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Differential form valued forms and distributional electromagnetic sources

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Differential form valued forms and distributional electromagnetic sources. / Tucker, Robin.
In: Journal of Mathematical Physics, Vol. 50, No. 3, 033506, 10.03.2009.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Tucker, R 2009, 'Differential form valued forms and distributional electromagnetic sources', Journal of Mathematical Physics, vol. 50, no. 3, 033506. https://doi.org/10.1063/1.3085761

APA

Tucker, R. (2009). Differential form valued forms and distributional electromagnetic sources. Journal of Mathematical Physics, 50(3), Article 033506. https://doi.org/10.1063/1.3085761

Vancouver

Tucker R. Differential form valued forms and distributional electromagnetic sources. Journal of Mathematical Physics. 2009 Mar 10;50(3):033506. doi: 10.1063/1.3085761

Author

Tucker, Robin. / Differential form valued forms and distributional electromagnetic sources. In: Journal of Mathematical Physics. 2009 ; Vol. 50, No. 3.

Bibtex

@article{8b69638378a246b49fd88aa3007b4199,
title = "Differential form valued forms and distributional electromagnetic sources",
abstract = "Properties of a fundamental double-form of bidegree (p,p) for p ≥ 0 are reviewed in order to establish a distributional framework for analyzing equations of the form Δ+λ2 = , where Δ is the Hodge–de Rham operator on p-forms on R3. Particular attention is devoted to singular distributional solutions that arise when the source is a singular p-form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in R3 is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time-dependent sources of certain physical attributes, such as electric charge, electric current, and polarization or magnetization, are concentrated on localized regions in space.",
keywords = "differential equations, electric charge , electric current , electromagnetic fields , geometry , magnetisation , mathematical operators , polarisation",
author = "Robin Tucker",
year = "2009",
month = mar,
day = "10",
doi = "10.1063/1.3085761",
language = "English",
volume = "50",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "3",

}

RIS

TY - JOUR

T1 - Differential form valued forms and distributional electromagnetic sources

AU - Tucker, Robin

PY - 2009/3/10

Y1 - 2009/3/10

N2 - Properties of a fundamental double-form of bidegree (p,p) for p ≥ 0 are reviewed in order to establish a distributional framework for analyzing equations of the form Δ+λ2 = , where Δ is the Hodge–de Rham operator on p-forms on R3. Particular attention is devoted to singular distributional solutions that arise when the source is a singular p-form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in R3 is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time-dependent sources of certain physical attributes, such as electric charge, electric current, and polarization or magnetization, are concentrated on localized regions in space.

AB - Properties of a fundamental double-form of bidegree (p,p) for p ≥ 0 are reviewed in order to establish a distributional framework for analyzing equations of the form Δ+λ2 = , where Δ is the Hodge–de Rham operator on p-forms on R3. Particular attention is devoted to singular distributional solutions that arise when the source is a singular p-form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in R3 is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time-dependent sources of certain physical attributes, such as electric charge, electric current, and polarization or magnetization, are concentrated on localized regions in space.

KW - differential equations

KW - electric charge

KW - electric current

KW - electromagnetic fields

KW - geometry

KW - magnetisation

KW - mathematical operators

KW - polarisation

U2 - 10.1063/1.3085761

DO - 10.1063/1.3085761

M3 - Journal article

VL - 50

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

M1 - 033506

ER -