Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multi-scale percolation behaviour of the effective conductivity for
  the lattice model   Macroscopic properties of heterogeneous media are frequently modelled by
regular lattice models, which are based on a relatively small basic cluster of
lattice sites. Here, we extend one of such models to any cluster's size kxk. We
also explore its modified form. The focus is on the percolation behaviour of
the effective conductivity of random two- and three-phase systems. We consider
only the influence of geometrical features of local configurations at different
length scales k. At scales accessible numerically, we find that an increase in
the size of the basic cluster leads to characteristic displacements of the
percolation threshold. We argue that the behaviour is typical of materials,
whose conductivity is dominated by a few linear, percolation-like, conducting
paths. Such a system can be effectively treated as one-dimensional medium. We
also develop a simplified model that permits of an analysis at any scale. It is
worth mentioning that the latter approach keeps the same thresholds predicted
by the former one. We also briefly discuss a three-phase system, where the
double-thresholds paths appear on model surfaces.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
2
The categories of this paper are: math