Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From the Peierls-Nabarro model to the equation of motion of the
  dislocation continuum   We consider a semi-linear integro-differential equation in dimension one
associated to the half Laplacian %This model describes the evolution of phase
transitions associated to dislocations. whose solution represents the atom
dislocation in a crystal. The equation comprises the evolutive version of the
classical Peierls-Nabarro model. We show that for a large number of
dislocations, the solution, properly rescaled, converges to the solution of a
well known equation called by Head \cite{H} "the equation of motion of the
dislocation continuum". The limit equation is a model for the macroscopic
crystal plasticity with density of dislocations. In particular, we recover the
so called Orowan's law which states that dislocations move at a velocity
proportional to the effective stress.

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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat