Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On commutativity and near commutativity of translational and rotational
  averages: Analytical proofs and numerical examinations   We show that, in general, the translational average over a spatial
variable---discussed by Backus \cite{backus}, and referred to as the
equivalent-medium average---and the rotational average over a symmetry group at
a point---discussed by Gazis et al. \cite{gazis}, and referred to as the
effective-medium average---do not commute. However, they do commute in special
cases of particular symmetry classes, which correspond to special relations
among the elasticity parameters. We also show that this noncommutativity is a
function of the strength of anisotropy. Surprisingly, a perturbation of the
elasticity parameters about a point of weak anisotropy results in the
commutator of the two types of averaging being of the order of the {\it
square\/} of this perturbation. Thus, these averages nearly commute in the case
of weak anisotropy, which is of interest in such disciplines as quantitative
seismology, where the weak-anisotropy assumption results in empirically
adequate models.

0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an