Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of Embedded Curves by Doubly-Nonlocal Reaction-Diffusion
  Systems   We study a class of nonlocal, energy-driven dynamical models that govern the
motion of closed, embedded curves from both an energetic and dynamical
perspective. Our energetic results provide a variety of ways to understand
physically motivated energetic models in terms of more classical, combinatorial
measures of complexity for embedded curves. This line of investigation
culminates in a family of complexity bounds that relate a rather broad class of
models to a generalized, or weighted, variant of the crossing number. Our
dynamic results include global well-posedness of the associated partial
differential equations, regularity of equilibria for these flows as well as a
more detailed investigation of dynamics near such equilibria. Finally, we
explore a few global dynamical properties of these models numerically.

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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph