Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stress-free states of continuum dislocation fields: Rotations, grain
  boundaries, and the Nye dislocation density tensor   We derive general relations between grain boundaries, rotational
deformations, and stress-free states for the mesoscale continuum Nye
dislocation density tensor. Dislocations generally are associated with
long-range stress fields. We provide the general form for dislocation density
fields whose stress fields vanish. We explain that a grain boundary (a
dislocation wall satisfying Frank's formula) has vanishing stress in the
continuum limit. We show that the general stress-free state can be written
explicitly as a (perhaps continuous) superposition of flat Frank walls. We show
that the stress-free states are also naturally interpreted as configurations
generated by a general spatially-dependent rotational deformation. Finally, we
propose a least-squares definition for the spatially-dependent rotation field
of a general (stressful) dislocation density field.

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The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs