Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective-medium theory for infinite-contrast, 2D-periodic, linear
  composites with strongly anisotropic matrix behavior: dilute limit and
  cross-over behavior   The overall behavior of a 2D lattice of voids embedded in an anisotropic
matrix is investigated in the limit of vanishing porosity f. An
effective-medium model (of the Hashin-Shtrikman type) which accounts for
elastic interactions between neighboring voids, is compared to Fast Fourier
Transform numerical solutions and, in the limits of infinite anisotropy, to
exact results. A cross-over between regular and singular dilute regimes is
found, driven by a characteristic length which depends on f and on the
anisotropy strength. The singular regime, where the leading dilute correction
to the elastic moduli is an O(f^{1/2}), is related to strain localization and
to change in character - from elliptic to hyperbolic - of the governing
equations.

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The categories of this paper are: acc-phys
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics