Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Log-periodic oscillations for diffusion on self-similar finitely
  ramified structures   Under certain circumstances, the time behavior of a random walk is modulated
by logarithmic periodic oscillations. The goal of this paper is to present a
simple and pedagogical explanation of the origin of this modulation for
diffusion on a substrate with two properties: self-similarity and finite
ramification order. On these media, the time dependence of the mean-square
displacement shows log-periodic modulations around a leading power law, which
can be understood on the base of a hierarchical set of diffusion constants.
Both the random walk exponent and the period of oscillations are analytically
obtained for a pair of examples, one fractal, the other non-fractal, and
confirmed by Monte Carlo simulations.

6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas