Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing cluster morphology using vector-valued Minkowski
  functionals   The morphology of galaxy clusters is quantified using Minkowski functionals,
especially the vector-valued ones, which contain directional information and
are related to curvature centroids. The asymmetry of clusters and the amount of
their substructure can be characterized in a unique way using these measures.
-- We briefly introduce vector-valued Minkowski functionals (also known as
Querma\ss vectors) and suggest their application to cluster data in terms of a
morphological characterization of excursion sets. Furthermore, we develop
robust structure functions which describe the dynamical state of a cluster and
study the evolution of clusters using numerical simulations.

3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom