Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp bounds on the volume fractions of two materials in a
  two-dimensional body from electrical boundary measurements: the translation
  method   We deal with the problem of estimating the volume of inclusions using a
finite number of boundary measurements in electrical impedance tomography. We
derive upper and lower bounds on the volume fractions of inclusions, or more
generally two phase mixtures, using two boundary measurements in two
dimensions. These bounds are optimal in the sense that they are attained by
certain configurations with some boundary data. We derive the bounds using the
translation method which uses classical variational principles with a null
Lagrangian. We then obtain necessary conditions for the bounds to be attained
and prove that these bounds are attained by inclusions inside which the field
is uniform. When special boundary conditions are imposed the bounds reduce to
those obtained by Milton and these in turn are shown here to reduce to those of
Capdeboscq-Vogelius in the limit when the volume fraction tends to zero. The
bounds of this paper, and those of Milton, work for inclusions of arbitrary
volume fractions. We then perform some numerical experiments to demonstrate how
good these bounds are.

37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex