Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Giant dielectric anisotropy via homogenization   A random mixture of two isotropic dielectric materials, one composed of
oriented spheroidal particles of relative permittivity $\epsilon_a$ and the
other composed of oriented spheroidal particles of relative permittivity
$\epsilon_b$, was considered in the long wavelength regime. The permittivity
dyadic of the resulting homogenized composite material (HCM) was estimated
using the Bruggeman homogenization formalism. The HCM was an orthorhombic
biaxial material if the symmetry axes of the two populations of spheroids were
mutually perpendicular and a uniaxial material if these two axes were mutually
aligned. The degree of anisotropy of the HCM, as gauged by the ratio of the
eigenvalues of the HCM's permittivity dyadic, increased as the shape of the
constituent particles became more eccentric. The greatest degrees of HCM
anisotropy were achieved for the limiting cases wherein the constituent
particles were shaped as needles or discs. In these instances explicit formulas
for the HCM anisotropy were derived from the dyadic Bruggeman equation. Using
these formulas it was found that the degrees of HCM anisotropy are proportional
to $\sqrt{\epsilon_b}$ or $\epsilon_b$, at fixed values of volume fraction and
$\epsilon_a$, for $\epsilon_b > \epsilon_a$. Thus, in principle, there is no
limit to degree of anisotropy that may be attained via homogenization. In
practice, the degree of anisotropy would be limited by the available value of
$\epsilon_b$ (and/or $\epsilon_a$).

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The categories of this paper are: ao-sci
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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: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph