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The effective potential W and the dual one Ws as functions of y and α with α1 ≤ α ≤ α2. The parameters are set to k = 1, B = 2 (a, b), and B = 4 (c, d).
Source publication
Recently, a family of interesting analytical brane solutions were found in
$f(R)$ gravity with $f(R)=R+\alpha R^2$ in Ref. [Phys. Lett. B 729, 127
(2014)]. In these solutions, inner brane structure can be turned on by tuning
the value of $\alpha$. In this paper, we investigate how the parameter $\alpha$
affects the localization and the quasilocaliz...
Contexts in source publication
Context 1
... we have defined ¯ α = αk 2 . In this representation, the potential is independent of the parameter k, which implies that the changing the value of k does nothing but magnify or minify the new parameter ¯ α, so we only need to consider different values of B and α to search for resonant modes. The structure of W and W s is shown in Fig. ...
Context 2
... relation of these quantities is α s < α ′ < α ′′ < 0. This implies that both the effective potential and the corresponding dual one have an interval structure in the range of α 1 < α < α ′ and α 1 < α < α ′′ , respectively, see Fig. 3. Furthermore, it can be seen from Fig. 3 that there is also another interesting quasiwell with singularity for large B and α satisfying the constrain conditions ...
Context 3
... relation of these quantities is α s < α ′ < α ′′ < 0. This implies that both the effective potential and the corresponding dual one have an interval structure in the range of α 1 < α < α ′ and α 1 < α < α ′′ , respectively, see Fig. 3. Furthermore, it can be seen from Fig. 3 that there is also another interesting quasiwell with singularity for large B and α satisfying the constrain conditions ...
Context 4
... is clear that large rel- ative probabilities P (m 2 ) for finding massive KK modes within a narrow range −z b < z < z b around the brane location indicate the existence of resonant modes. From Fig. 3, we can see that there is a quasiwell when α → α 1 , which is consistent with what we analyse. So, it seems that we may find resonant modes for small α. ...
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