{"id":"https://openalex.org/W6929316896","doi":"https://doi.org/10.48550/arxiv.2508.02675","title":"Full Vectorial Maxwell Equations with Continuous Angular Indices","display_name":"Full Vectorial Maxwell Equations with Continuous Angular Indices","publication_year":2025,"publication_date":"2025-07-10","ids":{"openalex":"https://openalex.org/W6929316896","doi":"https://doi.org/10.48550/arxiv.2508.02675"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2508.02675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.02675","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2508.02675","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bakr, Mustafa","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bakr, Mustafa","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.24240000545978546,"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":0.24240000545978546,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.225600004196167,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.11620000004768372,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5023000240325928},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.4887000024318695},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.487199991941452},{"id":"https://openalex.org/keywords/biorthogonal-system","display_name":"Biorthogonal system","score":0.43799999356269836},{"id":"https://openalex.org/keywords/spherical-harmonics","display_name":"Spherical harmonics","score":0.4169999957084656},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4124000072479248},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.4065999984741211},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.38769999146461487},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.37209999561309814},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.37059998512268066}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419999837875366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6506999731063843},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5023000240325928},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4887000024318695},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.487199991941452},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.43799999356269836},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.4065999984741211},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.38769999146461487},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.37209999561309814},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C80845027","wikidata":"https://www.wikidata.org/wiki/Q15144062","display_name":"Continuous spectrum","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C77730005","wikidata":"https://www.wikidata.org/wiki/Q326905","display_name":"Spherical geometry","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C159737794","wikidata":"https://www.wikidata.org/wiki/Q124274","display_name":"Azimuth","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C20569695","wikidata":"https://www.wikidata.org/wiki/Q7577353","display_name":"Spin-weighted spherical harmonics","level":4,"score":0.2712000012397766},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C77237485","wikidata":"https://www.wikidata.org/wiki/Q7917842","display_name":"Vector spherical harmonics","level":3,"score":0.2614000141620636},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C39176672","wikidata":"https://www.wikidata.org/wiki/Q8073864","display_name":"Zonal spherical harmonics","level":4,"score":0.2565999925136566},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C206844423","wikidata":"https://www.wikidata.org/wiki/Q5157313","display_name":"Computational electromagnetics","level":3,"score":0.2556999921798706}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2508.02675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.02675","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2508.02675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.02675","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"a":[3,27],"mathematical":[4],"framework":[5,72,94,136],"for":[6,80,129],"solving":[7],"Maxwell's":[8],"equations":[9],"in":[10,65,74],"cylindrical":[11,98],"and":[12,61,84,106,132,141],"spherical":[13,108],"geometries":[14],"with":[15,100],"continuous":[16,28,51,101],"angular":[17,52],"indices.":[18],"We":[19,118],"extend":[20],"beyond":[21],"standard":[22],"discrete":[23],"harmonic":[24],"decomposition":[25],"to":[26],"spectral":[29,33,87,130,143],"representation":[30],"using":[31],"generalized":[32],"integrals,":[34],"capturing":[35],"electromagnetic":[36],"solutions":[37,64],"that":[38],"exhibit":[39],"singular":[40,123],"behavoiur":[41],"yet":[42],"yield":[43],"finite-energy":[44],"fields":[45],"at":[46],"the":[47,71,134],"geometric":[48],"center.":[49],"For":[50],"indices":[53],"$\\ell,":[54],"m":[55],"\\in":[56],"\\mathbb{R}$,":[57],"we":[58],"study":[59],"existence":[60],"uniqueness":[62],"of":[63,122],"weighted":[66],"Sobolev":[67],"spaces":[68],"$H^s_{\u03b1(\\ell,m)}(\u03a9)$":[69],"following":[70],"established":[73],"~\\cite{adams2003,":[75],"reed1975},":[76],"prove":[77],"finite":[78],"energy":[79],"$\\ell":[81],">":[82],"-\\frac{1}{2}$,":[83],"construct":[85],"explicit":[86],"kernels":[88],"via":[89],"biorthogonal":[90],"function":[91],"systems.":[92],"The":[93],"encompasses":[95],"both":[96],"separable":[97],"modes":[99,109],"azimuthal":[102],"index":[103],"$\u03bd\\in":[104],"(0,1)$":[105],"non-separable":[107],"where":[110],"field":[111,124],"components":[112],"couple":[113],"through":[114,137],"vectorial":[115],"curl":[116],"operations.":[117],"present":[119],"asymptotic":[120],"analysis":[121],"behavior,":[125],"investigate":[126],"convergence":[127],"rates":[128],"approximations,":[131],"validate":[133],"theoretical":[135],"Galerkin":[138],"projection":[139],"methods":[140],"numerical":[142],"integration.":[144]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}