313 research outputs found
Construction of inclusions with vanishing generalized polarization tensors by imperfect interfaces
We investigate the problem of planar conductivity inclusion with imperfect
interface conditions. We assume that the inclusion is simply connected. The
presence of the inclusion causes a perturbation in the incident background
field. This perturbation admits a multipole expansion of which coefficients we
call the generalized polarization tensors (GPTs), extending the previous
terminology for inclusions with perfect interfaces. We derive explicit matrix
expressions for the GPTs in terms of the incident field, material parameters,
and geometry of the inclusion. As an application, we construct GPT-vanishing
structures of general shape that result in negligible perturbations for all
uniform incident fields. The structure consists of a simply connected core with
an imperfect interface. We provide numerical examples of GPT-vanishing
structures obtained by our proposed scheme.Comment: 21 pages, 2 figure
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