{"id":"https://openalex.org/W2069856464","doi":"https://doi.org/10.1109/tmtt.1971.1127443","title":"An E Vector Variational Formulation of the Maxwell Equations for Cylindrical Waveguide Problems","display_name":"An E Vector Variational Formulation of the Maxwell Equations for Cylindrical Waveguide Problems","publication_year":1971,"publication_date":"1971-01-01","ids":{"openalex":"https://openalex.org/W2069856464","doi":"https://doi.org/10.1109/tmtt.1971.1127443","mag":"2069856464"},"language":"en","primary_location":{"id":"doi:10.1109/tmtt.1971.1127443","doi":"https://doi.org/10.1109/tmtt.1971.1127443","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmtt.1971.1127443","pdf_url":null,"source":{"id":"https://openalex.org/S198879913","display_name":"IEEE Transactions on Microwave Theory and Techniques","issn_l":"0018-9480","issn":["0018-9480","1557-9670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","ki-jl-1","norway-1","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320754","host_organization_name":"IEEE Microwave Theory and Techniques Society","host_organization_lineage":["https://openalex.org/P4310320754"],"host_organization_lineage_names":["IEEE Microwave Theory and Techniques Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Microwave Theory and Techniques","raw_type":"journal-article"},"volume":null,"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":null,"display_name":"W.J. English","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W.J. English","raw_affiliation_strings":["COMSAT Laboratories, Communication Satellite Corporation, Clarksburg, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"COMSAT Laboratories, Communication Satellite Corporation, Clarksburg, MD, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110103418","display_name":"F. J. Young","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I9217761","display_name":"Westinghouse Electric (United States)","ror":"https://ror.org/04p8w0f39","country_code":"US","type":"company","lineage":["https://openalex.org/I9217761"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"F.J. Young","raw_affiliation_strings":["Department of Applied Space Sciences, Carnegie Mellon University, Pittsburgh, PA, USA","Westinghouse Research and Development Laboratories, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Space Sciences, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Westinghouse Research and Development Laboratories, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I9217761"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":1.5364,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.83829995,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"1","first_page":"40","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.7836999893188477,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.7836999893188477,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.12700000405311584,"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/T10262","display_name":"Microwave Engineering and Waveguides","score":0.08250000327825546,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/maxwell-s-equations","display_name":"Maxwell's equations","score":0.9819999933242798},{"id":"https://openalex.org/keywords/circular-waveguide","display_name":"circular waveguide","score":0.9649999737739563},{"id":"https://openalex.org/keywords/parallel-plate-waveguide","display_name":"parallel-plate waveguide","score":0.8830000162124634},{"id":"https://openalex.org/keywords/rectangular-waveguide","display_name":"rectangular waveguide","score":1.0},{"id":"https://openalex.org/keywords/variational-integrals","display_name":"variational integrals","score":0.6340000033378601}],"concepts":[{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.7285102605819702},{"id":"https://openalex.org/C200687136","wikidata":"https://www.wikidata.org/wiki/Q11233438","display_name":"Waveguide","level":2,"score":0.6886502504348755},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.5947482585906982},{"id":"https://openalex.org/C2027888","wikidata":"https://www.wikidata.org/wiki/Q521126","display_name":"Vector potential","level":3,"score":0.5205974578857422},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5174410939216614},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5014886856079102},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4950851500034332},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46679431200027466},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45941978693008423},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.44376426935195923},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.4291665256023407},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36819982528686523},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3473152816295624},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.16987240314483643},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.15514257550239563},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1211627721786499},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tmtt.1971.1127443","doi":"https://doi.org/10.1109/tmtt.1971.1127443","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmtt.1971.1127443","pdf_url":null,"source":{"id":"https://openalex.org/S198879913","display_name":"IEEE Transactions on Microwave Theory and Techniques","issn_l":"0018-9480","issn":["0018-9480","1557-9670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","ki-jl-1","norway-1","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320754","host_organization_name":"IEEE Microwave Theory and Techniques Society","host_organization_lineage":["https://openalex.org/P4310320754"],"host_organization_lineage_names":["IEEE Microwave Theory and Techniques Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Microwave Theory and Techniques","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1608315681","https://openalex.org/W1991621289","https://openalex.org/W2009067222","https://openalex.org/W2023412501","https://openalex.org/W2039787011","https://openalex.org/W2066650375","https://openalex.org/W2112843438","https://openalex.org/W2127819220","https://openalex.org/W2135222579"],"related_works":["https://openalex.org/W3026729890","https://openalex.org/W2371315936","https://openalex.org/W4384488634","https://openalex.org/W2545967715","https://openalex.org/W179942262","https://openalex.org/W4210635634","https://openalex.org/W1976500340","https://openalex.org/W2353328784","https://openalex.org/W2899243769","https://openalex.org/W2946268021"],"abstract_inverted_index":{"A":[0],"vector":[1,24,104],"variational":[2,82,105],"formulation":[3,25,49],"of":[4,17,30,40,61,88],"the":[5,18,64,89],"Maxwell":[6],"equations":[7],"applicable":[8],"to":[9,100],"cylindrical":[10],"waveguide":[11,32,98],"problems":[12],"is":[13,50,84],"developed":[14],"in":[15,38,71,86],"terms":[16,39,87],"electric":[19],"E":[20],"field.":[21],"This":[22],"three-component":[23,48],"allows":[26],"an":[27],"approximate":[28],"solution":[29,65,106],"loaded":[31,94],"structures":[33],"which":[34,67],"cannot":[35],"be":[36],"described":[37],"a":[41,58,102],"single-field":[42],"component":[43],"or":[44],"potential":[45],"function.":[46],"The":[47,80],"more":[51],"economical":[52],"than":[53],"corresponding":[54],"six-component":[55],"formulations":[56],"for":[57,92],"given":[59],"order":[60],"approximation":[62],"because":[63],"matrices":[66],"result":[68],"are":[69],"reduced":[70],"size":[72],"(/spl":[73],"sim/1/2)":[74],"and":[75,96],"contain":[76],"fewer":[77],"zero":[78],"elements.":[79],"E-field":[81],"integral":[83],"expanded":[85],"field":[90],"components":[91],"inhomogeneously":[93],"parallel-plate":[95],"rectangular":[97],"geometries":[99],"illustrate":[101],"computer-assisted":[103],"procedure.":[107]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}