Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/6104
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dc.contributor.authorKuştepeli, Alp-
dc.date.accessioned2017-08-14T13:25:49Z-
dc.date.available2017-08-14T13:25:49Z-
dc.date.issued2016-04-02-
dc.identifier.citationKuştepeli, A. (2016). On the helmholtz theorem and its generalization for multi-layers. Electromagnetics, 36(3), 135-148. doi:10.1080/02726343.2016.1149755en_US
dc.identifier.issn0272-6343-
dc.identifier.urihttp://doi.org/10.1080/02726343.2016.1149755-
dc.identifier.urihttp://hdl.handle.net/11147/6104-
dc.description.abstractThe decomposition of a vector field to its curl-free and divergence-free components in terms of a scalar and a vector potential function, which is also considered as the fundamental theorem of vector analysis, is known as the Helmholtz theorem or decomposition. In the literature, it is mentioned that the theorem was previously presented by Stokes, but it is also mentioned that Stokes did not introduce any scalar and vector potentials in his expressions, which causes a contradiction. Therefore, in this article, Stokess and Helmholtzs representations are examined in detail to reveal and emphasize their differences, similarities and important points. The Helmholtz theorem is obtained for all kinds of spaces by using the theory of distributions in a comprehensive and rigorous manner with detailed explanations, which also leads to a new surface version of the Helmholtz theorem or a new surface decomposition, resulting in the canonical form; hence, it is different than the one suggested previously in terms of two scalar functions. The generalized form of the Helmholtz theorem is also presented by employing the same approach when there is a multi-layer on the surface of discontinuity, which also corresponds to the extension of the theorem to fields with singularities of higher order.en_US
dc.language.isoenen_US
dc.publisherTaylor and Francis Ltd.en_US
dc.relation.ispartofElectromagneticsen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectDiscontinuitiesen_US
dc.subjectDistribution theoryen_US
dc.subjectHelmholtz theoremen_US
dc.subjectHigher order singularitiesen_US
dc.titleOn the helmholtz theorem and its generalization for multi-layersen_US
dc.typeArticleen_US
dc.authoridTR130575en_US
dc.institutionauthorKuştepeli, Alp-
dc.departmentIzmir Institute of Technology. Electronics and Communication Engineeringen_US
dc.identifier.volume36en_US
dc.identifier.issue3en_US
dc.identifier.startpage135en_US
dc.identifier.endpage148en_US
dc.identifier.wosWOS:000376026600001en_US
dc.identifier.scopus2-s2.0-84963604275en_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.doi10.1080/02726343.2016.1149755-
dc.relation.doi10.1080/02726343.2016.1149755en_US
dc.coverage.doi10.1080/02726343.2016.1149755en_US
dc.identifier.scopusqualityQ2-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.grantfulltextopen-
item.languageiso639-1en-
crisitem.author.dept03.05. Department of Electrical and Electronics Engineering-
Appears in Collections:Electrical - Electronic Engineering / Elektrik - Elektronik Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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