Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A proof of Taylor scaling for curvature-driven dislocation motion
  through random arrays of obstacles   We prove Taylor scaling for dislocation lines characterized by line-tension
and moving by curvature under the action of an applied shear stress in a plane
containing a random array of obstacles. Specifically, we show--in the sense of
optimal scaling--that the critical applied shear stress for yielding, or
percolation-like unbounded motion of the dislocation, scales in proportion to
the square root of the obstacle density. For sufficiently small obstacle
densities, Taylor scaling dominates the linear-scaling that results from purely
energetic considerations and, therefore, characterizes the dominant
rate-limiting mechanism in that regime.

14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin