Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Theory of Defects   A description of dislocations and disclinations defects in terms of
Riemann--Cartan geometry is given, with the curvature and torsion tensors being
interpreted as the surface densities of the Frank and Burgers vectors,
respectively. A new free energy expression describing the static distribution
of defects is presented, and equations of nonlinear elasticity theory are used
to specify the coordinate system. Application of the Lorentz gauge leads to
equations for the principal chiral SO(3)-field. In the defect-free case, the
geometric model reduces to elasticity theory for the displacement vector field
and to a principal chiral SO(3)-field model for the spin structure. As
illustrated by the example of a wedge dislocation, elasticity theory reproduces
only the linear approximation of the geometric theory of defects. It is shown
that the equations of asymmetric elasticity theory for the Cosserat media can
also be naturally incorporated into the geometric theory as the gauge
conditions. As an application of the theory, phonon scattering on a wedge
dislocation is considered. The energy spectrum of impurity in the field of a
wedge dislocation is also discussed.

16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph