Nonclassical fields with singularities on a moving surface

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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 }+λδS̃, where { f } is the distribution determined by a field f and λδS̃ 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 } +αδS̃ +βδ∂S̃ +γ∇n(⋅)δS̃. 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(⋅)δS̃.

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