{"id":"https://openalex.org/W2596693598","doi":"https://doi.org/10.1016/j.jqsrt.2017.02.015","title":"A review of the matrix-exponential formalism in radiative transfer","display_name":"A review of the matrix-exponential formalism in radiative transfer","publication_year":2017,"publication_date":"2017-03-19","ids":{"openalex":"https://openalex.org/W2596693598","doi":"https://doi.org/10.1016/j.jqsrt.2017.02.015","mag":"2596693598"},"language":"en","primary_location":{"id":"doi:10.1016/j.jqsrt.2017.02.015","doi":"https://doi.org/10.1016/j.jqsrt.2017.02.015","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jqsrt.2017.02.015","pdf_url":null,"source":{"id":"https://openalex.org/S100373537","display_name":"Journal of Quantitative Spectroscopy and Radiative Transfer","issn_l":"0022-4073","issn":["0022-4073","1879-1352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1"],"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":"Journal of Quantitative Spectroscopy and Radiative Transfer","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/A5037324415","display_name":"Dmitry Efremenko","orcid":"https://orcid.org/0000-0002-7449-5072","observed_orcids":["https://orcid.org/0000-0002-7449-5072"]},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dmitry S. Efremenko","raw_affiliation_strings":["Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022882259","display_name":"V\u00edctor Molina Garc\u00eda","orcid":"https://orcid.org/0000-0002-2564-5396","observed_orcids":["https://orcid.org/0000-0002-2564-5396"]},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"V\u00edctor Molina Garc\u00eda","raw_affiliation_strings":["Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103600168","display_name":"Sebasti\u00e1n Gimeno Garc\u00eca","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebasti\u00e1n Gimeno Garc\u00eda","raw_affiliation_strings":["Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046286337","display_name":"Adrian Doicu","orcid":"https://orcid.org/0000-0002-3637-5299","observed_orcids":["https://orcid.org/0000-0002-3637-5299"]},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Adrian Doicu","raw_affiliation_strings":["Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt (DLR), Institut f\u00fcr Methodik der Fernerkundung (IMF), 82234 Oberpfaffenhofen, Germany","institution_ids":["https://openalex.org/I2898391981"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037324415"],"corresponding_institution_ids":["https://openalex.org/I2898391981"],"apc_list":{"value":2870,"currency":"USD","value_usd":2870},"apc_paid":null,"fwci":2.8671,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.89566341,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"196","issue":null,"first_page":"17","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.8881999850273132,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.8881999850273132,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10347","display_name":"Atmospheric aerosols and clouds","score":0.09719999879598618,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.004900000058114529,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"matrix exponential","score":0.8930000066757202},{"id":"https://openalex.org/keywords/radiative-transfer","display_name":"radiative transfer","score":0.9129999876022339},{"id":"https://openalex.org/keywords/discrete-ordinates-method","display_name":"discrete ordinates method","score":0.9350000023841858},{"id":"https://openalex.org/keywords/matrix-operator-method","display_name":"matrix operator method","score":0.796999990940094},{"id":"https://openalex.org/keywords/matrix-riccati-equation","display_name":"matrix Riccati equation","score":0.9860000014305115},{"id":"https://openalex.org/keywords/eigenvalue-decomposition","display_name":"eigenvalue decomposition","score":0.9890000224113464},{"id":"https://openalex.org/keywords/pade-approximants","display_name":"Pad\u00e9 approximants","score":0.8619999885559082},{"id":"https://openalex.org/keywords/taylor-expansion","display_name":"Taylor series expansion","score":0.9700000286102295},{"id":"https://openalex.org/keywords/asymptotic-theory","display_name":"asymptotic theory","score":0.8669999837875366},{"id":"https://openalex.org/keywords/water-cloud-model","display_name":"water cloud model","score":0.9490000009536743},{"id":"https://openalex.org/keywords/cloud-radiative-transfer","display_name":"cloud radiative transfer","score":0.5009999871253967}],"concepts":[{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.9112910032272339},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6300511360168457},{"id":"https://openalex.org/C74902906","wikidata":"https://www.wikidata.org/wiki/Q1190858","display_name":"Radiative transfer","level":2,"score":0.5609036087989807},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.5223285555839539},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4818097949028015},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.46541857719421387},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.44920316338539124},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41114020347595215},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3887234032154083},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.38843631744384766},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34891656041145325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.346821665763855},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2210180163383484},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11277970671653748},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.11129620671272278},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.jqsrt.2017.02.015","doi":"https://doi.org/10.1016/j.jqsrt.2017.02.015","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jqsrt.2017.02.015","pdf_url":null,"source":{"id":"https://openalex.org/S100373537","display_name":"Journal of Quantitative Spectroscopy and Radiative Transfer","issn_l":"0022-4073","issn":["0022-4073","1879-1352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1"],"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":"Journal of Quantitative Spectroscopy and Radiative Transfer","raw_type":"journal-article"},{"id":"pmh:oai:elib.dlr.de:111872","doi":null,"is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.jqsrt.2017.02.015>.","pdf_url":null,"source":{"id":"https://openalex.org/S4377196266","display_name":"elib (German Aerospace Center)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2898391981","host_organization_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","host_organization_lineage":["https://openalex.org/I2898391981"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Zeitschriftenbeitrag"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W57976962","https://openalex.org/W189988591","https://openalex.org/W578387667","https://openalex.org/W1611872163","https://openalex.org/W1966433698","https://openalex.org/W1969535121","https://openalex.org/W1970334805","https://openalex.org/W1971099220","https://openalex.org/W1976390556","https://openalex.org/W1979435267","https://openalex.org/W1980186665","https://openalex.org/W1981437432","https://openalex.org/W1982162561","https://openalex.org/W1985291954","https://openalex.org/W1987704992","https://openalex.org/W1991364317","https://openalex.org/W1992233007","https://openalex.org/W1995258902","https://openalex.org/W2001064114","https://openalex.org/W2003164020","https://openalex.org/W2003165523","https://openalex.org/W2006252323","https://openalex.org/W2021627187","https://openalex.org/W2025829739","https://openalex.org/W2032398489","https://openalex.org/W2035979240","https://openalex.org/W2042112467","https://openalex.org/W2044224212","https://openalex.org/W2045570539","https://openalex.org/W2050806470","https://openalex.org/W2060115035","https://openalex.org/W2067882674","https://openalex.org/W2071120183","https://openalex.org/W2073844425","https://openalex.org/W2080030922","https://openalex.org/W2085063499","https://openalex.org/W2086078193","https://openalex.org/W2090522437","https://openalex.org/W2100701253","https://openalex.org/W2102921597","https://openalex.org/W2123940238","https://openalex.org/W2149682597","https://openalex.org/W2153611211","https://openalex.org/W2156464932","https://openalex.org/W2157243979","https://openalex.org/W2174981545","https://openalex.org/W2176571038","https://openalex.org/W2338843794","https://openalex.org/W2464093295","https://openalex.org/W3021974146","https://openalex.org/W3135227555","https://openalex.org/W3139607195","https://openalex.org/W4248541166"],"related_works":["https://openalex.org/W4248541166","https://openalex.org/W2100701253","https://openalex.org/W1987704992","https://openalex.org/W2044224212","https://openalex.org/W2080030922","https://openalex.org/W2093105018","https://openalex.org/W2911939456","https://openalex.org/W2025829739","https://openalex.org/W2003571388","https://openalex.org/W2000287901"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2017-03-23T00:00:00"}
