Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of edge-dislocations as a weak limit of de-Rham currents   In the material science literature we find two continuum models for
crystalline defects: (i) A body with (finite) isolated defects is typically
modeled as a Riemannian manifold with singularities, and (ii) a body with
continuously distributed defects, which is modeled as a smooth (non-singular)
Riemannian manifold with an additional structure of an affine connection. In
this work we show how continuously distributed defects may be obtained as a
limit of singular ones . The defect structure is represented by layering
1-forms and their singular counterparts - de-Rham (n-1) currents. We then show
that every smooth layering $1$-form may be obtained as a limit, in the sense of
currents, of singular layering forms, corresponding to arrays of edge
dislocations. As a corollary, we investigated manifolds with full material
structure, i.e., a complete co-frame for the co-tangent bundle. We define the
notion of singular torsion current for manifolds with a parallel structure and
prove its convergence to the regular smooth torsion tensor at homogenization
limit. Thus establishing the so-called emergence of torsion at the
homogenization limit.

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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn