Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On applicability of differential mixing rules for statistically
  homogeneous and isotropic dispersions   The classical differential mixing rules are assumed to be independent
effective-medium approaches, applicable to certain classes of systems. In the
present work, the inconsistency of differential models for macroscopically
homogeneous and isotropic systems is illustrated with a model for the effective
permittivity of simple dielectric systems of impenetrable balls. The analysis
is carried out in terms of the compact group approach reformulated in a way
that allows one to analyze the role of different contributions to the
permittivity distribution in the system. It is shown that the asymmetrical
Bruggeman model (ABM) is physically inconsistent since the electromagnetic
interaction between previously added constituents and those being added is
replaced by the interaction of the latter with recursively formed effective
medium. The overall changes in the effective permittivity due to addition of
one constituent include the contributions from both constituents and depend on
the system structure before the addition. Ignoring the contribution from one of
the constituents, we obtain generalized versions of the original ABM mixing
rules. They still remain applicable only in a certain concentration ranges, as
is shown with the Hashin-Shtrikman bounds. The results obtained can be
generalized to macroscopically homogeneous and isotropic systems with complex
permittivities of constituents.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg