Helmholtz decomposition theorem and Blumenthal's extension by regularization
Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly decreasing vector field. He used a regularization method in...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2017
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156568 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Helmholtz decomposition theorem and Blumenthal's extension by regularization / D. Petrascheck, R. Folk // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13002: 1–11. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1565682019-06-19T01:27:13Z Helmholtz decomposition theorem and Blumenthal's extension by regularization Petrascheck, D. Folk, R. Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly decreasing vector field. He used a regularization method in his proof which can be extended to prove the theorem even for vector fields asymptotically increasing sublinearly. Blumenthal’s result is then applied to the time-dependent fields of the dipole radiation and an artificial sublinearly increasing field. Теорема про розвинення Гельмгольца для векторного поля зазвичай представляється з сильними обмеженнями на поле i лише для незалежних вiд часу полiв. У 1905 р. Блюменталь показав, що розвинення є можливим для любого асимптотично слабоспадного векторного поля. Вiн використав у доведеннi регуляризацiйний метод, який можна було розширити для доведення теореми для векторних полiв, що є асимптотично сублiнiйно висхiдними. Результат Блюменталя застосовано до часовозалежних полiв дипольного випромiнення i штучного сублiнiйно висхiдного поля. 2017 Article Helmholtz decomposition theorem and Blumenthal's extension by regularization / D. Petrascheck, R. Folk // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13002: 1–11. — Бібліогр.: 22 назв. — англ. 1607-324X PACS: 01.30.mm, 03.50.De, 41.20.Jb DOI:10.5488/CMP.20.13002 arXiv:1704.02287 http://dspace.nbuv.gov.ua/handle/123456789/156568 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the
fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for
any asymptotically weakly decreasing vector field. He used a regularization method in his proof which can be
extended to prove the theorem even for vector fields asymptotically increasing sublinearly. Blumenthal’s result
is then applied to the time-dependent fields of the dipole radiation and an artificial sublinearly increasing field. |
| format |
Article |
| author |
Petrascheck, D. Folk, R. |
| spellingShingle |
Petrascheck, D. Folk, R. Helmholtz decomposition theorem and Blumenthal's extension by regularization Condensed Matter Physics |
| author_facet |
Petrascheck, D. Folk, R. |
| author_sort |
Petrascheck, D. |
| title |
Helmholtz decomposition theorem and Blumenthal's extension by regularization |
| title_short |
Helmholtz decomposition theorem and Blumenthal's extension by regularization |
| title_full |
Helmholtz decomposition theorem and Blumenthal's extension by regularization |
| title_fullStr |
Helmholtz decomposition theorem and Blumenthal's extension by regularization |
| title_full_unstemmed |
Helmholtz decomposition theorem and Blumenthal's extension by regularization |
| title_sort |
helmholtz decomposition theorem and blumenthal's extension by regularization |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156568 |
| citation_txt |
Helmholtz decomposition theorem and Blumenthal's extension by regularization / D. Petrascheck, R. Folk // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13002: 1–11. — Бібліогр.: 22 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT petrascheckd helmholtzdecompositiontheoremandblumenthalsextensionbyregularization AT folkr helmholtzdecompositiontheoremandblumenthalsextensionbyregularization |
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2025-07-14T08:55:47Z |
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2025-07-14T08:55:47Z |
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1837611978944675840 |