Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On non-uniqueness issues related to the permeability of a porous medium
  with a random porous structure   This paper discusses the issue of non-uniqueness of the permeability of a
porous medium with a random structure. The permeability range for 12,000
realizations of a random porous structure is examined using a
recently-developed modelling approach, which results in up to two orders of
magnitude permeability variations in low porosities. These findings are
compared with previous results for 13,000 realizations with a scaled-down size,
and it is shown that the permeability histogram does not converge towards a
narrower spectrum using larger domain sizes. The similarity between advective
transport in an ensemble of porous media and a random walk phenomenon, accepted
in the literature, is revisited and the inadequacy of the assumptions employed
is discussed. It is shown that the conventional definition of advective
transport in a porous medium, which is generally assumed to follow Hadamard's
definition of well-posedness, cannot be realised. The reconstruction of a
porous structure from macroscopic parameters is in itself an ill-posed inverse
problem. To clarify this issue, explaining the ontic and epistemic
identifications of a porous medium, it is discussed that while ontic
identification cannot be employed for transport analysis, epistemic
identification leads to non-unique solutions. It is finally suggested that a
paradigm shift is required for better formulation of the transport
characteristics of porous media.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin