Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical shape recovery of a conductivity inclusion based on Faber
  polynomials   A conductivity inclusion, inserted in a homogeneous background, induces a
perturbation in the background potential. This perturbation admits a multipole
expansion whose coefficients are the so-called generalized polarization tensors
(GPTs). GPTs can be obtained from multistatic measurements. As a modification
of GPTs, the Faber polynomial polarization tensors (FPTs) were recently
introduced in two dimensions. In this study, we design two novel analytical
non-iterative methods for recovering the shape of a simply connected inclusion
from GPTs by employing the concept of FPTs. First, we derive an explicit
expression for the coefficients of the exterior conformal mapping associated
with an inclusion in a simple form in terms of GPTs, which allows us to
accurately reconstruct the shape of an inclusion with extreme or near-extreme
conductivity. Secondly, we provide an explicit asymptotic formula in terms of
GPTs for the shape of an inclusion with arbitrary conductivity by considering
the inclusion as a perturbation of its equivalent ellipse. With this formula,
one can non-iteratively approximate an inclusion of general shape with
arbitrary conductivity, including a straight or asymmetric shape. Numerical
experiments demonstrate the validity of the proposed analytical approaches.

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: chem-ph