Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Analysis of Piezoelectric Tensors   A third order real tensor is called a piezoelectric-type tensor if it is
partially symmetric with respect to its last two indices. The piezoelectric
tensor is a piezoelectric-type tensor of dimension three. We introduce
C-eigenvalues and C-eigenvectors for piezoelectric-type tensors. Here, "C"
names after Curie brothers, who first discovered the piezoelectric effect. We
show that C-eigenvalues always exist, they are invariant under orthonormal
transformations, and for a piezoelectric-type tensor, the largest C-eigenvalue
and its C-eigenvectors form the best rank-one piezoelectric-type approximation
of that tensor. This means that for the piezoelectric tensor, its largest
C-eigenvalue determines the highest piezoelectric coupling constant. We further
show that for the piezoelectric tensor, the largest C-eigenvalue corresponds to
the electric displacement vector with the largest $2$-norm in the piezoelectric
effect under unit uniaxial stress, and the strain tensor with the largest
$2$-norm in the converse piezoelectric effect under unit electric field vector.
Thus, C-eigenvalues and C-eigenvectors have concrete physical meanings in
piezoelectric effect and converse piezoelectric effect. Finally, we apply
C-eigenvalues and associated C-eigenvectors for various piezoelectric crystals
with different symmetries.

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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex