Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dislocation patterning in a 2D continuum theory of dislocations   Understanding the spontaneous emergence of dislocation patterns during
plastic deformation is a long standing challenge in dislocation theory. During
the past decades several phenomenological continuum models of dislocation
patterning were proposed, but few of them (if any) are derived from microscopic
considerations through systematic and controlled averaging procedures. In this
paper we present a 2D continuum theory that is obtained by systematic averaging
of the equations of motion of discrete dislocations. It is shown that in the
evolution equations of the dislocation densities diffusion like terms neglected
in earlier considerations play a crucial role in the length scale selection of
the dislocation density fluctuations. It is also shown that the formulated
continuum theory can be derived from an averaged energy functional using the
framework of phase field theories. However, in order to account for the flow
stress one has in that case to introduce a nontrivial dislocation mobility
function, which proves to be crucial for the instability leading to patterning.

21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph