Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering Signatures of Invasion Percolation   Motivated by recent experiments, we report on the scattering properties of
percolation clusters generated by numerical simulations on a three dimensional
cubic lattice. Individual clusters of given size are shown to present a fractal
structure up to a scale of order their extent, even far away from the
percolation point $p_c$. The influence of intercorrelations on the structure
factor of assemblies of clusters selected by an invasion phenomenon is studied
in detail. For invasion from bulk germs, we show that the scattering properties
are determined by three length scales, the correlation length $\xi$, the
average distance between germs $d_g$, and the spatial scale probed by
scattering, set by the inverse of the scattering wavevector $Q$. At small
scales, we find that the fractal structure of individual clusters is retained,
the structure factor decaying as $Q^{-d_f}$. At large scales, the structure
factor tends to a limit, set by the smaller of the $\xi$ and $d_g$, both below
and above $p_c$. We propose analytical expressions reproducing the simulated
structure factor for arbitrary $\xi$, $d_g$, and $Q$. For invasion from
surfaces, we find that, at the percolation point, the structure factor behaves
as $Q^{-d_f}$ at all $Q$, i.e. that the fractal structure is retained at
arbitrarily large scales. Results away from percolation are compared to the
case of bulk germs. Our results can be applied to discuss light or neutrons
scattering experiments on percolating systems. This is illustrated in the
context of evaporation from porous materials.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ