Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The dimple problem related to space-time modeling under the Lagrangian
  framework   Space-time covariance modeling under the Lagrangian framework has been
especially popular to study atmospheric phenomena in the presence of transport
effects, such as prevailing winds or ocean currents, which are incompatible
with the assumption of full symmetry. In this work, we assess the dimple
problem (Kent et al., 2011) for covariance functions coming from transport
phenomena. We work under two important cases: the spatial domain can be either
the $d$-dimensional Euclidean space $\mathbb{R}^d$ or the spherical shell of
$\mathbb{R}^d$. The choice is relevant for the type of metric chosen to
describe spatial dependence. In particular, in Euclidean spaces, we work under
very general assumptions with the case of radial symmetry being deduced as a
corollary of a more general result. We illustrate through examples that, under
this framework, the dimple is a natural and physically interpretable property.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga