidal\u2013spherical coordinates obtained via Green\u2019s function and perturbation methods","display_name":"Drawdown in prolate spheroidal\u2013spherical coordinates obtained via Green\u2019s function and perturbation methods","publication_year":2013,"publication_date":"2013-10-03","ids":{"openalex":"https://openalex.org/W2075057438","doi":"https://doi.org/10.1016/j.cnsns.2013.09.031","mag":"2075057438"},"language":"en","primary_location":{"id":"doi:10.1016/j.cnsns.2013.09.031","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cnsns.2013.09.031","pdf_url":null,"source":{"id":"https://openalex.org/S39612629","display_name":"Communications in Nonlinear Science and Numerical Simulation","issn_l":"1007-5704","issn":["1007-5704","1878-7274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Nonlinear Science and Numerical Simulation","raw_type":"journal-article"},"type":"article","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/A5082823020","display_name":"Abdon Atangana","orcid":"https://orcid.org/0000-0002-1886-3125"},"institutions":[{"id":"https://openalex.org/I26999989","display_name":"University of the Free State","ror":"https://ror.org/009xwd568","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26999989"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Abdon Atangana","raw_affiliation_strings":["Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, PO Box 9301, Bloemfontein, South Africa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, PO Box 9301, Bloemfontein, South Africa","institution_ids":["https://openalex.org/I26999989"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082823020"],"corresponding_institution_ids":["https://openalex.org/I26999989"],"apc_list":{"value":3460,"currency":"USD","value_usd":3460},"apc_paid":null,"fwci":3.8918,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92573598,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"5","first_page":"1259","last_page":"1269"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10716","display_name":"Soil and Unsaturated Flow","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12293","display_name":"Dam Engineering and Safety","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prolate-spheroidal-coordinates","display_name":"Prolate spheroidal coordinates","score":0.7184462547302246},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6430237293243408},{"id":"https://openalex.org/keywords/polar-coordinate-system","display_name":"Polar coordinate system","score":0.6166322231292725},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.6019025444984436},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5959681868553162},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.5896635055541992},{"id":"https://openalex.org/keywords/spherical-coordinate-system","display_name":"Spherical coordinate system","score":0.5722615718841553},{"id":"https://openalex.org/keywords/prolate-spheroid","display_name":"Prolate spheroid","score":0.5154258012771606},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.464415967464447},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.45285868644714355},{"id":"https://openalex.org/keywords/error-function","display_name":"Error function","score":0.4277442693710327},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.41035401821136475},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2679952383041382},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23867425322532654}],"concepts":[{"id":"https://openalex.org/C129094480","wikidata":"https://www.wikidata.org/wiki/Q7249552","display_name":"Prolate spheroidal coordinates","level":3,"score":0.7184462547302246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6430237293243408},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.6166322231292725},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6019025444984436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5959681868553162},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.5896635055541992},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.5722615718841553},{"id":"https://openalex.org/C197807790","wikidata":"https://www.wikidata.org/wiki/Q208395","display_name":"Prolate spheroid","level":2,"score":0.5154258012771606},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.464415967464447},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.45285868644714355},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.4277442693710327},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.41035401821136475},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2679952383041382},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23867425322532654},{"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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cnsns.2013.09.031","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.cnsns.2013.09.031","pdf_url":null,"source":{"id":"https://openalex.org/S39612629","display_name":"Communications in Nonlinear Science and Numerical Simulation","issn_l":"1007-5704","issn":["1007-5704","1878-7274"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Nonlinear Science and Numerical Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1606337696","https://openalex.org/W1978826141","https://openalex.org/W1987693938","https://openalex.org/W1993876595","https://openalex.org/W1996315355","https://openalex.org/W2032231305","https://openalex.org/W2041296131","https://openalex.org/W2050148511","https://openalex.org/W2054534892","https://openalex.org/W2065463790","https://openalex.org/W2075808477","https://openalex.org/W2077106134","https://openalex.org/W2102591969","https://openalex.org/W2118205048","https://openalex.org/W2313559663","https://openalex.org/W2463653876","https://openalex.org/W2801179766","https://openalex.org/W6670083026"],"related_works":["https://openalex.org/W4387664668","https://openalex.org/W4297954213","https://openalex.org/W2982602778","https://openalex.org/W2594448215","https://openalex.org/W3021938232","https://openalex.org/W4225614476","https://openalex.org/W2132019956","https://openalex.org/W4243707844","https://openalex.org/W2666173632","https://openalex.org/W4239038825"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}