{"id":"https://openalex.org/W2094046716","doi":"https://doi.org/10.1137/s0036144599352058","title":"On the Theory of Complex Rays","display_name":"On the Theory of Complex Rays","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2094046716","doi":"https://doi.org/10.1137/s0036144599352058","mag":"2094046716"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144599352058","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599352058","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ora.ox.ac.uk/objects/uuid:1f071350-5983-45b8-8f5d-8c4ab068530d","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081545907","display_name":"S. Jonathan Chapman","orcid":"https://orcid.org/0000-0003-3347-6024"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. J. Chapman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027016496","display_name":"J. M. H. Lawry","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. M. H. Lawry","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089772299","display_name":"J. R. Ockendon","orcid":"https://orcid.org/0000-0002-8125-9350"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. R. Ockendon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019023769","display_name":"R. H. Tew","orcid":"https://orcid.org/0000-0003-3793-8513"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. H. Tew","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081545907"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5977,"has_fulltext":false,"cited_by_count":115,"citation_normalized_percentile":{"value":0.89986029,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"41","issue":"3","first_page":"417","last_page":"509"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.998199999332428,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6867345571517944},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6390132308006287},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5654159188270569},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.560431182384491},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4960251748561859},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.4556591212749481},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44070690870285034},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.43371397256851196},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37594854831695557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35997363924980164},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3540748655796051},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35189616680145264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34976911544799805},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.33750733733177185},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.336145281791687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31118398904800415},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1800449788570404},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08692866563796997},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.072594553232193},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0699482262134552}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6867345571517944},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6390132308006287},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5654159188270569},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.560431182384491},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4960251748561859},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.4556591212749481},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44070690870285034},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.43371397256851196},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37594854831695557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35997363924980164},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3540748655796051},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35189616680145264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34976911544799805},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.33750733733177185},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.336145281791687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31118398904800415},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1800449788570404},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08692866563796997},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.072594553232193},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0699482262134552},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0036144599352058","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144599352058","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:1f071350-5983-45b8-8f5d-8c4ab068530d","is_oa":true,"landing_page_url":null,"pdf_url":"https://ora.ox.ac.uk/objects/uuid:1f071350-5983-45b8-8f5d-8c4ab068530d","source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/611","raw_type":"Journal article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.56.8918","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.8918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.ox.ac.uk/~lawry/complex.ps.gz","raw_type":"text"},{"id":"pmh:uuid:1f071350-5983-45b8-8f5d-8c4ab068530d","is_oa":false,"landing_page_url":"http://www.siam.org/journals/sirev/41-3/35205.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/611","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ora.ox.ac.uk:uuid:1f071350-5983-45b8-8f5d-8c4ab068530d","is_oa":true,"landing_page_url":null,"pdf_url":"https://ora.ox.ac.uk/objects/uuid:1f071350-5983-45b8-8f5d-8c4ab068530d","source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/611","raw_type":"Journal article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2094046716.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W79953704","https://openalex.org/W152553465","https://openalex.org/W1520858677","https://openalex.org/W1964082576","https://openalex.org/W1966526382","https://openalex.org/W1968696437","https://openalex.org/W1969273165","https://openalex.org/W1971892010","https://openalex.org/W1989787306","https://openalex.org/W1998502287","https://openalex.org/W2001431479","https://openalex.org/W2009090147","https://openalex.org/W2013013264","https://openalex.org/W2014748812","https://openalex.org/W2034649362","https://openalex.org/W2036158252","https://openalex.org/W2041363811","https://openalex.org/W2048936082","https://openalex.org/W2053574666","https://openalex.org/W2054709112","https://openalex.org/W2057817591","https://openalex.org/W2062072363","https://openalex.org/W2064622518","https://openalex.org/W2072558518","https://openalex.org/W2078486124","https://openalex.org/W2091931476","https://openalex.org/W2103158266","https://openalex.org/W2122536615","https://openalex.org/W2130927234","https://openalex.org/W2139131426","https://openalex.org/W2146034485","https://openalex.org/W2152183404","https://openalex.org/W2169164332","https://openalex.org/W2925018009","https://openalex.org/W2943046378","https://openalex.org/W2947410994","https://openalex.org/W4241478920","https://openalex.org/W4244319576","https://openalex.org/W4246774385","https://openalex.org/W4250978612"],"related_works":["https://openalex.org/W2092968426","https://openalex.org/W2540416959","https://openalex.org/W1992180138","https://openalex.org/W2094202238","https://openalex.org/W2038541754","https://openalex.org/W2067763583","https://openalex.org/W4365420316","https://openalex.org/W3193896743","https://openalex.org/W3176862315","https://openalex.org/W3120022531"],"abstract_inverted_index":{"The":[0,16,64],"article":[1],"surveys":[2],"the":[3,9,50,57,67,76,83,86,93,104],"application":[4,96],"of":[5,40,59,61,66,85,89,97,108,117],"complex-ray":[6],"theory":[7],"to":[8,20,31,82,103],"scalar":[10],"Helmholtz":[11],"equation":[12],"in":[13,36,46,55,75,100],"two":[14],"dimensions.":[15],"first":[17],"objective":[18],"is":[19,49],"motivate":[21],"a":[22,37,72],"framework":[23,48],"within":[24],"which":[25],"complex":[26,62,105],"rays":[27],"may":[28],"be":[29],"used":[30],"make":[32],"predictions":[33],"about":[34],"wavefields":[35],"wide":[38],"variety":[39],"geometrical":[41],"configurations.":[42],"A":[43],"crucial":[44],"ingredient":[45],"this":[47,80],"role":[51],"played":[52],"by":[53],"Sp{}":[54],"determining":[56],"regions":[58],"existence":[60],"rays.":[63],"identification":[65],"Stokes":[68,90],"surfaces":[69],"emerges":[70],"as":[71],"key":[73],"step":[74],"approximation":[77],"procedure,":[78],"and":[79,95],"leads":[81],"consideration":[84],"many":[87],"characterizations":[88],"surfaces,":[91],"including":[92],"adaptation":[94],"recent":[98],"developments":[99],"exponential":[101],"asymptotics":[102],"Wentzel--Kramers--Brilbuin":[106],"expansion":[107],"these":[109],"wavefields.":[110],"Examples":[111],"are":[112],"given":[113],"for":[114],"several":[115],"cases":[116],"physical":[118],"importance.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
