Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The mean conformation tensor in viscoelastic turbulence   This work demonstrates that the popular arithmetic mean conformation tensor
frequently used in the analysis of turbulent viscoelastic flows is not a good
representative of the ensemble. Alternative means based on recent developments
in the literature are proposed, namely, the geometric and log-Euclidean means.
These means are mathematically consistent with the Riemannian structure of the
manifold of positive-definite tensors, on which the conformation tensor lives,
and have useful properties that make them attractive alternatives to the
arithmetic mean. Using a turbulent FENE-P channel flow dataset, it is shown
that these two alternatives are physically representative of the ensemble. By
definition these means minimize the geodesic distance to realizations and
exactly preserve the scalar geometric mean of the volume and of the principal
stretches. The proposed geometric and log-Euclidean means have a clear physical
interpretation and provide an attractive quantity for turbulence modelling.

12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg