Sharp estimate of electric field from a conductive rod and application

Abstract

We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field on the geometry of the conductive rod. In particular, we accurately characterise the localisation of the gradient field (i.e. the electric current) near the boundary of the rod where the curvature is sufficiently large. We develop layer-potential techniques in deriving the quantitative estimates and the major difficulty comes from the anisotropic geometry of the rod.The result complements and sharpens several existing studies in the literature. It also generates an interesting application in EIT (electrical impedance tomography) in determining the conductive rod by a single measurement, which is also known as the Calderon's inverse inclusion problem in the literature.

arXiv comment16 pages, 6 figures

References in corpus (5)

• Full and Partial Cloaking in Electromagnetic Scattering
• Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak
• On Calderón's inverse inclusion problem with smooth shapes by a single partial boundary measurement
• Determining a piecewise conductive medium body by a single far-field measurement
• Mathematical analysis of plasmon resonances for curved nanorods