Nonclassical Fields With Singularities On a Moving Surface

Authors

David Betounes, University of Southern MississippiFollow

Document Type

Article

Publication Date

1-1-1982

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Fields with singularities on a moving surface S with boundary ∂S can be represented as distributions which have their support concentrated on S and ∂S. This paper considers such fields of the form F={ f }+λδ_S̃, where { f } is the distribution determined by a field f and λδ_S̃ is a Dirac delta distribution with density λ concentrated on the tube S̃ swept out by the moving surface. A straightforward calculation of the distributional gradient, curl, divergence, and time derivative of such fields yields fields of the following general form: G={ g } +αδ_S̃ +βδ_∂S̃ +γ∇_n(⋅)δ_S̃. The density α is shown to contain all the information which is customarily presented in the jump conditions for fields with singularities at a moving interface. Examples from electromagnetic field theory are presented to show the significance of the other terms { g }, βδ_∂S̃, and γ∇_n(⋅)δ_S̃.

Publication Title

Journal of Mathematical Physics

Volume

23

Issue

12

Recommended Citation

Betounes, D. (1982). Nonclassical Fields With Singularities On a Moving Surface. Journal of Mathematical Physics, 23(12).
Available at: https://aquila.usm.edu/fac_pubs/20712