19,719 research outputs found
Fractal and multifractal properties of a family of fractal networks
In this work, we study the fractal and multifractal properties of a family of
fractal networks introduced by Gallos {\it et al.} ({\it Proc. Natl. Acad. Sci.
U.S.A.}, 2007, {\bf 104}: 7746). In this fractal network model, there is a
parameter which is between and , and allows for tuning the level of
fractality in the network. Here we examine the multifractal behavior of these
networks, dependence relationship of fractal dimension and the multifractal
parameters on the parameter . First, we find that the empirical fractal
dimensions of these networks obtained by our program coincide with the
theoretical formula given by Song {\it et al.} ( {\it Nat. Phys}, 2006, {\bf
2}: 275). Then from the shape of the and curves, we find the
existence of multifractality in these networks. Last, we find that there exists
a linear relationship between the average information dimension and
the parameter .Comment: 12 pages, 7 figures, accepted by J. Stat. Mec
Full linear perturbations and localization of gravity on brane
We study the thick brane world system constructed in the recently proposed
theories of gravity, with the Ricci scalar and the trace of
the energy-momentum tensor. We try to get the analytic background solutions and
discuss the full linear perturbations, especially the scalar perturbations. We
compare how the brane world model is modified with that of general relativity
coupled to a canonical scalar field. It is found that some more interesting
background solutions are allowed, and only the scalar perturbation mode is
modified. There is no tachyon state exists in this model and only the massless
tensor mode can be localized on the brane, which recovers the effective
four-dimensional gravity. These conclusions hold provided that two constraints
on the original formalism of the action are satisfied.Comment: v3: 8 pages, 2 figures, improved version with minor corrections,
accepted by EPJ
Gravitational resonances on -brane
In this paper, we investigate various -brane models and compare their
gravitational resonance structures with the corresponding general relativity
(GR)-branes. {Starting from some known GR-brane solutions}, we derive thick
-brane solutions such that the metric, scalar field, and scalar potential
coincide with those of the corresponding GR-branes. {We find that for branes
generated by a single or several canonical scalar fields, there is no obvious
distinction between the GR-branes and corresponding -branes in terms of
gravitational resonance structure.} Then we discuss the branes generated by
K-fields. In this case, there could exist huge differences between GR-branes
and -branes.Comment: 17 pages, 14 figures, published versio
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