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...
Збережено в:
| 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 |
| Теги: |
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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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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