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Sharp estimate of electric field from a conductive rod and application
Author(s) -
Fang Xiaoping,
Deng Youjun,
Liu Hongyu
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12348
Subject(s) - electrical conductor , electric field , curvature , electrical impedance tomography , anisotropy , perturbation (astronomy) , conductivity , field (mathematics) , inverse problem , inverse , boundary (topology) , electrical impedance , boundary value problem , geometry , physics , electrical resistivity and conductivity , mechanics , mathematical analysis , optics , mathematics , quantum mechanics , pure mathematics
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 characterize the localization 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 Calderón's inverse inclusion problem in the literature.